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bayesian_nonparametric.py
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bayesian_nonparametric.py
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import torch
from torch.distributions import Normal, Dirichlet, Gamma, Categorical
class BayesianDistribution(torch.nn.Module):
EPS = 1e-18
def __init__(self):
super(BayesianDistribution, self).__init__()
self.emission_distr = None
def initialise_parameters(self):
raise NotImplementedError('Must be implented in subclasses')
def update_counts(self, data):
raise NotImplementedError('Must be implented in subclasses')
def update_parameters(self):
raise NotImplementedError('Must be implented in subclasses')
def get_data_log_likelihood(self, y_labels):
raise NotImplementedError('Must be implented in subclasses')
def __str__(self):
return str(self.emission_distr)
class BNPCategorical(BayesianDistribution):
def __init__(self, dim_target, alpha):
"""
:param dim_target: dimension of output alphabet
:param theta: the categorical emission distribution associated with a state
"""
super().__init__()
self.K = dim_target # discrete output labels
self.counts = torch.zeros(self.K)
self.alpha = torch.ones(self.K) * alpha
self.initialise_parameters()
def _flatten_labels(self, labels):
labels = torch.squeeze(labels)
if len(labels.shape) > 1:
# Compute discrete categories from one_hot_input
labels_squeezed = labels.argmax(dim=1)
return labels_squeezed
return labels.long()
def to(self, device):
super().to(device)
self.device = device
self.counts.to(device)
def initialise_parameters(self):
d_prior = Dirichlet(self.alpha)
self.emission_distr = Categorical(d_prior.sample())
def update_counts(self, xu):
self.counts[xu.argmax()] += 1
def update_parameters(self):
d_posterior = Dirichlet(self.counts + self.alpha)
self.emission_distr = Categorical(d_posterior.sample())
torch.zero_(self.counts)
def get_data_log_likelihood(self, y_labels):
y_labels_squeezed = self._flatten_labels(y_labels)
# Returns the emission probability associated to each observable
emission_obs_log = self.emission_distr.log_prob(y_labels_squeezed)
return emission_obs_log
class BNPCategoricalBatch(BayesianDistribution):
def __init__(self, dim_target, alpha):
"""
:param dim_target: dimension of output alphabet
:param theta: the value of the Dirichle prior
"""
super(BNPCategoricalBatch, self).__init__()
self.K = dim_target
self.counts = torch.zeros(self.K)
self.alpha = torch.ones(self.K) * alpha
self.device = None
self.initialise_parameters()
def to(self, device):
super().to(device)
self.device = device
self.counts.to(device)
def initialise_parameters(self):
d_prior = Dirichlet(self.alpha)
self.emission_distr = Categorical(d_prior.sample())
def update_counts(self, data):
# we assume one-hot labels
if len(data.shape) > 1:
self.counts += data.sum(0)
else:
self.counts += data
def get_data_log_likelihood(self, y_labels):
# we assume one-hot labels
# Returns the emission probability associated to each observable
return self.emission_distr.log_prob(torch.argmax(y_labels, -1))
def update_parameters(self):
d_posterior = Dirichlet(self.counts + self.alpha)
self.emission_distr = Categorical(d_posterior.sample())
torch.zero_(self.counts)
class BNPGaussian(BayesianDistribution):
def __init__(self, dim_target, mu0, lam0, a0, b0):
"""
:param mean: mean
:param var: variance
"""
super(BNPGaussian, self).__init__()
assert dim_target == 1, "only univariate case"
self.mu0 = mu0
self.lam0 = lam0
self.a0 = a0
self.b0 = b0
self.initialise_parameters()
self.device = None
self.all_data_list = []
def to(self, device):
super().to(device)
self.device = device
def initialise_parameters(self):
prec_prior = Gamma(self.a0, self.b0)
precision = prec_prior.sample() + self.EPS
mu_prior = Normal(self.mu0, 1. / torch.sqrt(self.lam0 * precision))
mean = mu_prior.sample()
self.emission_distr = Normal(mean, 1. / torch.sqrt(precision))
def get_data_log_likelihood(self, y_labels):
return self.emission_distr.log_prob(y_labels.squeeze())
def update_counts(self, xu):
self.all_data_list.append(xu)
def update_parameters(self):
# formulas taken from https://en.wikipedia.org/wiki/Normal-gamma_distribution
if len(self.all_data_list) > 0:
all_data = torch.cat(self.all_data_list, dim=0)
sample_mean = torch.mean(all_data, dim=0)
sample_var = torch.mean(torch.pow(all_data - sample_mean, 2), dim=0)
n = all_data.shape[0]
a0_post = self.a0 + n / 2.
b0_post = self.b0 + 0.5 * (
n * sample_var + (self.lam0 * n * (sample_mean - self.mu0) ** 2) / (self.lam0 + n))
mu0_post = (self.lam0 * self.mu0 + n * sample_mean) / (self.lam0 + n)
lam0_post = self.lam0 + n
prec_post = Gamma(a0_post, b0_post)
precision = prec_post.sample() + self.EPS
mu_post = Normal(mu0_post, 1. / torch.sqrt(lam0_post * precision))
mean = mu_post.sample()
self.emission_distr = Normal(mean, 1. / torch.sqrt(precision))
# throw away data
self.all_data_list = []
else:
# re-generate the parameters
self.initialise_parameters()
class BNPGaussianBatch(BayesianDistribution):
def __init__(self, dim_target, mu0, lam0, a0, b0):
"""
:param mean: mean
:param var: variance
"""
super(BNPGaussianBatch, self).__init__()
assert dim_target == 1, "only univariate case"
self.mu0 = mu0
self.lam0 = lam0
self.a0 = a0
self.b0 = b0
self.initialise_parameters()
self.device = None
self.all_data_list = []
def to(self, device):
super().to(device)
self.device = device
def initialise_parameters(self):
prec_prior = Gamma(self.a0, self.b0)
precision = prec_prior.sample() + self.EPS
mu_prior = Normal(self.mu0, 1. / torch.sqrt(self.lam0 * precision))
mean = mu_prior.sample()
self.emission_distr = Normal(mean, 1. / torch.sqrt(precision))
def get_data_log_likelihood(self, y_labels):
return self.emission_distr.log_prob(y_labels.squeeze())
def update_counts(self, data):
self.all_data_list.append(data)
def update_parameters(self):
# formulas taken from https://en.wikipedia.org/wiki/Normal-gamma_distribution
if len(self.all_data_list) > 0:
all_data = torch.cat(self.all_data_list, dim=0)
sample_mean = torch.mean(all_data, dim=0)
sample_var = torch.mean(torch.pow(all_data - sample_mean, 2), dim=0)
n = all_data.shape[0]
a0_post = self.a0 + n / 2.
b0_post = self.b0 + 0.5 * (
n * sample_var + (self.lam0 * n * (sample_mean - self.mu0) ** 2) / (self.lam0 + n))
mu0_post = (self.lam0 * self.mu0 + n * sample_mean) / (self.lam0 + n)
lam0_post = self.lam0 + n
prec_post = Gamma(a0_post, b0_post)
precision = prec_post.sample() + self.EPS
mu_post = Normal(mu0_post, 1. / torch.sqrt(lam0_post * precision))
mean = mu_post.sample()
self.emission_distr = Normal(mean, 1. / torch.sqrt(precision))
# throw away data
self.all_data_list = []
else:
# re-generate the parameters
self.initialise_parameters()