def sample_transition_full_rank(model, state, hyperparams, pseudo_dof=None, pseudo_sd=None):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
with full rank model
"""
Q = model.transition_covariance()
# Sampke a pseudo-observation to constrain the size of move
if pseudo_dof is not None:
extra_nu = pseudo_dof
extra_Psi = smp.sample_wishart(pseudo_dof, Q)
else:
extra_nu = 0
extra_Psi = 0
# Calculate sufficient statistics
suffStats = smp.evaluate_transition_sufficient_statistics(state)
# Sample a new projected transition matrix and transition covariance
nu0 = model.ds + extra_nu
Psi0 = model.ds*hyperparams['rPsi0'] + extra_Psi
nu,Psi,M,V = smp.hyperparam_update_basic_mniw_transition(
suffStats,
nu0,
Psi0,
hyperparams['M0'],
hyperparams['V0'])
Q = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
F = smp.sample_matrix_normal(M, Q, V)
model.parameters['F'] = F
model.parameters['Q']= Q
return model
def sample_transition_within_subspace(model, state, hyperparams):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
within the constrained subspace
"""
# Calculate sufficient statistics
suffStats = smp.evaluate_transition_sufficient_statistics(state)
# Convert to Givens factorisation form
U, D = model.convert_to_givens_form()
# Sample a new projected transition matrix and transition covariance
rank = model.parameters['rank'][0]
nu0 = rank
Psi0 = rank * hyperparams['rPsi0']
nu, Psi, M, V = smp.hyperparam_update_degenerate_mniw_transition(
suffStats, U, nu0, Psi0, hyperparams['M0'], hyperparams['V0'])
D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
FU = smp.sample_matrix_normal(M, D, V)
# Project out
Fold = model.parameters['F']
F = smp.project_degenerate_transition_matrix(Fold, FU, U)
model.parameters['F'] = F
# Convert back to eigen-decomposition form
model.update_from_givens_form(U, D)
return model
def sample_transition_within_subspace(model, state, hyperparams):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
within the constrained subspace
"""
# Calculate sufficient statistics
suffStats = smp.evaluate_transition_sufficient_statistics(state)
# Convert to Givens factorisation form
U,D = model.convert_to_givens_form()
# Sample a new projected transition matrix and transition covariance
rank = model.parameters['rank'][0]
nu0 = rank
Psi0 = rank*hyperparams['rPsi0']
nu,Psi,M,V = smp.hyperparam_update_degenerate_mniw_transition(
suffStats, U,
nu0,
Psi0,
hyperparams['M0'],
hyperparams['V0'])
D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
FU = smp.sample_matrix_normal(M, D, V)
# Project out
Fold = model.parameters['F']
F = smp.project_degenerate_transition_matrix(Fold, FU, U)
model.parameters['F'] = F
# Convert back to eigen-decomposition form
model.update_from_givens_form(U, D)
return model
def sample_transition_full_rank(model,
state,
hyperparams,
pseudo_dof=None,
pseudo_sd=None):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
with full rank model
"""
Q = model.transition_covariance()
# Sampke a pseudo-observation to constrain the size of move
if pseudo_dof is not None:
extra_nu = pseudo_dof
extra_Psi = smp.sample_wishart(pseudo_dof, Q)
else:
extra_nu = 0
extra_Psi = 0
# Calculate sufficient statistics
suffStats = smp.evaluate_transition_sufficient_statistics(state)
# Sample a new projected transition matrix and transition covariance
nu0 = model.ds + extra_nu
Psi0 = model.ds * hyperparams['rPsi0'] + extra_Psi
nu, Psi, M, V = smp.hyperparam_update_basic_mniw_transition(
suffStats, nu0, Psi0, hyperparams['M0'], hyperparams['V0'])
Q = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
F = smp.sample_matrix_normal(M, Q, V)
model.parameters['F'] = F
model.parameters['Q'] = Q
return model
def sample_transition(self):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
"""
# Calculate sufficient statistics using current state trajectory
suffStats = smp.evaluate_transition_sufficient_statistics(self.state)
# Update hyperparameters
nu,Psi,M,V = smp.hyperparam_update_basic_mniw_transition(
suffStats,
self.hyperparams['nu0'],
self.hyperparams['Psi0'],
self.hyperparams['M0'],
self.hyperparams['V0'])
# Sample new parameters
Q = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
F = smp.sample_matrix_normal(M, Q, V)
# Update the model
self.model.parameters['F'] = F
self.model.parameters['Q'] = Q
# self.flt and self.lhood are no longer up-to-date
self.filter_current = False
def sample_transition_within_subspace(model, state, hyperparams, pseudo_dof=None, pseudo_sd=None):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
within the constrained subspace
"""
# Calculate sufficient statistics
suffStats = smp.evaluate_transition_sufficient_statistics(state)
# Convert to Givens factorisation form
U,D = model.convert_to_givens_form()
# Sampke a pseudo-observation to constrain the size of move
if pseudo_dof is not None:
extra_nu = pseudo_dof
extra_Psi = smp.sample_wishart(pseudo_dof, D)
else:
extra_nu = 0
extra_Psi = 0
# Sample a new projected transition matrix and transition covariance
rank = model.parameters['rank'][0]
nu0 = rank + extra_nu
Psi0 = rank*hyperparams['rPsi0'] + np.dot(U, np.dot(extra_Psi, U.T))
nu,Psi,M,V = smp.hyperparam_update_degenerate_mniw_transition(
suffStats, U,
nu0,
Psi0,
hyperparams['M0'],
hyperparams['V0'])
D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
FU = smp.sample_matrix_normal(M, D, V)
# Project out
Fold = model.parameters['F']
F = smp.project_degenerate_transition_matrix(Fold, FU, U)
model.parameters['F'] = F
# Convert back to eigen-decomposition form
model.update_from_givens_form(U, D)
return model
def sample_transition_within_subspace(model,
state,
hyperparams,
pseudo_dof=None,
pseudo_sd=None):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
within the constrained subspace
"""
# Calculate sufficient statistics
suffStats = smp.evaluate_transition_sufficient_statistics(state)
# Convert to Givens factorisation form
U, D = model.convert_to_givens_form()
# Sampke a pseudo-observation to constrain the size of move
if pseudo_dof is not None:
extra_nu = pseudo_dof
extra_Psi = smp.sample_wishart(pseudo_dof, D)
else:
extra_nu = 0
extra_Psi = 0
# Sample a new projected transition matrix and transition covariance
rank = model.parameters['rank'][0]
nu0 = rank + extra_nu
Psi0 = rank * hyperparams['rPsi0'] + np.dot(U, np.dot(extra_Psi, U.T))
nu, Psi, M, V = smp.hyperparam_update_degenerate_mniw_transition(
suffStats, U, nu0, Psi0, hyperparams['M0'], hyperparams['V0'])
D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
FU = smp.sample_matrix_normal(M, D, V)
# Project out
Fold = model.parameters['F']
F = smp.project_degenerate_transition_matrix(Fold, FU, U)
model.parameters['F'] = F
# Convert back to eigen-decomposition form
model.update_from_givens_form(U, D)
return model
def sample_transition(self):
"""
MCMC iteration (Gibbs sampling) for transition matrix and covariance
"""
# Calculate sufficient statistics using current state trajectory
suffStats = smp.evaluate_transition_sufficient_statistics(self.state)
# Update hyperparameters
nu, Psi, M, V = smp.hyperparam_update_basic_mniw_transition(
suffStats, self.hyperparams['nu0'], self.hyperparams['Psi0'],
self.hyperparams['M0'], self.hyperparams['V0'])
# Sample new parameters
Q = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
F = smp.sample_matrix_normal(M, Q, V)
# Update the model
self.model.parameters['F'] = F
self.model.parameters['Q'] = Q
# self.flt and self.lhood are no longer up-to-date
self.filter_current = False
def sample_transition_matrix(self):
"""
MCMC iteration (Metropolis-Hastings) for transition matrix
"""
# Make sure there's a dictionary to store stats for this move type
moveType = 'perturb'
if moveType not in self.chain_accept:
self.chain_accept[moveType] = []
if moveType not in self.chain_algoparams:
self.chain_algoparams[moveType] = []
# Need to make sure the likelihood value is current
if not self.filter_current:
self.flt, _, self.lhood = self.model.kalman_filter(self.observ)
self.filter_current = True
# Copy model
ppsl_model = self.model.copy()
if self.verbose:
print("Metropolis-Hastings move for transition matrix.")
# Propose a new transition matrix
ds = ppsl_model.ds
I = np.identity(ds)
sf = smp.sample_matrix_normal(np.zeros((ds, ds)),
self.algoparams[moveType] * I, I)
ppsl_model.parameters['F'] *= np.exp(sf)
# ppsl_model.parameters['F'] = smp.sample_matrix_normal(
# self.model.parameters['F'], self.algoparams[moveType]*I, I)
self.chain_algoparams[moveType].append(self.algoparams[moveType])
# Random walk, so forward and backward probabilities are same
fwd_prob = 0
bwd_prob = 0
# # Propose a new transition matrix
# suffStats = smp.evaluate_transition_sufficient_statistics(self.state)
# padded_Q = ppsl_model.transition_covariance() + \
# self.algoparams[moveType]*np.identity(ppsl_model.ds)
# M,V = smp.hyperparam_update_basic_mn_transition_matrix(
# suffStats,
# self.hyperparams['M0'],
# self.hyperparams['V0'],)
# ppsl_F = smp.sample_matrix_normal(M,padded_Q,V)
# fwd_prob = smp.matrix_normal_density(ppsl_F,M,padded_Q,V)
# ppsl_model.parameters['F'] = ppsl_F
# self.chain_algoparams[moveType].append(self.algoparams[moveType])
#
# # Sample a new trajectory
# ppsl_state = ppsl_model.sample_posterior(self.observ)
# ppsl_suffStats = smp.evaluate_transition_sufficient_statistics(
# ppsl_state)
#
# # Reverse move probaility
# M,V = smp.hyperparam_update_basic_mn_transition_matrix(
# ppsl_suffStats,
# self.hyperparams['M0'],
# self.hyperparams['V0'],)
# bwd_prob = smp.matrix_normal_density(self.model.parameters['F'],
# M,padded_Q,V)
# Kalman filter
ppsl_flt, _, ppsl_lhood = ppsl_model.kalman_filter(self.observ)
# Prior terms
prior = self.transition_prior(self.model)
ppsl_prior = self.transition_prior(ppsl_model)
# print(ppsl_lhood-self.lhood)
# print(ppsl_prior-prior)
# Decide
acceptRatio = (ppsl_lhood-self.lhood) \
+ (ppsl_prior-prior) \
+ (bwd_prob-fwd_prob)
if self.verbose:
print(" Acceptance ratio: {}".format(acceptRatio))
if np.log(np.random.random()) < acceptRatio:
self.model = ppsl_model
self.flt = ppsl_flt
self.lhood = ppsl_lhood
# self.state = ppsl_state
self.chain_accept[moveType].append(True)
if self.verbose:
print(" accepted")
else:
self.chain_accept[moveType].append(False)
if self.verbose:
print(" rejected")
def sample_transition_matrix(self):
"""
MCMC iteration (Metropolis-Hastings) for transition matrix
"""
# Make sure there's a dictionary to store stats for this move type
moveType = 'perturb'
if moveType not in self.chain_accept:
self.chain_accept[moveType] = []
if moveType not in self.chain_algoparams:
self.chain_algoparams[moveType] = []
# Need to make sure the likelihood value is current
if not self.filter_current:
self.flt,_,self.lhood = self.model.kalman_filter(self.observ)
self.filter_current = True
# Copy model
ppsl_model = self.model.copy()
if self.verbose:
print("Metropolis-Hastings move for transition matrix.")
# Propose a new transition matrix
ds = ppsl_model.ds
I = np.identity(ds)
sf = smp.sample_matrix_normal(np.zeros((ds,ds)),
self.algoparams[moveType]*I, I)
ppsl_model.parameters['F'] *= np.exp(sf)
# ppsl_model.parameters['F'] = smp.sample_matrix_normal(
# self.model.parameters['F'], self.algoparams[moveType]*I, I)
self.chain_algoparams[moveType].append(self.algoparams[moveType])
# Random walk, so forward and backward probabilities are same
fwd_prob = 0
bwd_prob = 0
# # Propose a new transition matrix
# suffStats = smp.evaluate_transition_sufficient_statistics(self.state)
# padded_Q = ppsl_model.transition_covariance() + \
# self.algoparams[moveType]*np.identity(ppsl_model.ds)
# M,V = smp.hyperparam_update_basic_mn_transition_matrix(
# suffStats,
# self.hyperparams['M0'],
# self.hyperparams['V0'],)
# ppsl_F = smp.sample_matrix_normal(M,padded_Q,V)
# fwd_prob = smp.matrix_normal_density(ppsl_F,M,padded_Q,V)
# ppsl_model.parameters['F'] = ppsl_F
# self.chain_algoparams[moveType].append(self.algoparams[moveType])
#
# # Sample a new trajectory
# ppsl_state = ppsl_model.sample_posterior(self.observ)
# ppsl_suffStats = smp.evaluate_transition_sufficient_statistics(
# ppsl_state)
#
# # Reverse move probaility
# M,V = smp.hyperparam_update_basic_mn_transition_matrix(
# ppsl_suffStats,
# self.hyperparams['M0'],
# self.hyperparams['V0'],)
# bwd_prob = smp.matrix_normal_density(self.model.parameters['F'],
# M,padded_Q,V)
# Kalman filter
ppsl_flt,_,ppsl_lhood = ppsl_model.kalman_filter(self.observ)
# Prior terms
prior = self.transition_prior(self.model)
ppsl_prior = self.transition_prior(ppsl_model)
# print(ppsl_lhood-self.lhood)
# print(ppsl_prior-prior)
# Decide
acceptRatio = (ppsl_lhood-self.lhood) \
+ (ppsl_prior-prior) \
+ (bwd_prob-fwd_prob)
if self.verbose:
print(" Acceptance ratio: {}".format(acceptRatio))
if np.log(np.random.random()) < acceptRatio:
self.model = ppsl_model
self.flt = ppsl_flt
self.lhood = ppsl_lhood
# self.state = ppsl_state
self.chain_accept[moveType].append(True)
if self.verbose:
print(" accepted")
else:
self.chain_accept[moveType].append(False)
if self.verbose:
print(" rejected")
