# Tweedie Deviance Score¶

## Module Interface¶

class torchmetrics.TweedieDevianceScore(power=0.0, **kwargs)[source]

Compute the Tweedie Deviance Score.

$\begin{split}deviance\_score(\hat{y},y) = \begin{cases} (\hat{y} - y)^2, & \text{for }p=0\\ 2 * (y * log(\frac{y}{\hat{y}}) + \hat{y} - y), & \text{for }p=1\\ 2 * (log(\frac{\hat{y}}{y}) + \frac{y}{\hat{y}} - 1), & \text{for }p=2\\ 2 * (\frac{(max(y,0))^{2 - p}}{(1 - p)(2 - p)} - \frac{y(\hat{y})^{1 - p}}{1 - p} + \frac{( \hat{y})^{2 - p}}{2 - p}), & \text{otherwise} \end{cases}\end{split}$

where $$y$$ is a tensor of targets values, $$\hat{y}$$ is a tensor of predictions, and $$p$$ is the power.

As input to forward and update the metric accepts the following input:

• preds (Tensor): Predicted float tensor with shape (N,...)

• target (Tensor): Ground truth float tensor with shape (N,...)

As output of forward and compute the metric returns the following output:

Parameters:
• power (float) –

• power < 0 : Extreme stable distribution. (Requires: preds > 0.)

• power = 0 : Normal distribution. (Requires: targets and preds can be any real numbers.)

• power = 1 : Poisson distribution. (Requires: targets >= 0 and y_pred > 0.)

• 1 < p < 2 : Compound Poisson distribution. (Requires: targets >= 0 and preds > 0.)

• power = 2 : Gamma distribution. (Requires: targets > 0 and preds > 0.)

• power = 3 : Inverse Gaussian distribution. (Requires: targets > 0 and preds > 0.)

• otherwise : Positive stable distribution. (Requires: targets > 0 and preds > 0.)

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Example

>>> from torchmetrics.regression import TweedieDevianceScore
>>> targets = torch.tensor([1.0, 2.0, 3.0, 4.0])
>>> preds = torch.tensor([4.0, 3.0, 2.0, 1.0])
>>> deviance_score = TweedieDevianceScore(power=2)
>>> deviance_score(preds, targets)
tensor(1.2083)

plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import TweedieDevianceScore
>>> metric = TweedieDevianceScore()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()

>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import TweedieDevianceScore
>>> metric = TweedieDevianceScore()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)


## Functional Interface¶

torchmetrics.functional.tweedie_deviance_score(preds, targets, power=0.0)[source]

Compute the Tweedie Deviance Score.

$\begin{split}deviance\_score(\hat{y},y) = \begin{cases} (\hat{y} - y)^2, & \text{for }p=0\\ 2 * (y * log(\frac{y}{\hat{y}}) + \hat{y} - y), & \text{for }p=1\\ 2 * (log(\frac{\hat{y}}{y}) + \frac{y}{\hat{y}} - 1), & \text{for }p=2\\ 2 * (\frac{(max(y,0))^{2 - p}}{(1 - p)(2 - p)} - \frac{y(\hat{y})^{1 - p}}{1 - p} + \frac{( \hat{y})^{2 - p}}{2 - p}), & \text{otherwise} \end{cases}\end{split}$

where $$y$$ is a tensor of targets values, $$\hat{y}$$ is a tensor of predictions, and $$p$$ is the power.

Parameters:
• preds (Tensor) – Predicted tensor with shape (N,...)

• targets (Tensor) – Ground truth tensor with shape (N,...)

• power (float) –

• power < 0 : Extreme stable distribution. (Requires: preds > 0.)

• power = 0 : Normal distribution. (Requires: targets and preds can be any real numbers.)

• power = 1 : Poisson distribution. (Requires: targets >= 0 and y_pred > 0.)

• 1 < p < 2 : Compound Poisson distribution. (Requires: targets >= 0 and preds > 0.)

• power = 2 : Gamma distribution. (Requires: targets > 0 and preds > 0.)

• power = 3 : Inverse Gaussian distribution. (Requires: targets > 0 and preds > 0.)

• otherwise : Positive stable distribution. (Requires: targets > 0 and preds > 0.)

Return type:

Tensor

Example

>>> from torchmetrics.functional.regression import tweedie_deviance_score
>>> targets = torch.tensor([1.0, 2.0, 3.0, 4.0])
>>> preds = torch.tensor([4.0, 3.0, 2.0, 1.0])
>>> tweedie_deviance_score(preds, targets, power=2)
tensor(1.2083)