def entropy(self):
"""
Returns the entropy of the variational distribution as a tuple
"""
return (
-sum(_safe_x_log_x(q_zd).sum() for q_zd in self.q_z),
self.q_alpha.H,
self.q_beta.H,
self.q_gamma.H,
self.q_pi_bar.H.sum(),
self.q_tau.H,
)
def _log_likelihood(self):
"""
Returns the variational bound on the log likelihood.
"""
LL = [] # build a list of all the different terms in the LL
# n_d term
term = (gammaln(self.q_alpha.E) - gammaln(self.q_alpha.E + self.n_d)).sum()
assert numpy.isfinite(term)
LL.append(term)
# n_dk term
G_alpha_pi = self.q_alpha.G * self.G_pi
f = lambda n: gammaln(G_alpha_pi + n) - gammaln(G_alpha_pi)
f2 = lambda n: polygamma(1, (G_alpha_pi + n))
term = _approx_f_n(f, f2, self.counts.P_plus_n_dk, self.counts.E_plus_n_dk, self.counts.V_plus_n_dk).sum()
assert numpy.isfinite(term)
LL.append(term)
# n_k term
f = lambda n: gammaln(self.q_beta.G + n) - gammaln(self.q_beta.G)
f2 = lambda n: polygamma(1, (self.q_beta.G + n))
term = - _approx_f_n(f, f2, self.counts.P_plus_n_k, self.counts.E_plus_n_k, self.counts.V_plus_n_k).sum()
assert numpy.isfinite(term)
LL.append(term)
# n_kw term
G_beta_tau = self.q_beta.G * self.q_tau.G
f = lambda n: gammaln(G_beta_tau + n) - gammaln(G_beta_tau)
f2 = lambda n: polygamma(1, (G_beta_tau + n))
term = _approx_f_n(f, f2, self.counts.P_plus_n_kw, self.counts.E_plus_n_kw, self.counts.V_plus_n_kw).sum()
assert numpy.isfinite(term)
LL.append(term)
# KL(q(alpha)||p(alpha)) term
a_bar = self.a_alpha + self.E_s_dk.sum()
b_bar = self.b_alpha - self.E_log_eta.sum()
term = - _gamma_KL(a_bar, b_bar, self.a_alpha, self.b_alpha)
assert numpy.isfinite(term)
LL.append(term)
# KL(q(z)||p(z)) term
term = sum(- _safe_x_log_x(q_zd).sum() for q_zd in self.q_z)
LL.append(term)
assert numpy.isfinite(term)
# KL(q(beta)||p(beta)) term
a_bar = self.a_beta + self.E_t_kw.sum()
b_bar = self.b_beta - self.E_log_xi.sum()
term = - _gamma_KL(a_bar, b_bar, self.a_beta, self.b_beta)
assert numpy.isfinite(term)
LL.append(term)
# KL(q(pi)||p(pi)) term
E_s_k = self.E_s_dk.sum(axis=0)
assert E_s_k.shape == (self.K,)
E_s_greater_k = _greater_than(E_s_k)
# term = - (
# gammaln(1. + self.q_gamma.E + E_s_k + E_s_greater_k)
# - numpy.log(self.q_gamma.E)
# - gammaln(1. + E_s_k)
# - gammaln(self.q_gamma.E + E_s_greater_k)
# + E_s_k * numpy.log(self.q_pi_bar.G)
# + E_s_greater_k * numpy.log(self.q_1_minus_pi_bar.G)
# ).sum()
term = - (
(
gammaln(1. + self.q_gamma.E + E_s_k + E_s_greater_k)
- numpy.log(self.q_gamma.E)
- gammaln(1. + E_s_k)
- gammaln(self.q_gamma.E + E_s_greater_k)
)
* self.q_pi_bar.G ** E_s_k
* self.q_1_minus_pi_bar.G ** E_s_greater_k
).sum()
#assert numpy.allclose(term, _beta_KL(self.q_pi_bar.a, self.q_pi_bar.b, 1., self.q_gamma.E))
#term = _beta_KL(self.q_pi_bar.a, self.q_pi_bar.b, 1., self.q_gamma.G).sum()
assert numpy.isfinite(term)
LL.append(term)
# KL(q(tau)||p(tau)) term
a_bar = self.q_tau.a + self.E_t_kw.sum(axis=0)
term = - _dirichlet_KL(a_bar, self.q_tau.a)
assert numpy.isfinite(term)
LL.append(term)
return LL
