def init_mm_params(nb_components, latent_dims, alpha_scale=.1, beta_scale=1e-5, v_init=10., m_scale=1., C_scale=10.,
seed=0, as_variables=True, trainable=False, device='/gpu:0', name='gmm'):
with tf.name_scope('gmm_initialization'):
alpha_init = alpha_scale * tf.ones((nb_components,))
beta_init = beta_scale * tf.ones((nb_components,))
v_init = tf.tile([float(latent_dims + v_init)], [nb_components])
means_init = m_scale * tf.random_uniform((nb_components, latent_dims), minval=-1, maxval=1, seed=seed)
covariance_init = C_scale * tf.tile(tf.expand_dims(tf.eye(latent_dims), axis=0), [nb_components, 1, 1])
# transform to natural parameters
A, b, beta, v_hat = niw.standard_to_natural(beta_init, means_init, covariance_init, v_init)
alpha = dirichlet.standard_to_natural(alpha_init)
# init variable
if as_variables:
with tf.variable_scope(name):
alpha = variable_on_device('alpha_k', shape=None, initializer=alpha, trainable=trainable, device=device)
A = variable_on_device('beta_k', shape=None, initializer=A, trainable=trainable, device=device)
b = variable_on_device('m_k', shape=None, initializer=b, trainable=trainable, device=device)
beta = variable_on_device('C_k', shape=None, initializer=beta, trainable=trainable, device=device)
v_hat = variable_on_device('v_k', shape=None, initializer=v_hat, trainable=trainable, device=device)
params = alpha, A, b, beta, v_hat
return params
def __init__(self,
nb_components,
dimension,
alpha_scale=0.1,
beta_scale=1e-5,
v_init=10.,
m_scale=1.,
C_scale=10.,
name='normal_inverse_wishart'):
super(NormalInverseWishart, self).__init__(name=name)
with self._enter_variable_scope():
alpha_init = alpha_scale * tf.ones((nb_components, ))
beta_init = beta_scale * tf.ones((nb_components, ))
v_init = tf.tile([float(dimension + v_init)], [nb_components])
means_init = m_scale * tf.random_uniform(
(nb_components, dimension), minval=-1, maxval=1)
covariance_init = tf.matrix_inverse(
C_scale * tf.tile(tf.expand_dims(tf.eye(dimension), axis=0),
[nb_components, 1, 1]))
A, b, beta, v_hat = niw.standard_to_natural(
beta_init, means_init, covariance_init, v_init)
alpha = dirichlet.standard_to_natural(alpha_init)
self.alpha = tf.get_variable(
'alpha_k',
# shape=(nb_components),
dtype=tf.float32,
initializer=alpha,
trainable=False)
self.A = tf.get_variable(
"beta_k",
# shape=(nb_components, dimension),
dtype=tf.float32,
initializer=A,
trainable=False)
self.b = tf.get_variable(
"m_k",
# shape=(nb_components),
dtype=tf.float32,
initializer=b,
trainable=False)
self.beta = tf.get_variable(
"C_k",
# shape=(nb_components, dimension, dimension),
initializer=beta,
dtype=tf.float32,
trainable=False)
self.v_hat = tf.get_variable(
"v_k",
# shape=(nb_components),
dtype=tf.float32,
initializer=v_hat,
trainable=False)
def m_step_smm(smm_prior, r_nk):
"""
Args:
smm_prior: Dirichlet prior for Student-t mixture model
r_nk: responsibilities
Returns:
Dirichlet parameter obtained by executing Archambeau and Verleysen's M-step in their VEM algorithm for SMMs
"""
with tf.name_scope('m_step'):
# execute SMM-EM m-step to update multinomial
alpha_0 = dirichlet.natural_to_standard(smm_prior[0])
N_k = smm.update_Nk(r_nk)
alpha_k = smm.update_alphak(alpha_0, N_k)
alpha = dirichlet.standard_to_natural(alpha_k)
return tf.identity(alpha, name='alpha_star')
def m_step(gmm_prior, x_samples, r_nk):
"""
Args:
gmm_prior: Dirichlet+NiW prior for Gaussian mixture model
x_samples: samples of shape (N, S, L)
r_nk: responsibilities of shape (N, K)
Returns:
Dirichlet+NiW parameters obtained by executing Bishop's M-step in the VEM algorithm for GMMs
"""
with tf.name_scope('m_step'):
# execute GMM-EM m-step
beta_0, m_0, C_0, v_0 = niw.natural_to_standard(*gmm_prior[1:])
alpha_0 = dirichlet.natural_to_standard(gmm_prior[0])
alpha_k, beta_k, m_k, C_k, v_k, x_k, S_k = gmm.m_step(x_samples, r_nk, alpha_0, beta_0, m_0, C_0, v_0,
name='gmm_m_step')
A, b, beta, v_hat = niw.standard_to_natural(beta_k, m_k, C_k, v_k)
alpha = dirichlet.standard_to_natural(alpha_k)
return tf.tuple([alpha, A, b, beta, v_hat], name='theta_star')