def E_log_p_mu_lambda_samples(self, mus, lambdas):
prior_lambda = tfd.WishartTriL(df=self.dof0, #,
scale_tril=tf.linalg.cholesky(self.W0))
log_prior_lambdas = tf.reduce_sum( prior_lambda.log_prob(lambdas), -1 )
def get_prior_mu(beta0, m0, lambdas):
precisions = (lambdas*beta0)
covs = tf.linalg.inv(precisions)
covs = 0.5*(covs + tf.transpose(covs, [0, 1, 3, 2])) # numerical stability workaround
d = tfd.MultivariateNormalTriL(loc=m0,
scale_tril=tf.linalg.cholesky(covs))
return d
prior_mu = get_prior_mu(self.beta0, #,
self.m0,
lambdas)
log_prior_mus = tf.reduce_sum( prior_mu.log_prob(mus), -1)
return tf.reduce_mean(log_prior_lambdas+log_prior_mus)
def sample_posteriors_global(self, nsamples=1000):
posterior_pi = tfd.Dirichlet(self.alpha)
pis = posterior_pi.sample(nsamples)
W1 = np.tile(self.W, [nsamples,1,1,1]) #nsamples x K x N=2 x N=2
posterior_lambda = tfd.WishartTriL(df=self.dof,
scale_tril=tf.linalg.cholesky(W1))
lambdas = posterior_lambda.sample() #nsamples x K x N=2 x N=2
def get_posterior_mu(beta, mu, lambdas):
locations = np.broadcast_to(mu, lambdas.shape[0:1]+mu.shape)
precisions = (lambdas*beta[None,:,None,None])
covs = tf.linalg.inv(precisions) #!
covs = 0.5*(covs + tf.transpose(covs, [0, 1, 3, 2])) # numerical stability workaround
d = tfd.MultivariateNormalTriL(loc=locations,
scale_tril=tf.linalg.cholesky(covs))
return d
posterior_mu = get_posterior_mu(self.beta,
self.mu,
lambdas)
mus = posterior_mu.sample()
return posterior_pi, posterior_lambda, posterior_mu, pis, lambdas, mus
def _init_distribution(conditions, **kwargs):
df, scale = conditions["df"], conditions["scale"]
return tfd.WishartTriL(df=df, scale_tril=scale, **kwargs)