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

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

import torch.nn.functional as F

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

def _softmax(x):
return F.softmax(x, dim=-1)

[docs]class MultiClass(Likelihood):
"""
Implementation of MultiClass likelihood, which is used for multi-class
classification problems.

MultiClass likelihood uses :class:`~pyro.distributions.Categorical`
distribution, so ``response_function`` should normalize its input's rightmost axis.
By default, we use `softmax` function.

:param int num_classes: Number of classes for prediction.
:param callable response_function: A mapping to correct domain for MultiClass
likelihood.
"""

def __init__(self, num_classes, response_function=None):
super().__init__()
self.num_classes = num_classes
self.response_function = (
_softmax 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{Categorical}(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())()
if f.dim() < 2:
raise ValueError(
"Latent function output should have at least 2 "
"dimensions: one for number of classes and one for "
"number of data."
)

# swap class dimension and data dimension
f_swap = f.transpose(-2, -1)  # -> num_data x num_classes
if f_swap.size(-1) != self.num_classes:
raise ValueError(
"Number of Gaussian processes should be equal to the "
"number of classes. Expected {} but got {}.".format(
self.num_classes, f_swap.size(-1)
)
)
if self.response_function is _softmax:
y_dist = dist.Categorical(logits=f_swap)
else:
f_res = self.response_function(f_swap)
y_dist = dist.Categorical(f_res)
if y is not None:
y_dist = y_dist.expand_by(y.shape[: -f.dim() + 1]).to_event(y.dim())
return pyro.sample(self._pyro_get_fullname("y"), y_dist, obs=y)
```