GaussianNLLLoss#

classtorch.nn.modules.loss.GaussianNLLLoss(*,full=False,eps=1e-06,reduction='mean')[source]#

Gaussian negative log likelihood loss.

The targets are treated as samples from Gaussian distributions withexpectations and variances predicted by the neural network. For atarget tensor modelled as having Gaussian distribution with a tensorof expectationsinput and a tensor of positive variancesvar the loss is:

$$\text{loss}=\frac{1}{2}(\log \left(\text{max}(\text{var},\text{ eps})\right)+\frac{{(\text{input}-\text{target})}^2}{\text{max}(\text{var},\text{ eps})})+\text{const.}$$loss=21​(log(max(var, eps))+max(var, eps)(input−target)2​)+const.

whereeps is used for stability. By default, the constant term ofthe loss function is omitted unlessfull isTrue. Ifvar is not the samesize asinput (due to a homoscedastic assumption), it must either have a final dimensionof 1 or have one fewer dimension (with all other sizes being the same) for correct broadcasting.

Parameters

• full (bool,optional) – include the constant term in the losscalculation. Default:False.

• eps (float,optional) – value used to clampvar (see note below), forstability. Default: 1e-6.

• reduction (str,optional) – specifies the reduction to apply to theoutput:'none' |'mean' |'sum'.'none': no reductionwill be applied,'mean': the output is the average of all batchmember losses,'sum': the output is the sum of all batch memberlosses. Default:'mean'.

Shape:

• Input:$(N,\ast )$(N,∗) or$(\ast )$(∗) where$\ast$∗ means any number of additionaldimensions

• Target:$(N,\ast )$(N,∗) or$(\ast )$(∗), same shape as the input, or same shape as the inputbut with one dimension equal to 1 (to allow for broadcasting)

• Var:$(N,\ast )$(N,∗) or$(\ast )$(∗), same shape as the input, or same shape as the input butwith one dimension equal to 1, or same shape as the input but with one fewerdimension (to allow for broadcasting), or a scalar value

• Output: scalar ifreduction is'mean' (default) or'sum'. Ifreduction is'none', then$(N,\ast )$(N,∗), sameshape as the input

Examples

>>>loss=nn.GaussianNLLLoss()>>>input=torch.randn(5,2,requires_grad=True)>>>target=torch.randn(5,2)>>>var=torch.ones(5,2,requires_grad=True)# heteroscedastic>>>output=loss(input,target,var)>>>output.backward()

>>>loss=nn.GaussianNLLLoss()>>>input=torch.randn(5,2,requires_grad=True)>>>target=torch.randn(5,2)>>>var=torch.ones(5,1,requires_grad=True)# homoscedastic>>>output=loss(input,target,var)>>>output.backward()

Note

The clamping ofvar is ignored with respect to autograd, and so thegradients are unaffected by it.

Reference:

Nix, D. A. and Weigend, A. S., “Estimating the mean and variance of thetarget probability distribution”, Proceedings of 1994 IEEE InternationalConference on Neural Networks (ICNN’94), Orlando, FL, USA, 1994, pp. 55-60vol.1, doi: 10.1109/ICNN.1994.374138.

forward(input,target,var)[source]#

Runs the forward pass.

Return type

Tensor