def log_joint(x, w, epsilon, tau, alpha, beta):
log_p_epsilon = log_probs.norm_gen_log_prob(epsilon, 0, 1)
log_p_w = log_probs.norm_gen_log_prob(w, 0, 1)
log_p_tau = log_probs.gamma_gen_log_prob(tau, alpha, beta)
# TODO(mhoffman): The transposed version below should work.
# log_p_x = log_probs.norm_gen_log_prob(x, np.dot(epsilon, w), 1. / np.sqrt(tau))
log_p_x = log_probs.norm_gen_log_prob(x, np.einsum('ik,jk->ij', epsilon, w),
1. / np.sqrt(tau))
return log_p_epsilon + log_p_w + log_p_tau + log_p_x
def log_joint(pi, z, mu, tau):
log_p_pi = log_probs.dirichlet_gen_log_prob(pi, alpha)
log_p_mu = log_probs.norm_gen_log_prob(mu, 0.,
1. / np.sqrt(kappa * tau))
log_p_z = log_probs.categorical_gen_log_prob(z, pi)
log_p_tau = log_probs.gamma_gen_log_prob(tau, a, b)
z_one_hot = one_hot(z, len(pi))
mu_z = np.dot(z_one_hot, mu)
log_p_x = log_probs.norm_gen_log_prob(x, mu_z, 1. / np.sqrt(tau))
return log_p_pi + log_p_z + log_p_mu + log_p_x
def log_joint(tau, mu, x, alpha, beta, kappa, mu0):
log_p_tau = log_probs.gamma_gen_log_prob(tau, alpha, beta)
log_p_mu = log_probs.norm_gen_log_prob(mu, mu0, 1. / np.sqrt(kappa * tau))
log_p_x = log_probs.norm_gen_log_prob(x, mu, 1. / np.sqrt(tau))
return log_p_tau + log_p_mu + log_p_x
def log_joint(x, precision, a, b): log_p_precision = log_probs.gamma_gen_log_prob(precision, a, b) log_p_x = log_probs.norm_gen_log_prob(x, 0., 1. / np.sqrt(precision)) return log_p_precision + log_p_x
def log_joint(x, y, a, b): log_prior = log_probs.gamma_gen_log_prob(x, a, b) log_likelihood = np.sum(log_probs.gamma_gen_log_prob(y, a, a * x)) return log_prior + log_likelihood
def log_joint(x, y, a, b): log_prior = log_probs.gamma_gen_log_prob(x, a, b) log_likelihood = np.sum(-special.gammaln(y + 1) + y * np.log(x) - x) return log_prior + log_likelihood