def __init__(self, K, n, C=None, sigma_C=1, mu=None, mu_pi=None):
"""
Create a PGMultinomial distribution with mean and covariance for psi.
:param K: Dimensionality of the multinomial distribution
:param mu_C: Mean of the matrix normal distribution over C
"""
assert isinstance(K, int) and K >= 2, "K must be an integer >= 2"
self.K = K
assert isinstance(n, int) and n >= 1, "n must be an integer >= 1"
self.n = n
# Initialize emission matrix C
self.sigma_C = sigma_C
if C is None:
self.C = self.sigma_C * np.random.randn(self.K-1, self.n)
# mu, sigma = compute_psi_cmoments(np.ones(K))
# self.C = compute_psi_cmoments(np.ones(K))[0][:,None] * np.ones((self.K-1, self.n))
else:
assert C.shape == (self.K-1, self.n)
self.C = C
# Initialize the observation mean (mu)
if mu is None and mu_pi is None:
self.mu = np.zeros(self.K-1)
elif mu is not None:
assert mu.shape == (self.K-1,)
self.mu = mu
else:
assert mu_pi.shape == (self.K,)
self.mu = pi_to_psi(mu_pi)
# Initialize Polya-gamma augmentation variables
self.ppgs = initialize_polya_gamma_samplers()
def __init__(self, data, T, alpha_beta):
mu, sigma = np.zeros(T), np.eye(T)
self.theta_prior = Gaussian(mu=mu, sigma=sigma, mu_0=mu, sigma_0=T * sigma / 10.0, nu_0=T / 10.0, kappa_0=10.0)
self.ppgs = initialize_polya_gamma_samplers()
self.omega = np.zeros((data.shape[0], T))
super(LogisticNormalCorrelatedLDA, self).__init__(data, T, alpha_beta)
def __init__(self, data, T, alpha_beta):
mu, sigma = compute_uniform_mean_psi(T)
self.theta_prior = Gaussian(
mu=mu, sigma=sigma, mu_0=mu, sigma_0=T * sigma / 10.0, nu_0=T / 10.0, kappa_0=1.0 / 10
)
self.ppgs = initialize_polya_gamma_samplers()
self.omega = np.zeros((data.shape[0], T - 1))
super(StickbreakingCorrelatedLDA, self).__init__(data, T, alpha_beta)
def __init__(self, data, T, alpha_beta):
mu, sigma = np.zeros(T), np.eye(T)
self.theta_prior = \
Gaussian(
mu=mu, sigma=sigma, mu_0=mu, sigma_0=T*sigma/10.,
nu_0=T/10., kappa_0=10.)
self.ppgs = initialize_polya_gamma_samplers()
self.omega = np.zeros((data.shape[0], T))
super(LogisticNormalCorrelatedLDA, self).__init__(data, T, alpha_beta)
def __init__(self, data, T, alpha_beta):
mu, sigma = compute_uniform_mean_psi(T)
self.theta_prior = Gaussian(mu=mu,
sigma=sigma,
mu_0=mu,
sigma_0=T * sigma / 10.,
nu_0=T / 10.,
kappa_0=1. / 10)
self.ppgs = initialize_polya_gamma_samplers()
self.omega = np.zeros((data.shape[0], T - 1))
super(StickbreakingCorrelatedLDA, self).__init__(data, T, alpha_beta)
def __init__(self, K, pi=None, psi=None, mu=None, Sigma=None):
"""
Create a PGMultinomial distribution with mean and covariance for psi.
:param K: Dimensionality of the multinomial distribution
:param pi: Multinomial probability vector (must sum to 1)
:param psi: Transformed multinomial probability vector
:param mu: Mean of \psi
:param Sigma: Covariance of \psi
"""
assert isinstance(K, int) and K >= 2, "K must be an integer >= 2"
self.K = K
assert pi is not None or psi is not None or None not in (mu, Sigma), \
"pi, psi, or (mu and Sigma) must be specified"
if pi is not None:
assert isinstance(pi, np.ndarray) and \
pi.shape == (K,) and \
np.allclose(pi.sum(), 1.0), \
"Pi must be a normalized length-K vector"
self.pi = pi
if psi is not None:
assert isinstance(psi, np.ndarray) and \
psi.shape == (K-1,), \
"Psi must be a length-K vector of reals"
self.psi = psi
if None not in (mu, Sigma):
assert isinstance(mu, np.ndarray) and mu.shape == (K,), \
"Mu must be a length-K vector"
assert isinstance(Sigma, np.ndarray) and Sigma.shape == (K,K), \
"Sigma must be a KxK Covariance matrix"
self.mu = mu
self.Sigma = Sigma
self.Lambda = np.linalg.inv(Sigma)
# If psi and pi have not been given, sample from the prior
if psi is None and pi is None:
self.psi = np.random.multivariate_normal(self.mu, self.Sigma)
# Initialize Polya-gamma augmentation variables
self.ppgs = initialize_polya_gamma_samplers()
self.omega = np.ones(self.K)
# Initialize the space for the transformed psi variables, rho
self.rho = np.zeros(self.K)
def monte_carlo_approx(M=100000):
ppgs = initialize_polya_gamma_samplers()
# Compute the left hand side analytically
loglhs = psi * a - b * np.log1p(np.exp(psi))
# Compute the right hand side with Monte Carlo
omegas = np.ones(M)
ppg.pgdrawvpar(ppgs, b * np.ones(M), np.zeros(M), omegas)
logrhss = -b * np.log(2) + (a - b / 2.) * psi - 0.5 * omegas * psi**2
logrhs = logsumexp(logrhss) - np.log(M)
print("Monte Carlo")
print("log LHS: ", loglhs)
print("log RHS: ", logrhs)
def monte_carlo_approx(M=100000):
ppgs = initialize_polya_gamma_samplers()
# Compute the left hand side analytically
loglhs = psi*a - b * np.log1p(np.exp(psi))
# Compute the right hand side with Monte Carlo
omegas = np.ones(M)
ppg.pgdrawvpar(ppgs, b*np.ones(M), np.zeros(M), omegas)
logrhss = -b * np.log(2) + (a-b/2.)*psi -0.5 * omegas*psi**2
logrhs = logsumexp(logrhss) - np.log(M)
print("Monte Carlo")
print("log LHS: ", loglhs)
print("log RHS: ", logrhs)
def __init__(self, data, timestamps, K, alpha_theta):
assert isinstance(data, scipy.sparse.csr.csr_matrix)
self.alpha_theta = alpha_theta
self.D, self.V = data.shape
self.K = K
self.data = data
self.timestamps = timestamps
self.timeidx = self._get_timeidx(timestamps, data)
self.T = self.timeidx.max() - self.timeidx.min() + 1
self.ppgs = initialize_polya_gamma_samplers()
self.pyrngs = initialize_pyrngs()
self.initialize_parameters()
self._training_gammalns = gammaln(data.sum(1) + 1).sum() - gammaln(data.data + 1).sum()
def __init__(self, K, pi=None, psi=None, mu=None, Sigma=None):
"""
Create a PGMultinomial distribution with mean and covariance for psi.
:param K: Dimensionality of the multinomial distribution
:param pi: Multinomial probability vector (must sum to 1)
:param psi: Transformed multinomial probability vector
:param mu: Mean of \psi
:param Sigma: Covariance of \psi
"""
assert isinstance(K, int) and K >= 2, "K must be an integer >= 2"
self.K = K
if all(param is None for param in (pi,psi,mu,Sigma)):
mu, sigma = compute_psi_cmoments(np.ones(K))
Sigma = np.diag(sigma)
if pi is not None:
if not (isinstance(pi, np.ndarray) and pi.shape == (K,)
and np.isclose(pi.sum(), 1.0)):
raise ValueError("Pi must be a normalized length-K vector")
self.pi = pi
if psi is not None:
if not (isinstance(psi, np.ndarray) and psi.shape == (K-1,)):
raise ValueError("Psi must be a (K-1) vector of reals")
self.psi = psi
if mu is not None and Sigma is not None:
if not (isinstance(mu, np.ndarray) and mu.shape == (K-1,)):
raise ValueError("Mu must be a (K-1) vector")
if not (isinstance(Sigma, np.ndarray) and Sigma.shape == ((K-1), (K-1))):
raise ValueError("Sigma must be a K-1 Covariance matrix")
self.mu = mu
self.Sigma = Sigma
# If psi and pi have not been given, sample from the prior
if psi is None and pi is None:
self.psi = np.random.multivariate_normal(self.mu, self.Sigma)
# Initialize Polya-gamma augmentation variables
self.ppgs = initialize_polya_gamma_samplers()
self.omega = np.ones(self.K-1)
def __init__(self, data, timestamps, K, alpha_theta):
assert isinstance(data, scipy.sparse.csr.csr_matrix)
self.alpha_theta = alpha_theta
self.D, self.V = data.shape
self.K = K
self.data = data
self.timestamps = timestamps
self.timeidx = self._get_timeidx(timestamps, data)
self.T = self.timeidx.max() - self.timeidx.min() + 1
self.ppgs = initialize_polya_gamma_samplers()
self.pyrngs = initialize_pyrngs()
self.initialize_parameters()
self._training_gammalns = \
gammaln(data.sum(1)+1).sum() - gammaln(data.data+1).sum()
def __init__(self, K, kernel, D, Z=None, X=None, mu=None, mu_0=None, Sigma_0=None):
super(_MultinomialGPGibbsSampling, self).__init__(K, kernel, D, Z, X, mu=mu, mu_0=mu_0, Sigma_0=Sigma_0)
self.ppgs = initialize_polya_gamma_samplers()