# Source code for pyro.contrib.gp.likelihoods.poisson

```# Copyright (c) 2017-2019 Uber Technologies, Inc.

import torch

import pyro
import pyro.distributions as dist
from pyro.contrib.gp.likelihoods.likelihood import Likelihood

[docs]class Poisson(Likelihood):
"""
Implementation of Poisson likelihood, which is used for count data.

Poisson likelihood uses the :class:`~pyro.distributions.Poisson`
distribution, so the output of ``response_function`` should be positive.
By default, we use :func:`torch.exp` as response function, corresponding
to a log-Gaussian Cox process.

:param callable response_function: A mapping to positive real numbers.
"""

def __init__(self, response_function=None):
super().__init__()
self.response_function = (
torch.exp if response_function is None else response_function
)

[docs]    def forward(self, f_loc, f_var, y=None):
r"""
Samples :math:`y` given :math:`f_{loc}`, :math:`f_{var}` according to

.. math:: f & \sim \mathbb{Normal}(f_{loc}, f_{var}),\\
y & \sim \mathbb{Poisson}(\exp(f)).

.. note:: The log likelihood is estimated using Monte Carlo with 1 sample of
:math:`f`.

:param torch.Tensor f_loc: Mean of latent function output.
:param torch.Tensor f_var: Variance of latent function output.
:param torch.Tensor y: Training output tensor.
:returns: a tensor sampled from likelihood
:rtype: torch.Tensor
"""
# calculates Monte Carlo estimate for E_q(f) [logp(y | f)]
f = dist.Normal(f_loc, f_var.sqrt())()
f_res = self.response_function(f)

y_dist = dist.Poisson(f_res)
if y is not None:
y_dist = y_dist.expand_by(y.shape[: -f_res.dim()]).to_event(y.dim())
return pyro.sample(self._pyro_get_fullname("y"), y_dist, obs=y)
```