Poisson loss function

1

I want to predict count data using a simple fully connected network. I could in principle frame it as a classification problem where each class corresponds to the event count, but I would like to do it properly using a Poisson loss function. Two quick questions:

  1. I can’t seem to find the implementation of this loss function, am I missing anything?
  2. I also cannot seem to find any examples of using pytorch to predict count data, any pointers?

Thank you.

2

This article provides the definition of the Poisson loss. You can calculate it using a few pytorch functions.

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3

Super simple question: since lambda > 0 [because of the log(lambda_hat)] how could I go about defining the loss function to guarantee proper lambdas? In principle implementing it with pytorch functions is straightforward:

def poissonLoss(predicted, observed):
    """Custom loss function for Poisson model."""
    loss=torch.mean(predicted-observed*torch.log(predicted))
    return loss

But I obviously need to force the output to be strictly positive otherwise I’ll get -inf and nans. What sort of correction for the last layer could I use? Like ReLU with a floor>0 of sorts?

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4

Lambda should be exp(theta * x).

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5

I think that Poisson loss function is not supported by default in PyTorch. You may try this:

BTW, I think that one should focus on loss functions that can manage learning rates self adaption instead of probabilities.

6

I’ve implemented the following poisson loss function using the first suggested link:

def poissonLoss(xbeta, y):
    """Custom loss function for Poisson model."""
    loss=torch.mean(torch.exp(xbeta)-y*xbeta)
    return loss

Training:

optimizer=torch.optim.SGD(net.parameters())
lossFn=poissonLoss

output_ = net(input_)
loss = lossFn(output_, target_)
net.zero_grad()
loss.backward()
optimizer.step()

Since I’m using pytorch internals, is this the right way to train/backprop/optimize? Not sure about this because my model is not learning.

Thanks,

7

You should use optimizer.zero_grad() instead of it.

https://pytorch.org/tutorials/beginner/pytorch_with_examples.html#pytorch-optim

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