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):
# N = number of data vectors
# K = number of clusters
# D = dimensionality
# Construct the Gaussian mixture model
# K prior weights (for components)
alpha = nodes.Dirichlet(1 * 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.Gaussian(np.zeros(D),
0.01 * np.identity(D),
plates=(K, ),
name='X')
# 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(nodes.Gaussian)(z, X, Lambda, plates=(N, ), name='Y')
# TODO: Plates should be learned automatically if not given (it
# would be the smallest shape broadcasted from the shapes of the
# parents)
return (Y, X, Lambda, z, alpha)