def log_likelihood(self):
# evaluate the likelihood of the labelling (which is,
# conveniently, just the likelihood of the current mixture
# model)
# FIXME: This should really be cached for the last invocation
score = Counter()
for c_idx, cluster in self._cluster_to_datum.iteritems():
if not cluster: continue
# Evaluate the likelihood of each individual cluster
cluster_size = len(cluster)
# The mean of the data points belonging to this cluster
cluster_datum_mean = sum(cluster) / cluster_size
# p(c)
score += Gaussian.log_prob(cluster_datum_mean, self._prior_mean,
self._prior_precision)
# p(x|c)
score += sum(
Gaussian.log_prob(datum, cluster_datum_mean,
self._cluster_precision)
for datum in cluster)
# score => p(x, c)
# for the gaussian the dimensions are independent so we should
# just be able to combine them directly
return score.total_count()
class BLinear(nn.Module):
"""Bayesian Linear layer, default prior is Gaussian for weights and bias"""
def __init__(self, in_features, out_features):
super().__init__()
self.in_features = in_features
self.out_features = out_features
# Weight parameters
self.weight_mu = nn.Parameter(
torch.Tensor(out_features, in_features).uniform_(-0.2, 0.2))
self.weight_rho = nn.Parameter(
torch.Tensor(out_features, in_features).uniform_(1e-1, 2))
# variational posterior for the weights
self.weight = Gaussian(self.weight_mu, self.weight_rho)
# Bias parameters
self.bias_mu = nn.Parameter(
torch.Tensor(out_features).uniform_(-0.2, 0.2))
self.bias_rho = nn.Parameter(
torch.Tensor(out_features).uniform_(1e-1, 2))
# variational posterior for the bias
self.bias = Gaussian(self.bias_mu, self.bias_rho)
# Prior distributions
self.weight_prior = Gaussian(torch.Tensor([0.]), torch.Tensor([1.]))
self.bias_prior = Gaussian(torch.Tensor([0.]), torch.Tensor([1.]))
# initialize log_prior and log_posterior as 0
self.log_prior = 0
self.log_variational_posterior = 0
def forward(self, input, sample=False, calculate_log_probs=False):
# 1. Sample weights and bias from variational posterior
if self.training or sample:
weight = self.weight.sample()
bias = self.bias.sample()
else:
weight = self.weight.mu
bias = self.bias.mu
# 2. Update log_prior and log_posterior according to current approximation
if self.training or calculate_log_probs:
self.log_prior = self.weight_prior.log_prob(
weight) + self.bias_prior.log_prob(bias)
self.log_variational_posterior = self.weight.log_prob(
weight) + self.bias.log_prob(bias)
else:
self.log_prior, self.log_variational_posterior = 0, 0
# 3. Do a forward pass through the layer
return F.linear(input, weight, bias)
def elbo(self, input, target, samples=20):
outputs = []
log_priors = torch.zeros(samples)
log_variational_posteriors = torch.zeros(samples)
# draw n_samples from the posterior (run n_samples forward passes)
for i in range(samples):
outputs.append(self(input, sample=True))
log_priors[i] = self.log_prior()
log_variational_posteriors[i] = self.log_variational_posterior()
log_prior = log_priors.sum()
log_variational_posterior = log_variational_posteriors.sum()
outputs = torch.stack(outputs)
y_dist = Gaussian(outputs.mean(0), self.noise)
# negative_log_likelihood = self.loss_function(
# outputs.mean(0), target, reduction='sum')
negative_log_likelihood = -y_dist.log_prob(target) / len(input)
# loss = nll + kl
loss = negative_log_likelihood
kl = (log_variational_posterior - log_prior) / self.n_training
loss += kl
return loss, log_prior, log_variational_posterior, negative_log_likelihood
def _cluster_log_probs(self, cluster, cluster_size, cluster_mean, cluster_covariance, new_point): """ Return the posterior, prior, and likelihood of new_point being in the cluster of size cluster_size centered at cluster_mean """ # the updated mean new_mean = (cluster_mean * cluster_size + new_point) / (cluster_size + 1) posterior_precision = self._prior_precision + self._cluster_precision # convex combination for mean posterior_mean = self._prior_mean * self._prior_precision posterior_mean += cluster_mean * self._cluster_precision posterior_mean /= posterior_precision posterior = Gaussian.log_prob(new_mean, posterior_mean, posterior_precision) # prior is keyed on the (potentially) updated params prior = Gaussian.log_prob(new_mean, self._prior_mean, self._prior_precision) likelihood = Gaussian.log_prob(new_point, new_mean, self._cluster_precision) return posterior, prior, likelihood
def _cluster_log_probs(self, cluster, cluster_size, cluster_mean,
cluster_covariance, new_point):
""" Return the posterior, prior, and likelihood of new_point
being in the cluster of size cluster_size centered at cluster_mean
"""
# the updated mean
new_mean = (cluster_mean * cluster_size + new_point) / (cluster_size +
1)
posterior_precision = self._prior_precision + self._cluster_precision
# convex combination for mean
posterior_mean = self._prior_mean * self._prior_precision
posterior_mean += cluster_mean * self._cluster_precision
posterior_mean /= posterior_precision
posterior = Gaussian.log_prob(new_mean, posterior_mean,
posterior_precision)
# prior is keyed on the (potentially) updated params
prior = Gaussian.log_prob(new_mean, self._prior_mean,
self._prior_precision)
likelihood = Gaussian.log_prob(new_point, new_mean,
self._cluster_precision)
return posterior, prior, likelihood
def log_likelihood(self): # evaluate the likelihood of the labelling (which is, # conveniently, just the likelihood of the current mixture # model) # FIXME: This should really be cached for the last invocation score = Counter() for c_idx, cluster in self._cluster_to_datum.iteritems(): if not cluster: continue # Evaluate the likelihood of each individual cluster cluster_size = len(cluster) # The mean of the data points belonging to this cluster cluster_datum_mean = sum(cluster) / cluster_size # p(c) score += Gaussian.log_prob(cluster_datum_mean, self._prior_mean, self._prior_precision) # p(x|c) score += sum(Gaussian.log_prob(datum, cluster_datum_mean, self._cluster_precision) for datum in cluster) # score => p(x, c) # for the gaussian the dimensions are independent so we should # just be able to combine them directly return score.total_count()
