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The Poisson loss is a loss function used for regression when modeling count data. The loss takes the form of:

Poisson loss

where ŷ is the predicted expected value.

Minimizing the Poisson loss is equivalent of maximizing the likelihood of the data under the assumption that the target comes from a Poisson distribution, conditioned on the input.

When to use Poisson loss function

Use the Poisson loss when you believe that the target value comes from a Poisson distribution and want to model the rate parameter conditioned on some input. Examples of this are the number of customers that will enter a store on a given day, the number of emails that will arrive within the next hour, or how many customers that will churn next week.

Further reading

Poisson regression (Wikipedia)

Poisson distribution (Wikipedia)