def test_constant(self):
"""
Test the constant moments of Dirichlet nodes.
"""
p = Dirichlet([1, 1, 1])
p.initialize_from_value([0.5, 0.4, 0.1])
u = p._message_to_child()
self.assertAllClose(u[0], np.log([0.5, 0.4, 0.1]))
pass
def test_constant(self):
"""
Test the constant moments of Dirichlet nodes.
"""
p = Dirichlet([1, 1, 1])
p.initialize_from_value([0.5, 0.4, 0.1])
u = p._message_to_child()
self.assertAllClose(u[0],
np.log([0.5, 0.4, 0.1]))
pass
def model(M=20, N=100, D=10, K=3):
"""
Construct the linear state-space model with switching dynamics.
"""
#
# Switching dynamics (HMM)
#
# Prior for initial state probabilities
rho = Dirichlet(1e-3 * np.ones(K), name='rho')
# Prior for state transition probabilities
V = Dirichlet(1e-3 * np.ones(K), plates=(K, ), name='V')
v = 10 * np.identity(K) + 1 * np.ones((K, K))
v /= np.sum(v, axis=-1, keepdims=True)
V.initialize_from_value(v)
# Hidden states (with unknown initial state probabilities and state
# transition probabilities)
Z = CategoricalMarkovChain(rho,
V,
states=N - 1,
name='Z',
plotter=bpplt.CategoricalMarkovChainPlotter(),
initialize=False)
Z.u[0] = np.random.dirichlet(np.ones(K))
Z.u[1] = np.reshape(
np.random.dirichlet(0.5 * np.ones(K * K), size=(N - 2)), (N - 2, K, K))
#
# Linear state-space models
#
# Dynamics matrix with ARD
# (K,D) x ()
alpha = Gamma(1e-5, 1e-5, plates=(K, 1, D), name='alpha')
# (K,1,1,D) x (D)
A = GaussianARD(0,
alpha,
shape=(D, ),
plates=(K, D),
name='A',
plotter=bpplt.GaussianHintonPlotter())
A.initialize_from_value(
np.identity(D) * np.ones((K, D, D)) + 0.1 * np.random.randn(K, D, D))
# Latent states with dynamics
# (K,1) x (N,D)
X = SwitchingGaussianMarkovChain(
np.zeros(D), # mean of x0
1e-3 * np.identity(D), # prec of x0
A, # dynamics
Z, # dynamics selection
np.ones(D), # innovation
n=N, # time instances
name='X',
plotter=bpplt.GaussianMarkovChainPlotter())
X.initialize_from_value(10 * np.random.randn(N, D))
# Mixing matrix from latent space to observation space using ARD
# (K,1,1,D) x ()
gamma = Gamma(1e-5, 1e-5, plates=(D, ), name='gamma')
# (K,M,1) x (D)
C = GaussianARD(0,
gamma,
shape=(D, ),
plates=(M, 1),
name='C',
plotter=bpplt.GaussianHintonPlotter(rows=-3, cols=-1))
C.initialize_from_value(np.random.randn(M, 1, D))
# Underlying noiseless function
# (K,M,N) x ()
F = SumMultiply('i,i', C, X, name='F')
#
# Mixing the models
#
# Observation noise
tau = Gamma(1e-5, 1e-5, name='tau')
tau.initialize_from_value(1e2)
# Emission/observation distribution
Y = GaussianARD(F, tau, name='Y')
Q = VB(Y, F, Z, rho, V, C, gamma, X, A, alpha, tau)
return Q
def model(M=20, N=100, D=10, K=3):
"""
Construct the linear state-space model with switching dynamics.
"""
#
# Switching dynamics (HMM)
#
# Prior for initial state probabilities
rho = Dirichlet(1e-3*np.ones(K),
name='rho')
# Prior for state transition probabilities
V = Dirichlet(1e-3*np.ones(K),
plates=(K,),
name='V')
v = 10*np.identity(K) + 1*np.ones((K,K))
v /= np.sum(v, axis=-1, keepdims=True)
V.initialize_from_value(v)
# Hidden states (with unknown initial state probabilities and state
# transition probabilities)
Z = CategoricalMarkovChain(rho, V,
states=N-1,
name='Z',
plotter=bpplt.CategoricalMarkovChainPlotter(),
initialize=False)
Z.u[0] = np.random.dirichlet(np.ones(K))
Z.u[1] = np.reshape(np.random.dirichlet(0.5*np.ones(K*K), size=(N-2)),
(N-2, K, K))
#
# Linear state-space models
#
# Dynamics matrix with ARD
# (K,D) x ()
alpha = Gamma(1e-5,
1e-5,
plates=(K,1,D),
name='alpha')
# (K,1,1,D) x (D)
A = GaussianARD(0,
alpha,
shape=(D,),
plates=(K,D),
name='A',
plotter=bpplt.GaussianHintonPlotter())
A.initialize_from_value(np.identity(D)*np.ones((K,D,D))
+ 0.1*np.random.randn(K,D,D))
# Latent states with dynamics
# (K,1) x (N,D)
X = SwitchingGaussianMarkovChain(np.zeros(D), # mean of x0
1e-3*np.identity(D), # prec of x0
A, # dynamics
Z, # dynamics selection
np.ones(D), # innovation
n=N, # time instances
name='X',
plotter=bpplt.GaussianMarkovChainPlotter())
X.initialize_from_value(10*np.random.randn(N,D))
# Mixing matrix from latent space to observation space using ARD
# (K,1,1,D) x ()
gamma = Gamma(1e-5,
1e-5,
plates=(D,),
name='gamma')
# (K,M,1) x (D)
C = GaussianARD(0,
gamma,
shape=(D,),
plates=(M,1),
name='C',
plotter=bpplt.GaussianHintonPlotter(rows=-3,cols=-1))
C.initialize_from_value(np.random.randn(M,1,D))
# Underlying noiseless function
# (K,M,N) x ()
F = SumMultiply('i,i',
C,
X,
name='F')
#
# Mixing the models
#
# Observation noise
tau = Gamma(1e-5,
1e-5,
name='tau')
tau.initialize_from_value(1e2)
# Emission/observation distribution
Y = GaussianARD(F, tau,
name='Y')
Q = VB(Y, F,
Z, rho, V,
C, gamma, X, A, alpha,
tau)
return Q
