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# Metrics

NOTE: metrics 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

We have added the possibility of using the metrics available at the torchmetrics library. Note that this library is still in its early versions and therefore this option should be used with caution. To use `torchmetrics` simply import them and use them as any of the `pytorch-widedeep` metrics described below.

    from torchmetrics import Accuracy, Precision

    accuracy = Accuracy(average=None, num_classes=2)
    precision = Precision(average='micro', num_classes=2)

    trainer = Trainer(model, objective="binary", metrics=[accuracy, precision])

A functioning example for `pytorch-widedeep` using `torchmetrics` can be found in the Examples folder

NOTE: the forward method for all metrics in this module takes two tensors, `y_pred` and `y_true` (in that order). Therefore, we do not include the method in the documentation.

## Accuracy

Bases: `Metric`

Class to calculate the accuracy for both binary and categorical problems

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`top_k` | `int` | Accuracy will be computed using the top k most likely classes in multiclass problems | `1`

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.metrics import Accuracy
    >>>
    >>> acc = Accuracy()
    >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
    >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
    >>> acc(y_pred, y_true)
    array(0.5)
    >>>
    >>> acc = Accuracy(top_k=2)
    >>> y_true = torch.tensor([0, 1, 2])
    >>> y_pred = torch.tensor([[0.3, 0.5, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
    >>> acc(y_pred, y_true)
    array(0.66666667)

Source code in `pytorch_widedeep/metrics.py`

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    class Accuracy(Metric):
        r"""Class to calculate the accuracy for both binary and categorical problems

        Parameters
        ----------
        top_k: int, default = 1
            Accuracy will be computed using the top k most likely classes in
            multiclass problems

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.metrics import Accuracy
        >>>
        >>> acc = Accuracy()
        >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
        >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
        >>> acc(y_pred, y_true)
        array(0.5)
        >>>
        >>> acc = Accuracy(top_k=2)
        >>> y_true = torch.tensor([0, 1, 2])
        >>> y_pred = torch.tensor([[0.3, 0.5, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
        >>> acc(y_pred, y_true)
        array(0.66666667)
        """

        def __init__(self, top_k: int = 1):
            super(Accuracy, self).__init__()

            self.top_k = top_k
            self.correct_count = 0
            self.total_count = 0
            self._name = "acc"

        def reset(self):
            """
            resets counters to 0
            """
            self.correct_count = 0
            self.total_count = 0

        def __call__(self, y_pred: Tensor, y_true: Tensor) -> np.ndarray:
            num_classes = y_pred.size(1)

            if num_classes == 1:
                y_pred = y_pred.round()
                y_true = y_true
            elif num_classes > 1:
                y_pred = y_pred.topk(self.top_k, 1)[1]
                y_true = y_true.view(-1, 1).expand_as(y_pred)

            self.correct_count += y_pred.eq(y_true).sum().item()  # type: ignore[assignment]
            self.total_count += len(y_pred)
            accuracy = float(self.correct_count) / float(self.total_count)
            return np.array(accuracy)

### reset

    reset()

resets counters to 0

Source code in `pytorch_widedeep/metrics.py`

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    def reset(self):
        """
        resets counters to 0
        """
        self.correct_count = 0
        self.total_count = 0

## Precision

Bases: `Metric`

Class to calculate the precision for both binary and categorical problems

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`average` | `bool` | This applies only to multiclass problems. if `True` calculate precision for each label, and finds their unweighted mean. | `True`

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.metrics import Precision
    >>>
    >>> prec = Precision()
    >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
    >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
    >>> prec(y_pred, y_true)
    array(0.5)
    >>>
    >>> prec = Precision(average=True)
    >>> y_true = torch.tensor([0, 1, 2])
    >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
    >>> prec(y_pred, y_true)
    array(0.33333334)

Source code in `pytorch_widedeep/metrics.py`

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    class Precision(Metric):
        r"""Class to calculate the precision for both binary and categorical problems

        Parameters
        ----------
        average: bool, default = True
            This applies only to multiclass problems. if ``True`` calculate
            precision for each label, and finds their unweighted mean.

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.metrics import Precision
        >>>
        >>> prec = Precision()
        >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
        >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
        >>> prec(y_pred, y_true)
        array(0.5)
        >>>
        >>> prec = Precision(average=True)
        >>> y_true = torch.tensor([0, 1, 2])
        >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
        >>> prec(y_pred, y_true)
        array(0.33333334)
        """

        def __init__(self, average: bool = True):
            super(Precision, self).__init__()

            self.average = average
            self.true_positives = 0
            self.all_positives = 0
            self.eps = 1e-20
            self._name = "prec"

        def reset(self):
            """
            resets counters to 0
            """
            self.true_positives = 0
            self.all_positives = 0

        def __call__(self, y_pred: Tensor, y_true: Tensor) -> np.ndarray:
            num_class = y_pred.size(1)

            if num_class == 1:
                y_pred = y_pred.round()
                y_true = y_true
            elif num_class > 1:
                y_true = torch.eye(num_class)[y_true.squeeze().cpu().long()]
                y_pred = y_pred.topk(1, 1)[1].view(-1)
                y_pred = torch.eye(num_class)[y_pred.cpu().long()]

            self.true_positives += (y_true * y_pred).sum(dim=0)  # type:ignore
            self.all_positives += y_pred.sum(dim=0)  # type:ignore

            precision = self.true_positives / (self.all_positives + self.eps)

            if self.average:
                return np.array(precision.mean().item())  # type:ignore
            else:
                return precision.detach().cpu().numpy()  # type: ignore[attr-defined]

### reset

    reset()

resets counters to 0

Source code in `pytorch_widedeep/metrics.py`

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    def reset(self):
        """
        resets counters to 0
        """
        self.true_positives = 0
        self.all_positives = 0

## Recall

Bases: `Metric`

Class to calculate the recall for both binary and categorical problems

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`average` | `bool` | This applies only to multiclass problems. if `True` calculate recall for each label, and finds their unweighted mean. | `True`

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.metrics import Recall
    >>>
    >>> rec = Recall()
    >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
    >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
    >>> rec(y_pred, y_true)
    array(0.5)
    >>>
    >>> rec = Recall(average=True)
    >>> y_true = torch.tensor([0, 1, 2])
    >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
    >>> rec(y_pred, y_true)
    array(0.33333334)

Source code in `pytorch_widedeep/metrics.py`

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    class Recall(Metric):
        r"""Class to calculate the recall for both binary and categorical problems

        Parameters
        ----------
        average: bool, default = True
            This applies only to multiclass problems. if ``True`` calculate recall
            for each label, and finds their unweighted mean.

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.metrics import Recall
        >>>
        >>> rec = Recall()
        >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
        >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
        >>> rec(y_pred, y_true)
        array(0.5)
        >>>
        >>> rec = Recall(average=True)
        >>> y_true = torch.tensor([0, 1, 2])
        >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
        >>> rec(y_pred, y_true)
        array(0.33333334)
        """

        def __init__(self, average: bool = True):
            super(Recall, self).__init__()

            self.average = average
            self.true_positives = 0
            self.actual_positives = 0
            self.eps = 1e-20
            self._name = "rec"

        def reset(self):
            """
            resets counters to 0
            """
            self.true_positives = 0
            self.actual_positives = 0

        def __call__(self, y_pred: Tensor, y_true: Tensor) -> np.ndarray:
            num_class = y_pred.size(1)

            if num_class == 1:
                y_pred = y_pred.round()
                y_true = y_true
            elif num_class > 1:
                y_true = torch.eye(num_class)[y_true.squeeze().cpu().long()]
                y_pred = y_pred.topk(1, 1)[1].view(-1)
                y_pred = torch.eye(num_class)[y_pred.cpu().long()]

            self.true_positives += (y_true * y_pred).sum(dim=0)  # type: ignore
            self.actual_positives += y_true.sum(dim=0)  # type: ignore

            recall = self.true_positives / (self.actual_positives + self.eps)

            if self.average:
                return np.array(recall.mean().item())  # type:ignore
            else:
                return recall.detach().cpu().numpy()  # type: ignore[attr-defined]

### reset

    reset()

resets counters to 0

Source code in `pytorch_widedeep/metrics.py`

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    def reset(self):
        """
        resets counters to 0
        """
        self.true_positives = 0
        self.actual_positives = 0

## FBetaScore

Bases: `Metric`

Class to calculate the fbeta score for both binary and categorical problems

\[ F_{\beta} = ((1 + {\beta}^2) * \frac{(precision * recall)}{({\beta}^2 * precision + recall)} \]

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`beta` | `int` | Coefficient to control the balance between precision and recall | required
`average` | `bool` | This applies only to multiclass problems. if `True` calculate fbeta for each label, and find their unweighted mean. | `True`

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.metrics import FBetaScore
    >>>
    >>> fbeta = FBetaScore(beta=2)
    >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
    >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
    >>> fbeta(y_pred, y_true)
    array(0.5)
    >>>
    >>> fbeta = FBetaScore(beta=2)
    >>> y_true = torch.tensor([0, 1, 2])
    >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
    >>> fbeta(y_pred, y_true)
    array(0.33333334)

Source code in `pytorch_widedeep/metrics.py`

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    class FBetaScore(Metric):
        r"""Class to calculate the fbeta score for both binary and categorical problems

        $$
        F_{\beta} = ((1 + {\beta}^2) * \frac{(precision * recall)}{({\beta}^2 * precision + recall)}
        $$

        Parameters
        ----------
        beta: int
            Coefficient to control the balance between precision and recall
        average: bool, default = True
            This applies only to multiclass problems. if ``True`` calculate fbeta
            for each label, and find their unweighted mean.

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.metrics import FBetaScore
        >>>
        >>> fbeta = FBetaScore(beta=2)
        >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
        >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
        >>> fbeta(y_pred, y_true)
        array(0.5)
        >>>
        >>> fbeta = FBetaScore(beta=2)
        >>> y_true = torch.tensor([0, 1, 2])
        >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
        >>> fbeta(y_pred, y_true)
        array(0.33333334)
        """

        def __init__(self, beta: int, average: bool = True):
            super(FBetaScore, self).__init__()

            self.beta = beta
            self.average = average
            self.precision = Precision(average=False)
            self.recall = Recall(average=False)
            self.eps = 1e-20
            self._name = "".join(["f", str(self.beta)])

        def reset(self):
            """
            resets precision and recall
            """
            self.precision.reset()
            self.recall.reset()

        def __call__(self, y_pred: Tensor, y_true: Tensor) -> np.ndarray:
            prec = self.precision(y_pred, y_true)
            rec = self.recall(y_pred, y_true)
            beta2 = self.beta**2

            fbeta = ((1 + beta2) * prec * rec) / (beta2 * prec + rec + self.eps)

            if self.average:
                return np.array(fbeta.mean().item())  # type: ignore[attr-defined]
            else:
                return fbeta

### reset

    reset()

resets precision and recall

Source code in `pytorch_widedeep/metrics.py`

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    def reset(self):
        """
        resets precision and recall
        """
        self.precision.reset()
        self.recall.reset()

## F1Score

Bases: `Metric`

Class to calculate the f1 score for both binary and categorical problems

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`average` | `bool` | This applies only to multiclass problems. if `True` calculate f1 for each label, and find their unweighted mean. | `True`

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.metrics import F1Score
    >>>
    >>> f1 = F1Score()
    >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
    >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
    >>> f1(y_pred, y_true)
    array(0.5)
    >>>
    >>> f1 = F1Score()
    >>> y_true = torch.tensor([0, 1, 2])
    >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
    >>> f1(y_pred, y_true)
    array(0.33333334)

Source code in `pytorch_widedeep/metrics.py`

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    class F1Score(Metric):
        r"""Class to calculate the f1 score for both binary and categorical problems

        Parameters
        ----------
        average: bool, default = True
            This applies only to multiclass problems. if ``True`` calculate f1 for
            each label, and find their unweighted mean.

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.metrics import F1Score
        >>>
        >>> f1 = F1Score()
        >>> y_true = torch.tensor([0, 1, 0, 1]).view(-1, 1)
        >>> y_pred = torch.tensor([[0.3, 0.2, 0.6, 0.7]]).view(-1, 1)
        >>> f1(y_pred, y_true)
        array(0.5)
        >>>
        >>> f1 = F1Score()
        >>> y_true = torch.tensor([0, 1, 2])
        >>> y_pred = torch.tensor([[0.7, 0.1, 0.2], [0.1, 0.1, 0.8], [0.1, 0.5, 0.4]])
        >>> f1(y_pred, y_true)
        array(0.33333334)
        """

        def __init__(self, average: bool = True):
            super(F1Score, self).__init__()

            self.average = average
            self.f1 = FBetaScore(beta=1, average=self.average)
            self._name = self.f1._name

        def reset(self):
            """
            resets counters to 0
            """
            self.f1.reset()

        def __call__(self, y_pred: Tensor, y_true: Tensor) -> np.ndarray:
            return self.f1(y_pred, y_true)

### reset

    reset()

resets counters to 0

Source code in `pytorch_widedeep/metrics.py`

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    def reset(self):
        """
        resets counters to 0
        """
        self.f1.reset()

## R2Score

Bases: `Metric`

Calculates R-Squared, the coefficient of determination:

\[ R^2 = 1 - \frac{\sum_{j=1}^n(y_j - \hat{y_j})^2}{\sum_{j=1}^n(y_j - \bar{y})^2} \]

where \(\hat{y_j}\) is the ground truth, \(y_j\) is the predicted value and \(\bar{y}\) is the mean of the ground truth.

Examples:

    >>> import torch
    >>>
    >>> from pytorch_widedeep.metrics import R2Score
    >>>
    >>> r2 = R2Score()
    >>> y_true = torch.tensor([3, -0.5, 2, 7]).view(-1, 1)
    >>> y_pred = torch.tensor([2.5, 0.0, 2, 8]).view(-1, 1)
    >>> r2(y_pred, y_true)
    array(0.94860814)

Source code in `pytorch_widedeep/metrics.py`

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    class R2Score(Metric):
        r"""
        Calculates R-Squared, the
        [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination>):

        $$
        R^2 = 1 - \frac{\sum_{j=1}^n(y_j - \hat{y_j})^2}{\sum_{j=1}^n(y_j - \bar{y})^2}
        $$

        where $\hat{y_j}$ is the ground truth, $y_j$ is the predicted value and
        $\bar{y}$ is the mean of the ground truth.

        Examples
        --------
        >>> import torch
        >>>
        >>> from pytorch_widedeep.metrics import R2Score
        >>>
        >>> r2 = R2Score()
        >>> y_true = torch.tensor([3, -0.5, 2, 7]).view(-1, 1)
        >>> y_pred = torch.tensor([2.5, 0.0, 2, 8]).view(-1, 1)
        >>> r2(y_pred, y_true)
        array(0.94860814)
        """

        def __init__(self):
            self.numerator = 0
            self.denominator = 0
            self.num_examples = 0
            self.y_true_sum = 0

            self._name = "r2"

        def reset(self):
            """
            resets counters to 0
            """
            self.numerator = 0
            self.denominator = 0
            self.num_examples = 0
            self.y_true_sum = 0

        def __call__(self, y_pred: Tensor, y_true: Tensor) -> np.ndarray:
            self.numerator += ((y_pred - y_true) ** 2).sum().item()

            self.num_examples += y_true.shape[0]
            self.y_true_sum += y_true.sum().item()
            y_true_avg = self.y_true_sum / self.num_examples
            self.denominator += ((y_true - y_true_avg) ** 2).sum().item()
            return np.array((1 - (self.numerator / self.denominator)))

### reset

    reset()

resets counters to 0

Source code in `pytorch_widedeep/metrics.py`

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    def reset(self):
        """
        resets counters to 0
        """
        self.numerator = 0
        self.denominator = 0
        self.num_examples = 0
        self.y_true_sum = 0