def pca_model(M, N, D):
# Construct the PCA model with ARD
# ARD
alpha = nodes.Gamma(1e-2, 1e-2, plates=(D, ), name='alpha')
# Loadings
W = nodes.Gaussian(np.zeros(D),
alpha.as_diagonal_wishart(),
name="W",
plates=(M, 1))
# States
X = nodes.Gaussian(np.zeros(D), np.identity(D), name="X", plates=(1, N))
# PCA
WX = nodes.Dot(W, X, name="WX")
# Noise
tau = nodes.Gamma(1e-2, 1e-2, name="tau", plates=())
# Noisy observations
Y = nodes.GaussianARD(WX, tau, name="Y", plates=(M, N))
return (Y, WX, W, X, tau, alpha)
def gaussianmix_model(N, K, D, covariance='full'):
# N = number of data vectors
# K = number of clusters
# D = dimensionality
# Construct the Gaussian mixture model
# K prior weights (for components)
alpha = nodes.Dirichlet(1e-3*np.ones(K),
name='alpha')
# N K-dimensional cluster assignments (for data)
z = nodes.Categorical(alpha,
plates=(N,),
name='z')
# K D-dimensional component means
X = nodes.GaussianARD(0, 1e-3,
shape=(D,),
plates=(K,),
name='X')
if covariance.lower() == 'full':
# K D-dimensional component covariances
Lambda = nodes.Wishart(D, 0.01*np.identity(D),
plates=(K,),
name='Lambda')
# N D-dimensional observation vectors
Y = nodes.Mixture(z, nodes.Gaussian, X, Lambda, plates=(N,), name='Y')
elif covariance.lower() == 'diagonal':
# Inverse variances
Lambda = nodes.Gamma(1e-3, 1e-3, plates=(K, D), name='Lambda')
# N D-dimensional observation vectors
Y = nodes.Mixture(z, nodes.GaussianARD, X, Lambda, plates=(N,), name='Y')
elif covariance.lower() == 'isotropic':
# Inverse variances
Lambda = nodes.Gamma(1e-3, 1e-3, plates=(K, 1), name='Lambda')
# N D-dimensional observation vectors
Y = nodes.Mixture(z, nodes.GaussianARD, X, Lambda, plates=(N,), name='Y')
z.initialize_from_random()
return VB(Y, X, Lambda, z, alpha)