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# PoissonNLLLoss

class torch.nn.PoissonNLLLoss(log_input=True, full=False, size_average=None, eps=1e-08, reduce=None, reduction='mean')

  Negative log likelihood loss with Poisson distribution of target.

  The loss can be described as:

  target∼P o i s s o n(input)loss(input,target)=input−target∗log⁡(input)+log⁡(target!)\text{target} \sim \mathrm{Poisson}(\text{input}) \text{loss}(\text{input}, \text{target}) = \text{input} - \text{target} * \log(\text{input}) + \log(\text{target!})target∼Poisson(input)loss(input,target)=input−target∗log(input)+log(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.

  Parameters:

    - log_input (bool, optional) – if `True` the loss is computed as exp⁡(input)−target∗input\exp(\text{input}) - \text{target}*\text{input}exp(input)−target∗input, if `False` the loss is input−target∗log⁡(input+eps)\text{input} - \text{target}*\log(\text{input}+\text{eps})input−target∗log(input+eps).

    - full (bool, optional) –

      whether to compute full loss, i. e. to add the Stirling approximation term

      target∗log⁡(target)−target+0.5∗log⁡(2 π target).\text{target}*\log(\text{target}) - \text{target} + 0.5 * \log(2\pi\text{target}). target∗log(target)−target+0.5∗log(2 π target).

    - size_average (bool, optional) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when `reduce` is `False`. Default: `True`

    - eps (float, optional) – Small value to avoid evaluation of log⁡(0)\log(0)log(0) when `log_input = False`. Default: 1e-8

    - reduce (bool, optional) – Deprecated (see `reduction`). By default, the losses are averaged or summed over observations for each minibatch depending on `size_average`. When `reduce` is `False`, returns a loss per batch element instead and ignores `size_average`. Default: `True`

    - reduction (str, 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. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: `'mean'`

  Examples:

      >>> loss = nn.PoissonNLLLoss()
      >>> log_input = torch.randn(5, 2, requires_grad=True)
      >>> target = torch.randn(5, 2)
      >>> output = loss(log_input, target)
      >>> output.backward()

  Shape:

    - Input: (∗)(*)(∗), where ∗*∗ means any number of dimensions.

    - Target: (∗)(*)(∗), same shape as the input.

    - Output: scalar by default. If `reduction` is `'none'`, then (∗)(*)(∗), the same shape as the input.

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