Negative log likelihood loss with Poisson distribution of target. The loss can be described as:

## Usage

nn_poisson_nll_loss(
log_input = TRUE,
full = FALSE,
eps = 1e-08,
reduction = "mean"
)

## Arguments

log_input

(bool, optional): if TRUE the loss is computed as $$\exp(\mbox{input}) - \mbox{target}*\mbox{input}$$, if FALSE the loss is $$\mbox{input} - \mbox{target}*\log(\mbox{input}+\mbox{eps})$$.

full

(bool, optional): whether to compute full loss, i. e. to add the Stirling approximation term $$\mbox{target}*\log(\mbox{target}) - \mbox{target} + 0.5 * \log(2\pi\mbox{target})$$.

eps

(float, optional): Small value to avoid evaluation of $$\log(0)$$ when log_input = FALSE. Default: 1e-8

reduction

(string, optional): Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed.

## Details

$$\mbox{target} \sim \mathrm{Poisson}(\mbox{input}) \mbox{loss}(\mbox{input}, \mbox{target}) = \mbox{input} - \mbox{target} * \log(\mbox{input}) + \log(\mbox{target!})$$

The last term can be omitted or approximated with Stirling formula. The approximation is used for target values more than 1. For targets less or equal to 1 zeros are added to the loss.

## Shape

• Input: $$(N, *)$$ where $$*$$ means, any number of additional dimensions

• Target: $$(N, *)$$, same shape as the input

• Output: scalar by default. If reduction is 'none', then $$(N, *)$$, the same shape as the input

## Examples

if (torch_is_installed()) {
loss <- nn_poisson_nll_loss()
log_input <- torch_randn(5, 2, requires_grad = TRUE)
target <- torch_randn(5, 2)
output <- loss(log_input, target)
output\$backward()
}