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# Losses

`pytorch-widedeep` accepts a number of losses and objectives that can be passed to the `Trainer` class via the parameter `objective` (see `pytorch-widedeep.training.Trainer`). For most cases the loss function that `pytorch-widedeep` will use internally is already implemented in Pytorch.

In addition, `pytorch-widedeep` implements a series of "custom" loss functions. These are described below for completion since, as mentioned before, they are used internally by the `Trainer`. Of course, onen could always use them on their own and can be imported as:

`from pytorch_widedeep.losses import FocalLoss`

NOTE: Losses in this module expect the predictions and ground truth to have the same dimensions for regression and binary classification problems \((N_{samples}, 1)\). In the case of multiclass classification problems the ground truth is expected to be a 1D tensor with the corresponding classes. See Examples below

## MSELoss

Bases: `Module`

Mean square error loss

Source code in `pytorch_widedeep/losses.py`

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    class MSELoss(nn.Module):
        r"""Mean square error loss"""

        # legacy code from when we used to support FDS-LDS and this class could
        # taked the corresponding params. At this stage probably you want to use
        # torch.nn.MSELoss
        def __init__(self):
            super().__init__()

        def forward(
            self,
            input: Tensor,
            target: Tensor,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions
            target: Tensor
                Target tensor with the actual values

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import MSELoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = MSELoss()(input, target)
            """
            loss = (input - target) ** 2
            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions | required
`target` | `Tensor` | Target tensor with the actual values | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import MSELoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = MSELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions
        target: Tensor
            Target tensor with the actual values

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import MSELoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = MSELoss()(input, target)
        """
        loss = (input - target) ** 2
        return torch.mean(loss)

## MSLELoss

Bases: `Module`

Mean square log error loss

Source code in `pytorch_widedeep/losses.py`

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    class MSLELoss(nn.Module):
        r"""Mean square log error loss"""

        def __init__(self):
            super().__init__()

        def forward(
            self,
            input: Tensor,
            target: Tensor,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import MSLELoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = MSLELoss()(input, target)
            """
            assert (
                input.min() >= 0
            ), """All input values must be >=0, if your model is predicting
                values <0 try to enforce positive values by activation function
                on last layer with `trainer.enforce_positive_output=True`"""
            assert target.min() >= 0, "All target values must be >=0"

            loss = (torch.log(input + 1) - torch.log(target + 1)) ** 2
            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import MSLELoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = MSLELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import MSLELoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = MSLELoss()(input, target)
        """
        assert (
            input.min() >= 0
        ), """All input values must be >=0, if your model is predicting
            values <0 try to enforce positive values by activation function
            on last layer with `trainer.enforce_positive_output=True`"""
        assert target.min() >= 0, "All target values must be >=0"

        loss = (torch.log(input + 1) - torch.log(target + 1)) ** 2
        return torch.mean(loss)

## RMSELoss

Bases: `Module`

Root mean square error loss

Source code in `pytorch_widedeep/losses.py`

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    class RMSELoss(nn.Module):
        r"""Root mean square error loss"""

        # legacy code from when we used to support FDS-LDS and this class could
        # taked the corresponding params. At this stage probably you want to use
        # torch.sqrt(nn.MSELoss)
        def __init__(self):
            super().__init__()

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import RMSELoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = RMSELoss()(input, target)
            """
            loss = (input - target) ** 2
            return torch.sqrt(torch.mean(loss))

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import RMSELoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = RMSELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import RMSELoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = RMSELoss()(input, target)
        """
        loss = (input - target) ** 2
        return torch.sqrt(torch.mean(loss))

## RMSLELoss

Bases: `Module`

Root mean square log error loss

Source code in `pytorch_widedeep/losses.py`

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    class RMSLELoss(nn.Module):
        r"""Root mean square log error loss"""

        def __init__(self):
            super().__init__()

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import RMSLELoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = RMSLELoss()(input, target)
            """
            assert (
                input.min() >= 0
            ), """All input values must be >=0, if your model is predicting
                values <0 try to enforce positive values by activation function
                on last layer with `trainer.enforce_positive_output=True`"""
            assert target.min() >= 0, "All target values must be >=0"

            loss = (torch.log(input + 1) - torch.log(target + 1)) ** 2
            return torch.sqrt(torch.mean(loss))

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import RMSLELoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = RMSLELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import RMSLELoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = RMSLELoss()(input, target)
        """
        assert (
            input.min() >= 0
        ), """All input values must be >=0, if your model is predicting
            values <0 try to enforce positive values by activation function
            on last layer with `trainer.enforce_positive_output=True`"""
        assert target.min() >= 0, "All target values must be >=0"

        loss = (torch.log(input + 1) - torch.log(target + 1)) ** 2
        return torch.sqrt(torch.mean(loss))

## QuantileLoss

Bases: `Module`

Quantile loss defined as:

\[ Loss = max(q \times (y-y_{pred}), (1-q) \times (y_{pred}-y)) \]

All credits go to the implementation at pytorch-forecasting.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`quantiles` | `List[float]` | List of quantiles | `[0.02, 0.1, 0.25, 0.5, 0.75, 0.9, 0.98]`

Source code in `pytorch_widedeep/losses.py`

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    class QuantileLoss(nn.Module):
        r"""Quantile loss defined as:

        $$
        Loss = max(q \times (y-y_{pred}), (1-q) \times (y_{pred}-y))
        $$

        All credits go to the implementation at
        [pytorch-forecasting](https://pytorch-forecasting.readthedocs.io/en/latest/_modules/pytorch_forecasting/metrics.html#QuantileLoss).

        Parameters
        ----------
        quantiles: List, default = [0.02, 0.1, 0.25, 0.5, 0.75, 0.9, 0.98]
            List of quantiles
        """

        def __init__(
            self,
            quantiles: List[float] = [0.02, 0.1, 0.25, 0.5, 0.75, 0.9, 0.98],
        ):
            super().__init__()
            self.quantiles = quantiles

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions
            target: Tensor
                Target tensor with the actual values

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import QuantileLoss
            >>>
            >>> # REGRESSION
            >>> target = torch.tensor([[0.6, 1.5]]).view(-1, 1)
            >>> input = torch.tensor([[.1, .2,], [.4, .5]])
            >>> qloss = QuantileLoss([0.25, 0.75])
            >>> loss = qloss(input, target)
            """

            assert input.shape == torch.Size([target.shape[0], len(self.quantiles)]), (
                "The input and target have inconsistent shape. The dimension of the prediction "
                "of the model that is using QuantileLoss must be equal to number of quantiles, "
                f"i.e. {len(self.quantiles)}."
            )
            target = target.view(-1, 1).float()
            losses = []
            for i, q in enumerate(self.quantiles):
                errors = target - input[..., i]
                losses.append(torch.max((q - 1) * errors, q * errors).unsqueeze(-1))

            loss = torch.cat(losses, dim=2)

            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions | required
`target` | `Tensor` | Target tensor with the actual values | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import QuantileLoss
    >>>
    >>> # REGRESSION
    >>> target = torch.tensor([[0.6, 1.5]]).view(-1, 1)
    >>> input = torch.tensor([[.1, .2,], [.4, .5]])
    >>> qloss = QuantileLoss([0.25, 0.75])
    >>> loss = qloss(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions
        target: Tensor
            Target tensor with the actual values

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import QuantileLoss
        >>>
        >>> # REGRESSION
        >>> target = torch.tensor([[0.6, 1.5]]).view(-1, 1)
        >>> input = torch.tensor([[.1, .2,], [.4, .5]])
        >>> qloss = QuantileLoss([0.25, 0.75])
        >>> loss = qloss(input, target)
        """

        assert input.shape == torch.Size([target.shape[0], len(self.quantiles)]), (
            "The input and target have inconsistent shape. The dimension of the prediction "
            "of the model that is using QuantileLoss must be equal to number of quantiles, "
            f"i.e. {len(self.quantiles)}."
        )
        target = target.view(-1, 1).float()
        losses = []
        for i, q in enumerate(self.quantiles):
            errors = target - input[..., i]
            losses.append(torch.max((q - 1) * errors, q * errors).unsqueeze(-1))

        loss = torch.cat(losses, dim=2)

        return torch.mean(loss)

## FocalLoss

Bases: `Module`

Implementation of the Focal loss for both binary and multiclass classification:

\[ FL(p_t) = \alpha (1 - p_t)^{\gamma} log(p_t) \]

where, for a case of a binary classification problem

\[ \begin{equation} p_t= \begin{cases}p, & \text{if $y=1$}.\\1-p, & \text{otherwise}. \end{cases} \end{equation} \]

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`alpha` | `float` | Focal Loss `alpha` parameter | `0.25`
`gamma` | `float` | Focal Loss `gamma` parameter | `1.0`

Source code in `pytorch_widedeep/losses.py`

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    class FocalLoss(nn.Module):
        r"""Implementation of the [Focal loss](https://arxiv.org/pdf/1708.02002.pdf)
        for both binary and multiclass classification:

        $$
        FL(p_t) = \alpha (1 - p_t)^{\gamma} log(p_t)
        $$

        where, for a case of a binary classification problem

        $$
        \begin{equation} p_t= \begin{cases}p, & \text{if $y=1$}.\\1-p, & \text{otherwise}. \end{cases} \end{equation}
        $$

        Parameters
        ----------
        alpha: float
            Focal Loss `alpha` parameter
        gamma: float
            Focal Loss `gamma` parameter
        """

        def __init__(self, alpha: float = 0.25, gamma: float = 1.0):
            super().__init__()
            self.alpha = alpha
            self.gamma = gamma

        def _get_weight(self, p: Tensor, t: Tensor) -> Tensor:
            pt = p * t + (1 - p) * (1 - t)  # type: ignore
            w = self.alpha * t + (1 - self.alpha) * (1 - t)  # type: ignore
            return (w * (1 - pt).pow(self.gamma)).detach()  # type: ignore

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import FocalLoss
            >>>
            >>> # BINARY
            >>> target = torch.tensor([0, 1, 0, 1]).view(-1, 1)
            >>> input = torch.tensor([[0.6, 0.7, 0.3, 0.8]]).t()
            >>> loss = FocalLoss()(input, target)
            >>>
            >>> # MULTICLASS
            >>> target = torch.tensor([1, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([[0.2, 0.5, 0.3], [0.8, 0.1, 0.1], [0.7, 0.2, 0.1]])
            >>> loss = FocalLoss()(input, target)
            """
            input_prob = torch.sigmoid(input)
            if input.size(1) == 1:
                input_prob = torch.cat([1 - input_prob, input_prob], axis=1)  # type: ignore
                num_class = 2
            else:
                num_class = input_prob.size(1)
            binary_target = torch.eye(num_class)[target.squeeze().cpu().long()]
            binary_target = binary_target.to(input.device)
            binary_target = binary_target.contiguous()
            weight = self._get_weight(input_prob, binary_target)

            return F.binary_cross_entropy(
                input_prob, binary_target, weight, reduction="mean"
            )

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import FocalLoss
    >>>
    >>> # BINARY
    >>> target = torch.tensor([0, 1, 0, 1]).view(-1, 1)
    >>> input = torch.tensor([[0.6, 0.7, 0.3, 0.8]]).t()
    >>> loss = FocalLoss()(input, target)
    >>>
    >>> # MULTICLASS
    >>> target = torch.tensor([1, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([[0.2, 0.5, 0.3], [0.8, 0.1, 0.1], [0.7, 0.2, 0.1]])
    >>> loss = FocalLoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import FocalLoss
        >>>
        >>> # BINARY
        >>> target = torch.tensor([0, 1, 0, 1]).view(-1, 1)
        >>> input = torch.tensor([[0.6, 0.7, 0.3, 0.8]]).t()
        >>> loss = FocalLoss()(input, target)
        >>>
        >>> # MULTICLASS
        >>> target = torch.tensor([1, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([[0.2, 0.5, 0.3], [0.8, 0.1, 0.1], [0.7, 0.2, 0.1]])
        >>> loss = FocalLoss()(input, target)
        """
        input_prob = torch.sigmoid(input)
        if input.size(1) == 1:
            input_prob = torch.cat([1 - input_prob, input_prob], axis=1)  # type: ignore
            num_class = 2
        else:
            num_class = input_prob.size(1)
        binary_target = torch.eye(num_class)[target.squeeze().cpu().long()]
        binary_target = binary_target.to(input.device)
        binary_target = binary_target.contiguous()
        weight = self._get_weight(input_prob, binary_target)

        return F.binary_cross_entropy(
            input_prob, binary_target, weight, reduction="mean"
        )

## BayesianSELoss

Bases: `Module`

Squared Loss (log Gaussian) for the case of a regression as specified in the original publication Weight Uncertainty in Neural Networks.

Source code in `pytorch_widedeep/losses.py`

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    class BayesianSELoss(nn.Module):
        r"""Squared Loss (log Gaussian) for the case of a regression as specified in
        the original publication
        [Weight Uncertainty in Neural Networks](https://arxiv.org/abs/1505.05424).
        """

        def __init__(self):
            super().__init__()

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import BayesianSELoss
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = BayesianSELoss()(input, target)
            """
            return (0.5 * (input - target) ** 2).sum()

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import BayesianSELoss
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = BayesianSELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import BayesianSELoss
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = BayesianSELoss()(input, target)
        """
        return (0.5 * (input - target) ** 2).sum()

## TweedieLoss

Bases: `Module`

Tweedie loss for extremely unbalanced zero-inflated data

All credits go to Wenbo Shi. See this post and the original publication for details.

Source code in `pytorch_widedeep/losses.py`

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    class TweedieLoss(nn.Module):
        """
        Tweedie loss for extremely unbalanced zero-inflated data

        All credits go to Wenbo Shi. See
        [this post](https://towardsdatascience.com/tweedie-loss-function-for-right-skewed-data-2c5ca470678f)
        and the [original publication](https://arxiv.org/abs/1811.10192) for details.
        """

        def __init__(self):
            super().__init__()

        def forward(
            self,
            input: Tensor,
            target: Tensor,
            p: float = 1.5,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions
            target: Tensor
                Target tensor with the actual values
            p: float, default = 1.5
                the power to be used to compute the loss. See the original
                publication for details

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import TweedieLoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = TweedieLoss()(input, target)
            """

            assert (
                input.min() > 0
            ), """All input values must be >=0, if your model is predicting
                values <0 try to enforce positive values by activation function
                on last layer with `trainer.enforce_positive_output=True`"""
            assert target.min() >= 0, "All target values must be >=0"
            loss = -target * torch.pow(input, 1 - p) / (1 - p) + torch.pow(input, 2 - p) / (
                2 - p
            )
            return torch.mean(loss)

### forward

    forward(input, target, p=1.5)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions | required
`target` | `Tensor` | Target tensor with the actual values | required
`p` | `float` | the power to be used to compute the loss. See the original publication for details | `1.5`

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import TweedieLoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = TweedieLoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
        p: float = 1.5,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions
        target: Tensor
            Target tensor with the actual values
        p: float, default = 1.5
            the power to be used to compute the loss. See the original
            publication for details

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import TweedieLoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = TweedieLoss()(input, target)
        """

        assert (
            input.min() > 0
        ), """All input values must be >=0, if your model is predicting
            values <0 try to enforce positive values by activation function
            on last layer with `trainer.enforce_positive_output=True`"""
        assert target.min() >= 0, "All target values must be >=0"
        loss = -target * torch.pow(input, 1 - p) / (1 - p) + torch.pow(input, 2 - p) / (
            2 - p
        )
        return torch.mean(loss)

## ZILNLoss

Bases: `Module`

Adjusted implementation of the Zero Inflated LogNormal Loss

See A Deep Probabilistic Model for Customer Lifetime Value Prediction and the corresponding code.

Source code in `pytorch_widedeep/losses.py`

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    class ZILNLoss(nn.Module):
        r"""Adjusted implementation of the Zero Inflated LogNormal Loss

        See [A Deep Probabilistic Model for Customer Lifetime Value Prediction](https://arxiv.org/pdf/1912.07753.pdf)
        and the corresponding
        [code](https://github.com/google/lifetime_value/blob/master/lifetime_value/zero_inflated_lognormal.py).
        """

        def __init__(self):
            super().__init__()

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions with spape (N,3), where N is the batch size
            target: Tensor
                Target tensor with the actual target values

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import ZILNLoss
            >>>
            >>> target = torch.tensor([[0., 1.5]]).view(-1, 1)
            >>> input = torch.tensor([[.1, .2, .3], [.4, .5, .6]])
            >>> loss = ZILNLoss()(input, target)
            """
            positive = target > 0
            positive = positive.float()

            assert input.shape == torch.Size([target.shape[0], 3]), (
                "Wrong shape of the 'input' tensor. The pred_dim of the "
                "model that is using ZILNLoss must be equal to 3."
            )

            positive_input = input[..., :1]

            classification_loss = F.binary_cross_entropy_with_logits(
                positive_input, positive, reduction="none"
            ).flatten()

            loc = input[..., 1:2]

            # when using max the two input tensors (input and other) have to be of
            # the same type
            max_input = F.softplus(input[..., 2:])
            max_other = self.get_eps(max_input)
            scale = torch.max(max_input, max_other)
            safe_labels = positive * target + (1 - positive) * torch.ones_like(target)

            regression_loss = -torch.mean(
                positive
                * torch.distributions.log_normal.LogNormal(loc=loc, scale=scale).log_prob(
                    safe_labels
                ),
                dim=-1,
            )

            return torch.mean(classification_loss + regression_loss)

        @staticmethod
        def get_eps(max_input: Tensor) -> Tensor:
            if max_input.device.type == "mps":
                # For MPS, use float32 and then convert to the input type
                eps = torch.finfo(torch.float32).eps
                max_other = (
                    torch.sqrt(torch.tensor([eps], device="cpu"))
                    .to(max_input.device)
                    .to(max_input.dtype)
                )
            else:
                # For other devices, use the original approach
                eps = torch.finfo(torch.double).eps
                max_other = (
                    torch.sqrt(torch.tensor([eps])).to(max_input.device).to(max_input.dtype)
                )

            return max_other

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions with spape (N,3), where N is the batch size | required
`target` | `Tensor` | Target tensor with the actual target values | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import ZILNLoss
    >>>
    >>> target = torch.tensor([[0., 1.5]]).view(-1, 1)
    >>> input = torch.tensor([[.1, .2, .3], [.4, .5, .6]])
    >>> loss = ZILNLoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions with spape (N,3), where N is the batch size
        target: Tensor
            Target tensor with the actual target values

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import ZILNLoss
        >>>
        >>> target = torch.tensor([[0., 1.5]]).view(-1, 1)
        >>> input = torch.tensor([[.1, .2, .3], [.4, .5, .6]])
        >>> loss = ZILNLoss()(input, target)
        """
        positive = target > 0
        positive = positive.float()

        assert input.shape == torch.Size([target.shape[0], 3]), (
            "Wrong shape of the 'input' tensor. The pred_dim of the "
            "model that is using ZILNLoss must be equal to 3."
        )

        positive_input = input[..., :1]

        classification_loss = F.binary_cross_entropy_with_logits(
            positive_input, positive, reduction="none"
        ).flatten()

        loc = input[..., 1:2]

        # when using max the two input tensors (input and other) have to be of
        # the same type
        max_input = F.softplus(input[..., 2:])
        max_other = self.get_eps(max_input)
        scale = torch.max(max_input, max_other)
        safe_labels = positive * target + (1 - positive) * torch.ones_like(target)

        regression_loss = -torch.mean(
            positive
            * torch.distributions.log_normal.LogNormal(loc=loc, scale=scale).log_prob(
                safe_labels
            ),
            dim=-1,
        )

        return torch.mean(classification_loss + regression_loss)

## L1Loss

Bases: `Module`

L1 loss

Source code in `pytorch_widedeep/losses.py`

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    class L1Loss(nn.Module):
        r"""L1 loss"""

        # legacy code from when we used to support FDS-LDS and this class could
        # taked the corresponding params. At this stage probably you want to use
        # torch.nn.L1Loss
        def __init__(self):
            super().__init__()

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions
            target: Tensor
                Target tensor with the actual values

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import L1Loss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = L1Loss()(input, target)
            """
            loss = F.l1_loss(input, target, reduction="none")
            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions | required
`target` | `Tensor` | Target tensor with the actual values | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import L1Loss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = L1Loss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions
        target: Tensor
            Target tensor with the actual values

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import L1Loss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = L1Loss()(input, target)
        """
        loss = F.l1_loss(input, target, reduction="none")
        return torch.mean(loss)

## FocalR_L1Loss

Bases: `Module`

Focal-R L1 loss

Based on Delving into Deep Imbalanced Regression.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`beta` | `float` | Focal Loss `beta` parameter in their implementation | `0.2`
`gamma` | `float` | Focal Loss `gamma` parameter | `1.0`
`activation_fn` | `Literal[sigmoid, tanh]` | Activation function to be used during the computation of the loss. Possible values are 'sigmoid' and 'tanh'. See the original publication for details. | `'sigmoid'`

Source code in `pytorch_widedeep/losses.py`

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    class FocalR_L1Loss(nn.Module):
        r"""Focal-R L1 loss

        Based on [Delving into Deep Imbalanced Regression](https://arxiv.org/abs/2102.09554).

        Parameters
        ----------
        beta: float
            Focal Loss `beta` parameter in their implementation
        gamma: float
            Focal Loss `gamma` parameter
        activation_fn: str, default = "sigmoid"
            Activation function to be used during the computation of the loss.
            Possible values are _'sigmoid'_ and _'tanh'_. See the original
            publication for details.
        """

        def __init__(
            self,
            beta: float = 0.2,
            gamma: float = 1.0,
            activation_fn: Literal["sigmoid", "tanh"] = "sigmoid",
        ):
            super().__init__()
            self.beta = beta
            self.gamma = gamma
            self.activation_fn = activation_fn

        def forward(
            self,
            input: Tensor,
            target: Tensor,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import FocalR_L1Loss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = FocalR_L1Loss()(input, target)
            """
            loss = F.l1_loss(input, target, reduction="none")
            if self.activation_fn == "tanh":
                loss *= (torch.tanh(self.beta * torch.abs(input - target))) ** self.gamma
            elif self.activation_fn == "sigmoid":
                loss *= (
                    2 * torch.sigmoid(self.beta * torch.abs(input - target)) - 1
                ) ** self.gamma
            else:
                ValueError(
                    "Incorrect activation function value - must be in ['sigmoid', 'tanh']"
                )
            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import FocalR_L1Loss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = FocalR_L1Loss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import FocalR_L1Loss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = FocalR_L1Loss()(input, target)
        """
        loss = F.l1_loss(input, target, reduction="none")
        if self.activation_fn == "tanh":
            loss *= (torch.tanh(self.beta * torch.abs(input - target))) ** self.gamma
        elif self.activation_fn == "sigmoid":
            loss *= (
                2 * torch.sigmoid(self.beta * torch.abs(input - target)) - 1
            ) ** self.gamma
        else:
            ValueError(
                "Incorrect activation function value - must be in ['sigmoid', 'tanh']"
            )
        return torch.mean(loss)

## FocalR_MSELoss

Bases: `Module`

Focal-R MSE loss

Based on Delving into Deep Imbalanced Regression.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`beta` | `float` | Focal Loss `beta` parameter in their implementation | `0.2`
`gamma` | `float` | Focal Loss `gamma` parameter | `1.0`
`activation_fn` | `Literal[sigmoid, tanh]` | Activation function to be used during the computation of the loss. Possible values are 'sigmoid' and 'tanh'. See the original publication for details. | `'sigmoid'`

Source code in `pytorch_widedeep/losses.py`

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    class FocalR_MSELoss(nn.Module):
        r"""Focal-R MSE loss

        Based on [Delving into Deep Imbalanced Regression](https://arxiv.org/abs/2102.09554).

        Parameters
        ----------
        beta: float
            Focal Loss `beta` parameter in their implementation
        gamma: float
            Focal Loss `gamma` parameter
        activation_fn: str, default = "sigmoid"
            Activation function to be used during the computation of the loss.
            Possible values are _'sigmoid'_ and _'tanh'_. See the original
            publication for details.
        """

        def __init__(
            self,
            beta: float = 0.2,
            gamma: float = 1.0,
            activation_fn: Literal["sigmoid", "tanh"] = "sigmoid",
        ):
            super().__init__()
            self.beta = beta
            self.gamma = gamma
            self.activation_fn = activation_fn

        def forward(
            self,
            input: Tensor,
            target: Tensor,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import FocalR_MSELoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = FocalR_MSELoss()(input, target)
            """
            loss = (input - target) ** 2
            if self.activation_fn == "tanh":
                loss *= (torch.tanh(self.beta * torch.abs(input - target))) ** self.gamma
            elif self.activation_fn == "sigmoid":
                loss *= (
                    2 * torch.sigmoid(self.beta * torch.abs((input - target) ** 2)) - 1
                ) ** self.gamma
            else:
                ValueError(
                    "Incorrect activation function value - must be in ['sigmoid', 'tanh']"
                )
            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import FocalR_MSELoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = FocalR_MSELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import FocalR_MSELoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = FocalR_MSELoss()(input, target)
        """
        loss = (input - target) ** 2
        if self.activation_fn == "tanh":
            loss *= (torch.tanh(self.beta * torch.abs(input - target))) ** self.gamma
        elif self.activation_fn == "sigmoid":
            loss *= (
                2 * torch.sigmoid(self.beta * torch.abs((input - target) ** 2)) - 1
            ) ** self.gamma
        else:
            ValueError(
                "Incorrect activation function value - must be in ['sigmoid', 'tanh']"
            )
        return torch.mean(loss)

## FocalR_RMSELoss

Bases: `Module`

Focal-R RMSE loss

Based on Delving into Deep Imbalanced Regression.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`beta` | `float` | Focal Loss `beta` parameter in their implementation | `0.2`
`gamma` | `float` | Focal Loss `gamma` parameter | `1.0`
`activation_fn` | `Literal[sigmoid, tanh]` | Activation function to be used during the computation of the loss. Possible values are 'sigmoid' and 'tanh'. See the original publication for details. | `'sigmoid'`

Source code in `pytorch_widedeep/losses.py`

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    class FocalR_RMSELoss(nn.Module):
        r"""Focal-R RMSE loss

        Based on [Delving into Deep Imbalanced Regression](https://arxiv.org/abs/2102.09554).

        Parameters
        ----------
        beta: float
            Focal Loss `beta` parameter in their implementation
        gamma: float
            Focal Loss `gamma` parameter
        activation_fn: str, default = "sigmoid"
            Activation function to be used during the computation of the loss.
            Possible values are _'sigmoid'_ and _'tanh'_. See the original
            publication for details.
        """

        def __init__(
            self,
            beta: float = 0.2,
            gamma: float = 1.0,
            activation_fn: Literal["sigmoid", "tanh"] = "sigmoid",
        ):
            super().__init__()
            self.beta = beta
            self.gamma = gamma
            self.activation_fn = activation_fn

        def forward(
            self,
            input: Tensor,
            target: Tensor,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import FocalR_RMSELoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = FocalR_RMSELoss()(input, target)
            """
            loss = (input - target) ** 2
            if self.activation_fn == "tanh":
                loss *= (torch.tanh(self.beta * torch.abs(input - target))) ** self.gamma
            elif self.activation_fn == "sigmoid":
                loss *= (
                    2 * torch.sigmoid(self.beta * torch.abs((input - target) ** 2)) - 1
                ) ** self.gamma
            else:
                ValueError(
                    "Incorrect activation function value - must be in ['sigmoid', 'tanh']"
                )
            return torch.sqrt(torch.mean(loss))

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import FocalR_RMSELoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = FocalR_RMSELoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import FocalR_RMSELoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = FocalR_RMSELoss()(input, target)
        """
        loss = (input - target) ** 2
        if self.activation_fn == "tanh":
            loss *= (torch.tanh(self.beta * torch.abs(input - target))) ** self.gamma
        elif self.activation_fn == "sigmoid":
            loss *= (
                2 * torch.sigmoid(self.beta * torch.abs((input - target) ** 2)) - 1
            ) ** self.gamma
        else:
            ValueError(
                "Incorrect activation function value - must be in ['sigmoid', 'tanh']"
            )
        return torch.sqrt(torch.mean(loss))

## HuberLoss

Bases: `Module`

Hubbler Loss

Based on Delving into Deep Imbalanced Regression.

Source code in `pytorch_widedeep/losses.py`

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    class HuberLoss(nn.Module):
        r"""Hubbler Loss

        Based on [Delving into Deep Imbalanced Regression](https://arxiv.org/abs/2102.09554).
        """

        def __init__(self, beta: float = 0.2):
            super().__init__()
            self.beta = beta

        def forward(
            self,
            input: Tensor,
            target: Tensor,
        ) -> Tensor:
            r"""
            Parameters
            ----------
            input: Tensor
                Input tensor with predictions (not probabilities)
            target: Tensor
                Target tensor with the actual classes

            Examples
            --------
            >>> import torch
            >>>
            >>> from pytorch_widedeep.losses import HuberLoss
            >>>
            >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
            >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
            >>> loss = HuberLoss()(input, target)
            """
            l1_loss = torch.abs(input - target)
            cond = l1_loss < self.beta
            loss = torch.where(
                cond, 0.5 * l1_loss**2 / self.beta, l1_loss - 0.5 * self.beta
            )
            return torch.mean(loss)

### forward

    forward(input, target)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`input` | `Tensor` | Input tensor with predictions (not probabilities) | required
`target` | `Tensor` | Target tensor with the actual classes | required

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.losses import HuberLoss
    >>>
    >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
    >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
    >>> loss = HuberLoss()(input, target)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        input: Tensor,
        target: Tensor,
    ) -> Tensor:
        r"""
        Parameters
        ----------
        input: Tensor
            Input tensor with predictions (not probabilities)
        target: Tensor
            Target tensor with the actual classes

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.losses import HuberLoss
        >>>
        >>> target = torch.tensor([1, 1.2, 0, 2]).view(-1, 1)
        >>> input = torch.tensor([0.6, 0.7, 0.3, 0.8]).view(-1, 1)
        >>> loss = HuberLoss()(input, target)
        """
        l1_loss = torch.abs(input - target)
        cond = l1_loss < self.beta
        loss = torch.where(
            cond, 0.5 * l1_loss**2 / self.beta, l1_loss - 0.5 * self.beta
        )
        return torch.mean(loss)

## InfoNCELoss

Bases: `Module`

InfoNCE Loss. Loss applied during the Contrastive Denoising Self Supervised Pre-training routine available in this library

NOTE: This loss is in principle not exposed to the user, as it is used internally in the library, but it is included here for completion.

See SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training and references therein

Partially inspired by the code in this repo

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`temperature` | `float` | The logits are divided by the temperature before computing the loss value | `0.1`
`reduction` | `str` | Loss reduction method | `'mean'`

Source code in `pytorch_widedeep/losses.py`

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    class InfoNCELoss(nn.Module):
        r"""InfoNCE Loss. Loss applied during the Contrastive Denoising Self
        Supervised Pre-training routine available in this library

        :information_source: **NOTE**: This loss is in principle not exposed to
         the user, as it is used internally in the library, but it is included
         here for completion.

        See [SAINT: Improved Neural Networks for Tabular Data via Row Attention
        and Contrastive Pre-Training](https://arxiv.org/abs/2106.01342) and
        references therein

        Partially inspired by the code in this [repo](https://github.com/RElbers/info-nce-pytorch)

        Parameters
        ----------
        temperature: float, default = 0.1
            The logits are divided by the temperature before computing the loss value
        reduction: str, default = "mean"
            Loss reduction method
        """

        def __init__(self, temperature: float = 0.1, reduction: str = "mean"):
            super(InfoNCELoss, self).__init__()

            self.temperature = temperature
            self.reduction = reduction

        def forward(self, g_projs: Tuple[Tensor, Tensor]) -> Tensor:
            r"""
            Parameters
            ----------
            g_projs: Tuple
                Tuple with the two tensors corresponding to the output of the two
                projection heads, as described 'SAINT: Improved Neural Networks
                for Tabular Data via Row Attention and Contrastive Pre-Training'.

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import InfoNCELoss
            >>> g_projs = (torch.rand(3, 5, 16), torch.rand(3, 5, 16))
            >>> loss = InfoNCELoss()
            >>> res = loss(g_projs)
            """
            z, z_ = g_projs[0], g_projs[1]

            norm_z = F.normalize(z, dim=-1).flatten(1)
            norm_z_ = F.normalize(z_, dim=-1).flatten(1)

            logits = (norm_z @ norm_z_.t()) / self.temperature
            logits_ = (norm_z_ @ norm_z.t()) / self.temperature

            # the target/labels are the entries on the diagonal
            target = torch.arange(len(norm_z), device=norm_z.device)

            loss = F.cross_entropy(logits, target, reduction=self.reduction)
            loss_ = F.cross_entropy(logits_, target, reduction=self.reduction)

            return (loss + loss_) / 2.0

### forward

    forward(g_projs)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`g_projs` | `Tuple[Tensor, Tensor]` | Tuple with the two tensors corresponding to the output of the two projection heads, as described 'SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training'. | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import InfoNCELoss
    >>> g_projs = (torch.rand(3, 5, 16), torch.rand(3, 5, 16))
    >>> loss = InfoNCELoss()
    >>> res = loss(g_projs)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, g_projs: Tuple[Tensor, Tensor]) -> Tensor:
        r"""
        Parameters
        ----------
        g_projs: Tuple
            Tuple with the two tensors corresponding to the output of the two
            projection heads, as described 'SAINT: Improved Neural Networks
            for Tabular Data via Row Attention and Contrastive Pre-Training'.

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import InfoNCELoss
        >>> g_projs = (torch.rand(3, 5, 16), torch.rand(3, 5, 16))
        >>> loss = InfoNCELoss()
        >>> res = loss(g_projs)
        """
        z, z_ = g_projs[0], g_projs[1]

        norm_z = F.normalize(z, dim=-1).flatten(1)
        norm_z_ = F.normalize(z_, dim=-1).flatten(1)

        logits = (norm_z @ norm_z_.t()) / self.temperature
        logits_ = (norm_z_ @ norm_z.t()) / self.temperature

        # the target/labels are the entries on the diagonal
        target = torch.arange(len(norm_z), device=norm_z.device)

        loss = F.cross_entropy(logits, target, reduction=self.reduction)
        loss_ = F.cross_entropy(logits_, target, reduction=self.reduction)

        return (loss + loss_) / 2.0

## DenoisingLoss

Bases: `Module`

Denoising Loss. Loss applied during the Contrastive Denoising Self Supervised Pre-training routine available in this library

NOTE: This loss is in principle not exposed to the user, as it is used internally in the library, but it is included here for completion.

See SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training and references therein

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`lambda_cat` | `float` | Multiplicative factor that will be applied to loss associated to the categorical features | `1.0`
`lambda_cont` | `float` | Multiplicative factor that will be applied to loss associated to the continuous features | `1.0`
`reduction` | `str` | Loss reduction method | `'mean'`

Source code in `pytorch_widedeep/losses.py`

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    class DenoisingLoss(nn.Module):
        r"""Denoising Loss. Loss applied during the Contrastive Denoising Self
        Supervised Pre-training routine available in this library

        :information_source: **NOTE**: This loss is in principle not exposed to
         the user, as it is used internally in the library, but it is included
         here for completion.

        See [SAINT: Improved Neural Networks for Tabular Data via Row Attention
        and Contrastive Pre-Training](https://arxiv.org/abs/2106.01342) and
        references therein

        Parameters
        ----------
        lambda_cat: float, default = 1.
            Multiplicative factor that will be applied to loss associated to the
            categorical features
        lambda_cont: float, default = 1.
            Multiplicative factor that will be applied to loss associated to the
            continuous features
        reduction: str, default = "mean"
            Loss reduction method
        """

        def __init__(
            self, lambda_cat: float = 1.0, lambda_cont: float = 1.0, reduction: str = "mean"
        ):
            super(DenoisingLoss, self).__init__()

            self.lambda_cat = lambda_cat
            self.lambda_cont = lambda_cont
            self.reduction = reduction

        def forward(
            self,
            x_cat_and_cat_: Optional[
                Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]
            ],
            x_cont_and_cont_: Optional[
                Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]
            ],
        ) -> Tensor:
            r"""
            Parameters
            ----------
            x_cat_and_cat_: tuple of Tensors or lists of tuples
                Tuple of tensors containing the raw input features and their
                encodings, referred in the SAINT paper as $x$ and $x''$
                respectively. If one denoising MLP is used per categorical
                feature `x_cat_and_cat_` will be a list of tuples, one per
                categorical feature
            x_cont_and_cont_: tuple of Tensors or lists of tuples
                same as `x_cat_and_cat_` but for continuous columns

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import DenoisingLoss
            >>> x_cat_and_cat_ = (torch.empty(3).random_(3).long(), torch.randn(3, 3))
            >>> x_cont_and_cont_ = (torch.randn(3, 1), torch.randn(3, 1))
            >>> loss = DenoisingLoss()
            >>> res = loss(x_cat_and_cat_, x_cont_and_cont_)
            """

            loss_cat = (
                self._compute_cat_loss(x_cat_and_cat_)
                if x_cat_and_cat_ is not None
                else torch.tensor(0.0)
            )
            loss_cont = (
                self._compute_cont_loss(x_cont_and_cont_)
                if x_cont_and_cont_ is not None
                else torch.tensor(0.0)
            )

            return self.lambda_cat * loss_cat + self.lambda_cont * loss_cont

        def _compute_cat_loss(
            self, x_cat_and_cat_: Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]
        ) -> Tensor:
            loss_cat = torch.tensor(0.0, device=self._get_device(x_cat_and_cat_))
            if isinstance(x_cat_and_cat_, list):
                for x, x_ in x_cat_and_cat_:
                    loss_cat += F.cross_entropy(x_, x, reduction=self.reduction)
            elif isinstance(x_cat_and_cat_, tuple):
                x, x_ = x_cat_and_cat_
                loss_cat += F.cross_entropy(x_, x, reduction=self.reduction)

            return loss_cat

        def _compute_cont_loss(self, x_cont_and_cont_) -> Tensor:
            loss_cont = torch.tensor(0.0, device=self._get_device(x_cont_and_cont_))
            if isinstance(x_cont_and_cont_, list):
                for x, x_ in x_cont_and_cont_:
                    loss_cont += F.mse_loss(x_, x, reduction=self.reduction)
            elif isinstance(x_cont_and_cont_, tuple):
                x, x_ = x_cont_and_cont_
                loss_cont += F.mse_loss(x_, x, reduction=self.reduction)

            return loss_cont

        @staticmethod
        def _get_device(
            x_and_x_: Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]
        ):
            if isinstance(x_and_x_, tuple):
                device = x_and_x_[0].device
            elif isinstance(x_and_x_, list):
                device = x_and_x_[0][0].device
            return device

### forward

    forward(x_cat_and_cat_, x_cont_and_cont_)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`x_cat_and_cat_` | `Optional[Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]]` | Tuple of tensors containing the raw input features and their encodings, referred in the SAINT paper as \(x\) and \(x''\) respectively. If one denoising MLP is used per categorical feature `x_cat_and_cat_` will be a list of tuples, one per categorical feature | required
`x_cont_and_cont_` | `Optional[Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]]` | same as `x_cat_and_cat_` but for continuous columns | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import DenoisingLoss
    >>> x_cat_and_cat_ = (torch.empty(3).random_(3).long(), torch.randn(3, 3))
    >>> x_cont_and_cont_ = (torch.randn(3, 1), torch.randn(3, 1))
    >>> loss = DenoisingLoss()
    >>> res = loss(x_cat_and_cat_, x_cont_and_cont_)

Source code in `pytorch_widedeep/losses.py`

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    def forward(
        self,
        x_cat_and_cat_: Optional[
            Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]
        ],
        x_cont_and_cont_: Optional[
            Union[List[Tuple[Tensor, Tensor]], Tuple[Tensor, Tensor]]
        ],
    ) -> Tensor:
        r"""
        Parameters
        ----------
        x_cat_and_cat_: tuple of Tensors or lists of tuples
            Tuple of tensors containing the raw input features and their
            encodings, referred in the SAINT paper as $x$ and $x''$
            respectively. If one denoising MLP is used per categorical
            feature `x_cat_and_cat_` will be a list of tuples, one per
            categorical feature
        x_cont_and_cont_: tuple of Tensors or lists of tuples
            same as `x_cat_and_cat_` but for continuous columns

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import DenoisingLoss
        >>> x_cat_and_cat_ = (torch.empty(3).random_(3).long(), torch.randn(3, 3))
        >>> x_cont_and_cont_ = (torch.randn(3, 1), torch.randn(3, 1))
        >>> loss = DenoisingLoss()
        >>> res = loss(x_cat_and_cat_, x_cont_and_cont_)
        """

        loss_cat = (
            self._compute_cat_loss(x_cat_and_cat_)
            if x_cat_and_cat_ is not None
            else torch.tensor(0.0)
        )
        loss_cont = (
            self._compute_cont_loss(x_cont_and_cont_)
            if x_cont_and_cont_ is not None
            else torch.tensor(0.0)
        )

        return self.lambda_cat * loss_cat + self.lambda_cont * loss_cont

## EncoderDecoderLoss

Bases: `Module`

'Standard' Encoder Decoder Loss. Loss applied during the Endoder-Decoder Self-Supervised Pre-Training routine available in this library

NOTE: This loss is in principle not exposed to the user, as it is used internally in the library, but it is included here for completion.

The implementation of this lost is based on that at the tabnet repo, which is in itself an adaptation of that in the original paper TabNet: Attentive Interpretable Tabular Learning.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`eps` | `float` | Simply a small number to avoid dividing by zero | `1e-09`

Source code in `pytorch_widedeep/losses.py`

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    class EncoderDecoderLoss(nn.Module):
        r"""'_Standard_' Encoder Decoder Loss. Loss applied during the Endoder-Decoder
         Self-Supervised Pre-Training routine available in this library

        :information_source: **NOTE**: This loss is in principle not exposed to
         the user, as it is used internally in the library, but it is included
         here for completion.

        The implementation of this lost is based on that at the
        [tabnet repo](https://github.com/dreamquark-ai/tabnet), which is in itself an
        adaptation of that in the original paper [TabNet: Attentive
        Interpretable Tabular Learning](https://arxiv.org/abs/1908.07442).

        Parameters
        ----------
        eps: float
            Simply a small number to avoid dividing by zero
        """

        def __init__(self, eps: float = 1e-9):
            super(EncoderDecoderLoss, self).__init__()
            self.eps = eps

        def forward(self, x_true: Tensor, x_pred: Tensor, mask: Tensor) -> Tensor:
            r"""
            Parameters
            ----------
            x_true: Tensor
                Embeddings of the input data
            x_pred: Tensor
                Reconstructed embeddings
            mask: Tensor
                Mask with 1s indicated that the reconstruction, and therefore the
                loss, is based on those features.

            Examples
            --------
            >>> import torch
            >>> from pytorch_widedeep.losses import EncoderDecoderLoss
            >>> x_true = torch.rand(3, 3)
            >>> x_pred = torch.rand(3, 3)
            >>> mask = torch.empty(3, 3).random_(2)
            >>> loss = EncoderDecoderLoss()
            >>> res = loss(x_true, x_pred, mask)
            """

            errors = x_pred - x_true

            reconstruction_errors = torch.mul(errors, mask) ** 2

            x_true_means = torch.mean(x_true, dim=0)
            x_true_means[x_true_means == 0] = 1

            x_true_stds = torch.std(x_true, dim=0) ** 2
            x_true_stds[x_true_stds == 0] = x_true_means[x_true_stds == 0]

            features_loss = torch.matmul(reconstruction_errors, 1 / x_true_stds)
            nb_reconstructed_variables = torch.sum(mask, dim=1)
            features_loss_norm = features_loss / (nb_reconstructed_variables + self.eps)

            loss = torch.mean(features_loss_norm)

            return loss

### forward

    forward(x_true, x_pred, mask)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`x_true` | `Tensor` | Embeddings of the input data | required
`x_pred` | `Tensor` | Reconstructed embeddings | required
`mask` | `Tensor` | Mask with 1s indicated that the reconstruction, and therefore the loss, is based on those features. | required

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses import EncoderDecoderLoss
    >>> x_true = torch.rand(3, 3)
    >>> x_pred = torch.rand(3, 3)
    >>> mask = torch.empty(3, 3).random_(2)
    >>> loss = EncoderDecoderLoss()
    >>> res = loss(x_true, x_pred, mask)

Source code in `pytorch_widedeep/losses.py`

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    def forward(self, x_true: Tensor, x_pred: Tensor, mask: Tensor) -> Tensor:
        r"""
        Parameters
        ----------
        x_true: Tensor
            Embeddings of the input data
        x_pred: Tensor
            Reconstructed embeddings
        mask: Tensor
            Mask with 1s indicated that the reconstruction, and therefore the
            loss, is based on those features.

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses import EncoderDecoderLoss
        >>> x_true = torch.rand(3, 3)
        >>> x_pred = torch.rand(3, 3)
        >>> mask = torch.empty(3, 3).random_(2)
        >>> loss = EncoderDecoderLoss()
        >>> res = loss(x_true, x_pred, mask)
        """

        errors = x_pred - x_true

        reconstruction_errors = torch.mul(errors, mask) ** 2

        x_true_means = torch.mean(x_true, dim=0)
        x_true_means[x_true_means == 0] = 1

        x_true_stds = torch.std(x_true, dim=0) ** 2
        x_true_stds[x_true_stds == 0] = x_true_means[x_true_stds == 0]

        features_loss = torch.matmul(reconstruction_errors, 1 / x_true_stds)
        nb_reconstructed_variables = torch.sum(mask, dim=1)
        features_loss_norm = features_loss / (nb_reconstructed_variables + self.eps)

        loss = torch.mean(features_loss_norm)

        return loss

## MultiTargetRegressionLoss

Bases: `Module`

This class is a wrapper around the Pytorch MSELoss. It allows for multi-target regression problems. The user can provide a list of weights to apply to each target. The loss can be either the sum or the mean of the individual losses

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`weights` | `Optional[List[float]]` | List of weights to apply to the loss associated to each target. The length of the list must match the number of targets. Alias: 'target_weights' | `None`
`reduction` | `Literal[mean, sum]` | Specifies the reduction to apply to the loss associated to each target: 'mean' | 'sum'. Note that this is NOT the same as the reduction in the MSELoss. This reduction is applied after the loss for each target has been computed. Alias: 'target_reduction' | `'mean'`

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses_multitarget import MultiTargetRegressionLoss
    >>> input = torch.randn(3, 2)
    >>> target = torch.randn(3, 2)
    >>> loss = MultiTargetRegressionLoss(weights=[0.5, 0.5], reduction="mean")
    >>> output = loss(input, target)

Source code in `pytorch_widedeep/losses_multitarget.py`

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    class MultiTargetRegressionLoss(nn.Module):
        """
        This class is a wrapper around the Pytorch MSELoss. It allows for multi-target
        regression problems. The user can provide a list of weights to apply to each
        target. The loss can be either the sum or the mean of the individual losses

        Parameters
        ----------
        weights: Optional[List[float], default = None]
            List of weights to apply to the loss associated to each target. The
            length of the list must match the number of targets.
            Alias: 'target_weights'
        reduction: Literal["mean", "sum"], default = "mean
            Specifies the reduction to apply to the loss associated to each
            target: 'mean' | 'sum'. Note that this is NOT the same as the
            reduction in the MSELoss. This reduction is applied after the loss
            for each target has been computed. Alias: 'target_reduction'

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses_multitarget import MultiTargetRegressionLoss
        >>> input = torch.randn(3, 2)
        >>> target = torch.randn(3, 2)
        >>> loss = MultiTargetRegressionLoss(weights=[0.5, 0.5], reduction="mean")
        >>> output = loss(input, target)
        """

        @alias("reduction", ["target_reduction"])
        @alias("weights", ["target_weights"])
        def __init__(
            self,
            weights: Optional[List[float]] = None,
            reduction: Literal["mean", "sum"] = "mean",
        ):
            super(MultiTargetRegressionLoss, self).__init__()

            self.weights = weights
            self.reduction = reduction

            if self.reduction not in ["mean", "sum"]:
                raise ValueError("reduction must be either 'mean' or 'sum'")

        def forward(self, input: Tensor, target: Tensor) -> Tensor:

            assert input.size() == target.size()

            if self.weights is not None:

                assert len(self.weights) == input.size(1), (
                    "The number of weights must match the number of targets. "
                    f"Got {len(self.weights)} weights and {input.size(1)} targets"
                )

                loss = F.mse_loss(input, target, reduction="none") * torch.tensor(
                    self.weights
                ).to(input.device)
            else:
                loss = F.mse_loss(input, target, reduction="none")

            return loss.mean() if self.reduction == "mean" else loss.sum()

## MultiTargetClassificationLoss

Bases: `Module`

This class is a wrapper around the Pytorch binary_cross_entropy_with_logits and cross_entropy losses. It allows for multi-target classification problems. The user can provide a list of weights to apply to each target. The loss can be either the sum or the mean of the individual losses

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`binary_config` | `Optional[List[Union[int, Tuple[int, float]]]]` | List of integers with the index of the target for binary classification or tuples with two elements: the index of the targets or binary classification and the positive weight for binary classification | `None`
`multiclass_config` | `Optional[List[Union[Tuple[int, int], Tuple[int, int, List[float]]]]]` | List of tuples with two or three elements: the index of the target and the number of classes for multiclass classification, or a tuple with the index of the target, the number of classes and a list of weights to apply to each class (i.e. the 'weight' parameter in the cross_entropy loss) | `None`
`weights` | `Optional[List[float]]` | List of weights to apply to the loss associated to each target. The length of the list must match the number of targets. Alias: 'target_weights' | `None`
`reduction` | `Literal[mean, sum]` | Specifies the reduction to apply to the loss associated to each target: 'mean' | 'sum'. Note that this is NOT the same as the reduction in the cross_entropy loss or the binary_cross_entropy_with_logits. This reduction is applied after the loss for each target has been computed. Alias: 'target_reduction' | `'mean'`
`binary_trick` | `bool` | If True, each target will be considered independently and the loss will be computed as binary_cross_entropy_with_logits. This is a faster implementation. Note that the 'weights' parameter is not compatible with binary_trick=True. Also note that if binary_trick=True, the 'binary_config' must be a list of integers and the 'multiclass_config' must be a list of tuples with two integers: the index of the target and the number of classes. Finally, if binary_trick=True, the binary targets must be the first targets in the target tensor. NOTE: When using the binary_trick, the binary targets are considered as 2 classes. Therefore, the pred_dim parametere of the WideDeep class should be adjusted accordingly (adding 2 to per binary target). For example, in a problem with a binary target and a 4 class multiclassification target, the pred_dim should be 6. | `False`

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses_multitarget import MultiTargetClassificationLoss
    >>> input = torch.randn(5, 4)
    >>> input_binary_trick = torch.randn(5, 5)
    >>> target = torch.stack([torch.tensor([0, 1, 0, 1, 1]), torch.tensor([0, 1, 2, 0, 2])], 1)
    >>> loss_1 = MultiTargetClassificationLoss(binary_config=[0], multiclass_config=[(1, 3)], reduction="mean")
    >>> output_1 = loss_1(input, target)
    >>> loss_2 = MultiTargetClassificationLoss(binary_config=[(0, 0.5)], multiclass_config=[(1, 3, [1., 2., 3.])],
    ... reduction="sum", weights=[0.5, 0.5])
    >>> output_2 = loss_2(input, target)
    >>> loss_3 = MultiTargetClassificationLoss(binary_config=[0], multiclass_config=[(1, 3)], binary_trick=True)
    >>> output_3 = loss_3(input_binary_trick, target)

Source code in `pytorch_widedeep/losses_multitarget.py`

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    class MultiTargetClassificationLoss(nn.Module):
        """
        This class is a wrapper around the Pytorch binary_cross_entropy_with_logits and
        cross_entropy losses. It allows for multi-target classification problems. The
        user can provide a list of weights to apply to each target. The loss can be
        either the sum or the mean of the individual losses

        Parameters
        ----------
        binary_config: Optional[List[int | Tuple[int, float]]], default = None
            List of integers with the index of the target for binary
            classification or tuples with two elements: the index of the targets
            or binary classification and the positive weight for binary
            classification
        multiclass_config: Optional[Tuple[int, int] | Tuple[int, int, List[float]]], default = None
            List of tuples with two or three elements: the index of the target and the
            number of classes for multiclass classification, or a tuple with the index of
            the target, the number of classes and a list of weights to apply to each class
            (i.e. the 'weight' parameter in the cross_entropy loss)
        weights: Optional[List[float], default = None]
            List of weights to apply to the loss associated to each target. The
            length of the list must match the number of targets.
            Alias: 'target_weights'
        reduction: Literal["mean", "sum"], default = "sum
            Specifies the reduction to apply to the loss associated to each
            target: 'mean' | 'sum'. Note that this is NOT the same as the
            reduction in the cross_entropy loss or the
            binary_cross_entropy_with_logits. This reduction is applied after the
            loss for each target has been computed. Alias: 'target_reduction'
        binary_trick: bool, default = False
            If True, each target will be considered independently and the loss
            will be computed as binary_cross_entropy_with_logits. This is a
            faster implementation. Note that the 'weights' parameter is not
            compatible with binary_trick=True. Also note that if
            binary_trick=True, the 'binary_config' must be a list of integers and
            the 'multiclass_config' must be a list of tuples with two integers:
            the index of the target and the number of classes. Finally, if
            binary_trick=True, the binary targets must be the first targets in
            the target tensor.

            :information_source: **NOTE**: When using the binary_trick, the binary targets are
              considered as 2 classes. Therefore, the pred_dim parametere of the
              WideDeep class should be adjusted accordingly (adding 2 to per
              binary target). For example, in a problem with a binary target and
              a 4 class multiclassification target, the pred_dim should be 6.

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses_multitarget import MultiTargetClassificationLoss
        >>> input = torch.randn(5, 4)
        >>> input_binary_trick = torch.randn(5, 5)
        >>> target = torch.stack([torch.tensor([0, 1, 0, 1, 1]), torch.tensor([0, 1, 2, 0, 2])], 1)
        >>> loss_1 = MultiTargetClassificationLoss(binary_config=[0], multiclass_config=[(1, 3)], reduction="mean")
        >>> output_1 = loss_1(input, target)
        >>> loss_2 = MultiTargetClassificationLoss(binary_config=[(0, 0.5)], multiclass_config=[(1, 3, [1., 2., 3.])],
        ... reduction="sum", weights=[0.5, 0.5])
        >>> output_2 = loss_2(input, target)
        >>> loss_3 = MultiTargetClassificationLoss(binary_config=[0], multiclass_config=[(1, 3)], binary_trick=True)
        >>> output_3 = loss_3(input_binary_trick, target)
        """

        @alias("reduction", ["target_reduction"])
        @alias("weights", ["target_weights"])
        def __init__(  # noqa: C901
            self,
            binary_config: Optional[List[Union[int, Tuple[int, float]]]] = None,
            multiclass_config: Optional[
                List[Union[Tuple[int, int], Tuple[int, int, List[float]]]]
            ] = None,
            weights: Optional[List[float]] = None,
            reduction: Literal["mean", "sum"] = "mean",
            binary_trick: bool = False,
        ):
            super(MultiTargetClassificationLoss, self).__init__()

            if reduction not in ["mean", "sum"]:
                raise ValueError("reduction must be either 'mean' or 'sum'")

            self.binary_config = binary_config
            self.multiclass_config = multiclass_config
            self.weights = weights
            self.reduction = reduction
            self.binary_trick = binary_trick

            if self.weights is not None:
                if len(self.weights) != (
                    len(self.binary_config) if self.binary_config is not None else 0
                ) + (
                    len(self.multiclass_config) if self.multiclass_config is not None else 0
                ):
                    raise ValueError(
                        "The number of weights must match the number of binary and multiclass targets"
                    )

            if self.binary_trick:
                self._check_inputs_with_binary_trick()
                self._binary_config: List[int] = binary_config  # type: ignore[assignment]
                self._multiclass_config: List[Tuple[int, int]] = self.multiclass_config  # type: ignore[assignment]
            else:
                self.binary_config_with_pos_weights = (
                    (self._set_binary_config_without_binary_trick())
                    if self.binary_config is not None
                    else None
                )
                self.multiclass_config_with_weights = (
                    (self._set_multiclass_config_without_binary_trick())
                    if self.multiclass_config is not None
                    else None
                )

        def forward(self, input: Tensor, target: Tensor) -> Tensor:
            if self.binary_trick:
                return self._forward_binary_trick(input, target)
            else:
                return self._forward_without_binary_trick(input, target)

        def _forward_binary_trick(self, input: Tensor, target: Tensor) -> Tensor:
            binary_target_tensors: List[Tensor] = []
            if self._binary_config:
                for idx in self._binary_config:
                    binary_target_tensors.append(
                        torch.eye(2)[target[:, idx].long()].to(input.device)
                    )
            if self._multiclass_config:
                for idx, n_classes in self._multiclass_config:
                    binary_target_tensors.append(
                        torch.eye(n_classes)[target[:, idx].long()].to(input.device)
                    )
            binary_target = torch.cat(binary_target_tensors, 1)
            return F.binary_cross_entropy_with_logits(input, binary_target)

        def _forward_without_binary_trick(self, input: Tensor, target: Tensor) -> Tensor:
            losses: List[Tensor] = []
            if self.binary_config_with_pos_weights:
                for idx, bpos_weight in self.binary_config_with_pos_weights:
                    _loss = F.binary_cross_entropy_with_logits(
                        input[:, idx],
                        target[:, idx].float(),
                        pos_weight=(
                            torch.tensor(bpos_weight).to(input.device)
                            if bpos_weight is not None
                            else None
                        ),
                    )
                    losses.append(_loss)
            if self.multiclass_config_with_weights:
                for idx, n_classes, mpos_weight in self.multiclass_config_with_weights:
                    _loss = F.cross_entropy(
                        input[:, idx : idx + n_classes],
                        target[:, idx].long(),
                        weight=(
                            torch.tensor(mpos_weight).to(input.device)
                            if mpos_weight is not None
                            else None
                        ),
                    )
                    losses.append(_loss)

                if self.weights is not None:
                    losses = [l * w for l, w in zip(losses, self.weights)]  # noqa: E741

            return (
                torch.stack(losses).sum()
                if self.reduction == "sum"
                else torch.stack(losses).mean()
            )

        def _check_inputs_with_binary_trick(self):
            if self.binary_config is not None:
                if any(isinstance(bc, tuple) for bc in self.binary_config):
                    raise ValueError(
                        "binary_trick=True is only compatible with binary_config as a list of integers"
                    )

            if self.multiclass_config is not None:
                if not all(len(mc) == 2 for mc in self.multiclass_config):
                    raise ValueError(
                        "binary_trick=True is only compatible with multiclass_config as a list of "
                        "tuples with two integers: the index of the target and the number of classes"
                    )

            if self.binary_config is not None and self.multiclass_config is not None:
                last_binary_idx = (
                    self.binary_config[-1][0]
                    if isinstance(self.binary_config[-1], tuple)
                    else self.binary_config[-1]
                )
                if last_binary_idx >= self.multiclass_config[0][0]:
                    raise ValueError(
                        "When using binary_trick=True, the binary targets must be the first targets"
                        " in the target tensor"
                    )

        def _set_binary_config_without_binary_trick(
            self,
        ) -> List[Tuple[int, Optional[float]]]:
            binary_config_with_pos_weights: List[Tuple[int, Optional[float]]] = []
            for bc in self.binary_config:
                if isinstance(bc, tuple):
                    binary_config_with_pos_weights.append(bc)
                else:
                    binary_config_with_pos_weights.append((bc, None))
            return binary_config_with_pos_weights

        def _set_multiclass_config_without_binary_trick(
            self,
        ) -> List[Tuple[int, int, Optional[List[float]]]]:
            multiclass_config_with_weights: List[Tuple[int, int, Optional[List[float]]]] = (
                []
            )
            for mc in self.multiclass_config:
                if len(mc) == 3:
                    multiclass_config_with_weights.append(mc)  # type: ignore[arg-type]
                else:
                    multiclass_config_with_weights.append((mc[0], mc[1], None))
            return multiclass_config_with_weights

## MutilTargetRegressionAndClassificationLoss

Bases: `Module`

This class is a wrapper around the MultiTargetRegressionLoss and the MultiTargetClassificationLoss. It allows for multi-target regression and classification problems. The user can provide a list of weights to apply to each target. The loss can be either the sum or the mean of the individual losses

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`regression_config` | `List[int]` | List of integers with the indices of the regression targets | `[]`
`binary_config` | `Optional[List[Union[int, Tuple[int, float]]]]` | List of integers with the index of the target for binary classification or tuples with two elements: the index of the targets or binary classification and the positive weight for binary classification | `None`
`multiclass_config` | `Optional[List[Union[Tuple[int, int], Tuple[int, int, List[float]]]]]` | List of tuples with two or three elements: the index of the target and the number of classes for multiclass classification, or a tuple with the index of the target, the number of classes and a list of weights to apply to each class (i.e. the 'weight' parameter in the cross_entropy loss) | `None`
`weights` | `Optional[List[float]]` | List of weights to apply to the loss associated to each target. The length of the list must match the number of targets. Alias: 'target_weights' | `None`
`reduction` | `Literal[mean, sum]` | Specifies the reduction to apply to the output: 'mean' | 'sum'. Note that this is NOT the same as the reduction in the cross_entropy loss, the binary_cross_entropy_with_logits or the MSELoss. This reduction is applied after each target has been computed. Alias: 'target_reduction' | `'mean'`
`binary_trick` | `bool` | If True, each target will be considered independently and the loss will be computed as binary_cross_entropy_with_logits. This is a faster implementation. Note that the 'weights' parameter is not compatible with binary_trick=True. Also note that if binary_trick=True, the 'binary_config' must be a list of integers and the 'multiclass_config' must be a list of tuples with two integers: the index of the target and the number of classes. Finally, if binary_trick=True, the binary targets must be the first targets in the target tensor. NOTE: When using the binary_trick, the binary targets are considered as 2 classes. Therefore, the pred_dim parametere of the WideDeep class should be adjusted accordingly (adding 2 to per binary target). For example, in a problem with a binary target and a 4 class multiclassification target, the pred_dim should be 6. | `False`

Examples:

    >>> import torch
    >>> from pytorch_widedeep.losses_multitarget import MutilTargetRegressionAndClassificationLoss
    >>> input = torch.randn(5, 5)
    >>> target = torch.stack([torch.randn(5), torch.tensor([0, 1, 0, 1, 1]), torch.tensor([0, 1, 2, 0, 2])], 1)
    >>> loss = MutilTargetRegressionAndClassificationLoss(regression_config=[0], binary_config=[2],
    ... multiclass_config=[(2, 3)], reduction="mean")
    >>> output = loss(input, target)

Source code in `pytorch_widedeep/losses_multitarget.py`

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    class MutilTargetRegressionAndClassificationLoss(nn.Module):
        """
        This class is a wrapper around the MultiTargetRegressionLoss and the
        MultiTargetClassificationLoss. It allows for multi-target regression and
        classification problems. The user can provide a list of weights to apply to
        each target. The loss can be either the sum or the mean of the individual losses

        Parameters
        ----------
        regression_config: List[int], default = []
            List of integers with the indices of the regression targets
        binary_config: Optional[List[int | Tuple[int, float]]], default = None
            List of integers with the index of the target for binary
            classification or tuples with two elements: the index of the targets
            or binary classification and the positive weight for binary
            classification
        multiclass_config: Optional[Tuple[int, int] | Tuple[int, int, List[float]]], default = None
            List of tuples with two or three elements: the index of the target and the
            number of classes for multiclass classification, or a tuple with the index of
            the target, the number of classes and a list of weights to apply to each class
            (i.e. the 'weight' parameter in the cross_entropy loss)
        weights: Optional[List[float], default = None]
            List of weights to apply to the loss associated to each target. The
            length of the list must match the number of targets.
            Alias: 'target_weights'
        reduction: Literal["mean", "sum"], default = "sum
            Specifies the reduction to apply to the output: 'mean' | 'sum'. Note
            that this is NOT the same as the reduction in the cross_entropy loss,
            the binary_cross_entropy_with_logits or the MSELoss. This reduction
            is applied after each target has been computed. Alias: 'target_reduction'
        binary_trick: bool, default = False
            If True, each target will be considered independently and the loss
            will be computed as binary_cross_entropy_with_logits. This is a
            faster implementation. Note that the 'weights' parameter is not
            compatible with binary_trick=True. Also note that if
            binary_trick=True, the 'binary_config' must be a list of integers and
            the 'multiclass_config' must be a list of tuples with two integers:
            the index of the target and the number of classes. Finally, if
            binary_trick=True, the binary targets must be the first targets in
            the target tensor.

            :information_source: **NOTE**: When using the binary_trick, the binary targets are
              considered as 2 classes. Therefore, the pred_dim parametere of the
              WideDeep class should be adjusted accordingly (adding 2 to per
              binary target). For example, in a problem with a binary target and
              a 4 class multiclassification target, the pred_dim should be 6.

        Examples
        --------
        >>> import torch
        >>> from pytorch_widedeep.losses_multitarget import MutilTargetRegressionAndClassificationLoss
        >>> input = torch.randn(5, 5)
        >>> target = torch.stack([torch.randn(5), torch.tensor([0, 1, 0, 1, 1]), torch.tensor([0, 1, 2, 0, 2])], 1)
        >>> loss = MutilTargetRegressionAndClassificationLoss(regression_config=[0], binary_config=[2],
        ... multiclass_config=[(2, 3)], reduction="mean")
        >>> output = loss(input, target)
        """

        @alias("reduction", ["target_reduction"])
        @alias("weights", ["target_weights"])
        def __init__(  # noqa: C901
            self,
            regression_config: List[int] = [],
            binary_config: Optional[List[Union[int, Tuple[int, float]]]] = None,
            multiclass_config: Optional[
                List[Union[Tuple[int, int], Tuple[int, int, List[float]]]]
            ] = None,
            weights: Optional[List[float]] = None,
            reduction: Literal["mean", "sum"] = "mean",
            binary_trick: bool = False,
        ):

            super(MutilTargetRegressionAndClassificationLoss, self).__init__()

            self.regression_config = regression_config

            assert binary_config is not None or multiclass_config is not None, (
                "Either binary_config or multiclass_config must be provided. "
                "Otherwise, use the MultiTargetRegressionLoss"
            )

            if binary_trick:
                self._check_inputs_with_binary_trick(
                    regression_config, binary_config, multiclass_config
                )

            if weights is not None:
                if len(weights) != (
                    len(regression_config)
                    + (len(binary_config) if binary_config is not None else 0)
                    + (len(multiclass_config) if multiclass_config is not None else 0)
                ):
                    raise ValueError(
                        "The number of weights must match the number of regression, binary and multiclass targets"
                    )

                self.weights_regression = self._prepare_weights_for_regression_targets(
                    weights, regression_config
                )
                self.weights_binary = self._prepare_weights_per_binary_targets(
                    weights, binary_config
                )
                self.weights_multiclass = self._prepare_weights_per_multiclass_targets(
                    weights, multiclass_config
                )
                self.weights = weights
            else:
                self.weights_regression = None
                self.weights_binary = None
                self.weights_multiclass = None

            self.multi_target_regression_loss = MultiTargetRegressionLoss(
                weights=self.weights_regression, reduction=reduction
            )

            self.multi_target_classification_loss = MultiTargetClassificationLoss(
                binary_config=binary_config,
                multiclass_config=multiclass_config,
                weights=(
                    self.weights_binary + self.weights_multiclass
                    if self.weights_binary is not None
                    and self.weights_multiclass is not None
                    else (
                        self.weights_binary
                        if self.weights_binary is not None
                        else self.weights_multiclass
                    )
                ),
                reduction=reduction,
                binary_trick=binary_trick,
            )

        def forward(self, input: Tensor, target: Tensor) -> Tensor:

            regression_loss = self.multi_target_regression_loss(
                input[:, self.regression_config],
                target[:, self.regression_config],
            )

            if self.multi_target_classification_loss.binary_trick:
                classification_loss = self.multi_target_classification_loss(
                    input[:, len(self.regression_config) :], target
                )
            else:
                classification_loss = self.multi_target_classification_loss(input, target)

            return regression_loss + classification_loss

        def _check_inputs_with_binary_trick(
            self,
            regression_config: List[int],
            binary_config: Optional[List[Union[int, Tuple[int, float]]]],
            multiclass_config: Optional[
                List[Union[Tuple[int, int], Tuple[int, int, List[float]]]]
            ],
        ) -> None:

            error_msg = "When using binary_trick=True, the targets order must be: regression, binary and multiclass"

            first_regression_idx = regression_config[0]
            last_regression_idx = regression_config[-1]
            if first_regression_idx != 0:
                raise ValueError(error_msg)

            if binary_config is not None and multiclass_config is not None:
                first_binary_idx = (
                    binary_config[0][0]
                    if isinstance(binary_config[0], tuple)
                    else binary_config[0]
                )
                last_binary_idx = (
                    binary_config[-1][0]
                    if isinstance(binary_config[-1], tuple)
                    else binary_config[-1]
                )
                first_multiclass_idx = multiclass_config[0][0]

                if (first_binary_idx != last_regression_idx + 1) or (
                    last_binary_idx >= first_multiclass_idx
                ):
                    raise ValueError(error_msg)
            elif binary_config is not None:
                first_binary_idx = (
                    binary_config[0][0]
                    if isinstance(binary_config[0], tuple)
                    else binary_config[0]
                )
                if first_binary_idx != last_regression_idx + 1:
                    raise ValueError(error_msg)
            elif multiclass_config is not None:
                first_multiclass_idx = multiclass_config[0][0]
                if first_multiclass_idx != last_regression_idx + 1:
                    raise ValueError(error_msg)
            else:
                raise ValueError(
                    "Either binary_config or multiclass_config must be provided. "
                    "Otherwise, use the MultiTargetRegressionLoss"
                )

        def _prepare_weights_for_regression_targets(
            self,
            weights: List[float],
            regression_config: List[int],
        ) -> List[float]:

            weights_regression = [
                w for idx, w in enumerate(weights) if idx in regression_config
            ]

            return weights_regression

        def _prepare_weights_per_binary_targets(
            self,
            weights: List[float],
            binary_config: Optional[List[Union[int, Tuple[int, float]]]],
        ) -> Optional[List[float]]:

            if binary_config is not None:
                binary_idx: List[int] = []
                for bc in binary_config:
                    if isinstance(bc, tuple):
                        binary_idx.append(bc[0])
                    else:
                        binary_idx.append(bc)
                weights_binary = [w for idx, w in enumerate(weights) if idx in binary_idx]
            else:
                weights_binary = None

            return weights_binary

        def _prepare_weights_per_multiclass_targets(
            self,
            weights: List[float],
            multiclass_config: Optional[
                List[Union[Tuple[int, int], Tuple[int, int, List[float]]]]
            ],
        ) -> Optional[List[float]]:

            if multiclass_config is not None:
                multiclass_idx: List[int] = [mc[0] for mc in multiclass_config]
                weights_multiclass = [
                    w for idx, w in enumerate(weights) if idx in multiclass_idx
                ]
            else:
                weights_multiclass = None

            return weights_multiclass