Implementation:Sktime Pytorch forecasting NormalDistributionLoss

Knowledge Sources	pytorch-forecasting PyTorch Forecasting Docs
Domains	Time_Series, Loss_Functions, Probabilistic_Forecasting
Last Updated	2026-02-08 07:00 GMT

Overview

Concrete tool for computing Normal distribution negative log-likelihood loss for probabilistic forecasting provided by the pytorch-forecasting library.

Description

The NormalDistributionLoss class extends DistributionLoss to model targets as Gaussian-distributed. It uses PyTorch's torch.distributions.Normal as the underlying distribution. The model predicts two parameters per time step: loc (mean) and scale (standard deviation, enforced positive via softplus). The rescale_parameters method applies target normalization parameters (center, scale from GroupNormalizer) as an affine transformation. The map_x_to_distribution method constructs the full TransformedDistribution with optional inverse transformations (log, logit, etc.) from the normalizer.

Usage

Use as the default loss for DeepAR models. It is automatically set when no loss is specified in DeepAR.from_dataset(). Requires the target to be continuous and the normalizer to be a GroupNormalizer or TorchNormalizer (not NaNLabelEncoder).

Code Reference

Source Location

Repository: pytorch-forecasting
File: pytorch_forecasting/metrics/distributions.py
Lines: L18-58

Signature

class NormalDistributionLoss(DistributionLoss):
    """Normal distribution loss."""

    distribution_class = distributions.Normal
    distribution_arguments = ["loc", "scale"]

    def map_x_to_distribution(
        self, x: torch.Tensor
    ) -> distributions.TransformedDistribution:
        """Map network output to Normal distribution with affine rescaling."""

    def rescale_parameters(
        self,
        parameters: torch.Tensor,
        target_scale: torch.Tensor,
        encoder: BaseEstimator,
    ) -> torch.Tensor:
        """Apply softplus to scale and prepend target normalization params."""

Import

from pytorch_forecasting.metrics import NormalDistributionLoss

I/O Contract

Inputs

Name	Type	Required	Description
(constructor)	—	—	No required arguments; inherits from DistributionLoss
parameters	torch.Tensor	Yes (to rescale)	Raw model output (batch, horizon, 2) — loc and scale
target_scale	torch.Tensor	Yes (to rescale)	Normalization center and scale from GroupNormalizer

Outputs

Name	Type	Description
loss()	torch.Tensor	Negative log-likelihood per sample
map_x_to_distribution()	TransformedDistribution	Full Normal distribution with rescaling transforms

Usage Examples

DeepAR with Normal Loss

from pytorch_forecasting import DeepAR
from pytorch_forecasting.metrics import NormalDistributionLoss

model = DeepAR.from_dataset(
    training,
    loss=NormalDistributionLoss(),
    learning_rate=0.1,
    hidden_size=32,
)

Related Pages

Implements Principle

Principle:Sktime_Pytorch_forecasting_Distribution_Loss

Requires Environment

Uses Heuristic

Heuristic:Sktime_Pytorch_forecasting_Target_Normalization_Transforms

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Principle

Implementation

Heuristic

Environment