def resample_psi(self):
Lmbda = np.linalg.inv(self.theta_prior.sigma)
h = Lmbda.dot(self.theta_prior.mu)
randvec = np.random.randn(self.D, self.T - 1) # pre-generate randomness
for d, c in enumerate(self.doc_topic_counts):
self.psi[d] = sample_infogaussian(Lmbda + np.diag(self.omega[d]), h + kappa_vec(c), randvec[d])
def resample_psi(self):
Lmbda = np.linalg.inv(self.theta_prior.sigma)
h = Lmbda.dot(self.theta_prior.mu)
randvec = np.random.randn(self.D,
self.T - 1) # pre-generate randomness
for d, c in enumerate(self.doc_topic_counts):
self.psi[d] = sample_infogaussian(Lmbda + np.diag(self.omega[d]),
h + kappa_vec(c), randvec[d])
def _info_form_heldout_log_likelihood(self, X, M=10):
"""
We can analytically integrate out z (latent states)
given omega. To estimate the heldout log likelihood of a
data sequence, we Monte Carlo integrate over omega,
where omega is drawn from the prior.
:param data:
:param M: number of Monte Carlo samples for integrating out omega
:return:
"""
# assert len(self.data_list) == 1, "TODO: Support more than 1 data set"
T, K = X.shape
assert K == self.K
kappa = kappa_vec(X)
N = N_vec(X)
# Compute the data-specific normalization constant from the
# augmented multinomial distribution
Z_mul = (gammaln(N + 1) - gammaln(X[:, :-1] + 1) -
gammaln(N - X[:, :-1] + 1)).sum()
Z_mul += (-N * np.log(2.)).sum()
# Monte carlo integrate wrt omega ~ PG(N, 0)
import pypolyagamma as ppg
hlls = np.zeros(M)
for m in range(M):
# Sample omega using the emission distributions samplers
omega = np.zeros(N.size)
ppg.pgdrawvpar(self.emission_distn.ppgs, N.ravel(),
np.zeros(N.size), omega)
omega = omega.reshape((T, K - 1))
# Exactly integrate out the latent states z using message passing
# The "data" is the normal potential from the
states = MultinomialLDSStates(model=self, data=X)
conditional_mean = kappa / np.clip(
omega, 1e-64, np.inf) - self.emission_distn.mu[None, :]
conditional_prec = np.zeros((T, K - 1, K - 1))
for t in range(T):
conditional_prec[t, :, :] = np.diag(omega[t, :])
Z_lds = states.info_log_likelihood(conditional_mean,
conditional_prec)
# Sum them up to get the heldout log likelihood for this omega
hlls[m] = Z_mul + Z_lds
# Now take the log of the average to get the log likelihood
hll = logsumexp(hlls) - np.log(M)
# Use bootstrap to compute error bars
samples = np.random.choice(hlls, size=(100, M), replace=True)
hll_samples = logsumexp(samples, axis=1) - np.log(M)
std_hll = hll_samples.std()
return hll, std_hll
def _resample_X():
pis = model.pi(data)
X = np.array([np.random.multinomial(N_max, pis[m]) for m in xrange(M)])
N = N_vec(X).astype(np.float)
kappa = kappa_vec(X)
data["X"] = X
data["N"] = N
data["kappa"] = kappa
def _resample_X():
pis = model.pi(data)
X = np.array([np.random.multinomial(N_max, pis[m]) for m in xrange(M)])
N = N_vec(X).astype(np.float)
kappa = kappa_vec(X)
data["X"] = X
data["N"] = N
data["kappa"] = kappa
def _info_form_heldout_log_likelihood(self, X, M=10):
"""
We can analytically integrate out z (latent states)
given omega. To estimate the heldout log likelihood of a
data sequence, we Monte Carlo integrate over omega,
where omega is drawn from the prior.
:param data:
:param M: number of Monte Carlo samples for integrating out omega
:return:
"""
# assert len(self.data_list) == 1, "TODO: Support more than 1 data set"
T, K = X.shape
assert K == self.K
kappa = kappa_vec(X)
N = N_vec(X)
# Compute the data-specific normalization constant from the
# augmented multinomial distribution
Z_mul = (gammaln(N + 1) - gammaln(X[:,:-1]+1) - gammaln(N-X[:,:-1]+1)).sum()
Z_mul += (-N * np.log(2.)).sum()
# Monte carlo integrate wrt omega ~ PG(N, 0)
import pypolyagamma as ppg
hlls = np.zeros(M)
for m in range(M):
# Sample omega using the emission distributions samplers
omega = np.zeros(N.size)
ppg.pgdrawvpar(self.emission_distn.ppgs,
N.ravel(), np.zeros(N.size),
omega)
omega = omega.reshape((T, K-1))
# Exactly integrate out the latent states z using message passing
# The "data" is the normal potential from the
states = MultinomialLDSStates(model=self, data=X)
conditional_mean = kappa / np.clip(omega, 1e-64,np.inf) - self.emission_distn.mu[None, :]
conditional_prec = np.zeros((T, K-1, K-1))
for t in range(T):
conditional_prec[t,:,:] = np.diag(omega[t,:])
Z_lds = states.info_log_likelihood(conditional_mean, conditional_prec)
# Sum them up to get the heldout log likelihood for this omega
hlls[m] = Z_mul + Z_lds
# Now take the log of the average to get the log likelihood
hll = logsumexp(hlls) - np.log(M)
# Use bootstrap to compute error bars
samples = np.random.choice(hlls, size=(100, M), replace=True)
hll_samples = logsumexp(samples, axis=1) - np.log(M)
std_hll = hll_samples.std()
return hll, std_hll
def _get_lds_effective_params(self):
mu_uniform, sigma_uniform = compute_uniform_mean_psi(self.V)
mu_init = np.tile(mu_uniform, self.K)
sigma_init = np.tile(np.diag(sigma_uniform), self.K)
sigma_states = np.repeat(self.sigmasq_states, (self.V - 1) * self.K)
sigma_obs = 1.0 / self.omega
y = kappa_vec(self.time_word_topic_counts, axis=1) / self.omega
return mu_init, sigma_init, sigma_states, sigma_obs.reshape(y.shape[0], -1), y.reshape(y.shape[0], -1)
def _get_lds_effective_params(self):
mu_uniform, sigma_uniform = compute_uniform_mean_psi(self.V)
mu_init = np.tile(mu_uniform, self.K)
sigma_init = np.tile(np.diag(sigma_uniform), self.K)
sigma_states = np.repeat(self.sigmasq_states, (self.V - 1) * self.K)
sigma_obs = 1. / self.omega
y = kappa_vec(self.time_word_topic_counts, axis=1) / self.omega
return mu_init, sigma_init, sigma_states, \
sigma_obs.reshape(y.shape[0], -1), y.reshape(y.shape[0], -1)
def augment_data(self, augmented_data):
"""
Augment the data with auxiliary variables
:param augmented_data:
:return:
"""
x = augmented_data["x"]
T, K = x.shape
assert K == self.K
augmented_data["kappa"] = kappa_vec(x)
augmented_data["omega"] = np.ones((T,K-1))
self.resample_omega([augmented_data])
return augmented_data
def conditional_psi(self, x):
"""
Compute the conditional distribution over psi given observation x and omega
:param x:
:return:
"""
assert x.ndim == 2
Omega = np.diag(self.omega)
Sigma_cond = inv(Omega + inv(self.Sigma))
# kappa is the mean dot precision, i.e. the sufficient statistic of a Gaussian
# therefore we can sum over datapoints
kappa = kappa_vec(x).sum(0)
mu_cond = Sigma_cond.dot(kappa +
solve(self.Sigma, self.mu))
return mu_cond, Sigma_cond
def add_data(self, Z, X, fixed_kernel=True):
# Z is the array of points where multinomial vectors are observed
# X is the corresponding set of multinomial vectors
assert Z.ndim == 2 and Z.shape[1] == self.D
M = Z.shape[0]
assert X.shape == (M, self.K), "X must be MxK"
# Compute kappa and N for each of the m inputs
N = N_vec(X).astype(np.float)
kappa = kappa_vec(X)
# Initialize the auxiliary variables
omega = np.ones((M, self.K-1))
# Initialize a "sample" from psi
psi = np.zeros((M, self.K-1))
# Precompute the kernel for the case where it is fixed
if fixed_kernel:
C = self.kernel.K(Z)
C += 1e-6 * np.eye(M)
C_inv = np.linalg.inv(C)
else:
C = None
C_inv = None
# Pack all this up into a dict
augmented_data = \
{
"X": X,
"Z": Z,
"M": M,
"N": N,
"C": C,
"C_inv": C_inv,
"kappa": kappa,
"omega": omega,
"psi": psi
}
self.data_list.append(augmented_data)
return augmented_data
