def p_star(state, X, obs):
K = state.U.shape[1]
total = log_poisson(K, 1.)
var_prior = distributions.InverseGammaDistribution(A, B)
total += var_prior.loglik(state.ssq_U).sum()
assert np.isfinite(total)
U_dist = distributions.GaussianDistribution(0., state.ssq_U[nax, :])
total += U_dist.loglik(state.U).sum()
assert np.isfinite(total)
V_dist = distributions.GaussianDistribution(0., 1.)
total += V_dist.loglik(state.V).sum()
assert np.isfinite(total)
pred = np.dot(state.U, state.V)
X_dist = distributions.GaussianDistribution(pred, state.ssq_N)
total += X_dist.loglik(X)[obs].sum()
assert np.isfinite(total)
return total
def cond_mu_Z(state, by_column=False):
if by_column:
mu = state.Z.mean(0)
sigma_sq = state.sigma_sq_Z / state.Z.shape[0] * np.ones(state.Z.shape[1])
else:
mu = state.Z.mean()
sigma_sq = state.sigma_sq_Z / state.Z.size
return distributions.GaussianDistribution(mu, sigma_sq)
def cond_u(self, i):
idxs = np.where(self.obs[i, :])[0]
#lam = np.dot(self.v[idxs], self.v[idxs]) / self.ssq_N + 1. / self.ssq_u
v = self.v[idxs]
lam = (v**2).sum() / self.ssq_N + 1. / self.ssq_u
h = (self.resid[i, idxs] * v).sum() / self.ssq_N
if np.abs(h / lam) < 1e-10:
raise InstabilityError()
return distributions.GaussianDistribution(h / lam, 1. / lam)
def make_proposal(resid, obs, ssq_N, order=None):
pi = ProposalInfo(resid, obs, ssq_N)
N, D = resid.shape
if order is None:
order = range(N)
for i in order:
if i == order[0]:
dist = distributions.GaussianDistribution(0., 1.)
else:
dist = pi.cond_u(i)
pi.update_u(i, dist.sample())
pi.fit_v_and_var()
v = pi.cond_v().sample()
ssq_u = pi.cond_ssq_u().sample()
return Proposal(pi.u.copy(), v, ssq_u)
def proposal_probability(resid, obs, ssq_N, proposal, order=None):
pi = ProposalInfo(resid, obs, ssq_N)
N, D = resid.shape
if order is None:
order = range(N)
total = 0.
for i in order:
if i == order[0]:
dist = distributions.GaussianDistribution(0., 1.)
else:
dist = pi.cond_u(i)
total += dist.loglik(proposal.u[i])
pi.update_u(i, proposal.u[i])
pi.fit_v_and_var()
total += pi.cond_v().loglik(proposal.v).sum()
total += pi.cond_ssq_u().loglik(proposal.ssq_u)
return total
def cond_v(self):
return distributions.GaussianDistribution(self.h / self.lam,
1. / self.lam)