gaurav-gireesh commented on a change in pull request #12697: [MXNET -1004]
Poisson NegativeLog Likelihood loss
URL: https://github.com/apache/incubator-mxnet/pull/12697#discussion_r223801145
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File path: python/mxnet/gluon/loss.py
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@@ -706,3 +707,65 @@ def hybrid_forward(self, F, pred, positive, negative):
axis=self._batch_axis, exclude=True)
loss = F.relu(loss + self._margin)
return _apply_weighting(F, loss, self._weight, None)
+
+
+class PoissonNLLLoss(Loss):
+ r"""For a target (Random Variable) in a Poisson distribution, the function
calculates the Negative
+ Log likelihood loss.
+ PoissonNLLLoss measures the loss accrued from a poisson regression
prediction made by the model.
+
+ .. math::
+ L = \text{pred} - \text{target} * \log(\text{pred})
+\log(\text{target!})
Review comment:
@anirudhacharya The "!" is for factorial of the target value. The formula to
calculate the probability of the target value with the mean of the poisson
distribution contains a factorial term in the denominator which is approximated
by computing the Stirling approximation. Taking a log of the formula reduces to
the form mentioned in the documentation.
Some wikipedia pages that I have found helpful are:
[Poisson regression](https://en.wikipedia.org/wiki/Poisson_regression) and
[Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution).
Also, I have attached a link for reference to PyTorch's implementation of
the loss function in the description of the PR.
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