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_covariance_within_subspace(model, state, hyperparams, pseudo_dof=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 = smp.hyperparam_update_degenerate_iw_transition_covariance(
suffStats, U,
model.parameters['F'],
nu0,
Psi0)
D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
# Convert back to eigen-decomposition form
model.update_from_givens_form(U, D)
return model
def sample_transition_covariance_within_subspace(model,
state,
hyperparams,
pseudo_dof=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 = smp.hyperparam_update_degenerate_iw_transition_covariance(
suffStats, U, model.parameters['F'], nu0, Psi0)
D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
# 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_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(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_ncvm_covariance(self):
"""
MCMC iteration (Gibbs sampling) for diagonal observation covariance
matrix with inverse-gamma prior
"""
# Calculate sufficient statistics using current state trajectory
suffStats = smp.evaluate_transition_sufficient_statistics(self.state)
# Update hyperparameters
Qs = self.model.parameters['Q']
Qs /= Qs[0,0]
a,b = smp.hyperparam_update_ncvm_ig_transition_variance(
suffStats,
self.model.parameters['F'],
Qs,
self.hyperparams['a0'],
self.hyperparams['b0']) # This uses the same hyperparameters as the observation variance because I'm lazy and want to go to bed.
# Sample new parameter
s = stats.invgamma.rvs(a, scale=b)
self.model.parameters['Q'] = s*Qs
# self.flt and self.lhood are no longer up-to-date
self.filter_current = False
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_ncvm_covariance(self):
"""
MCMC iteration (Gibbs sampling) for diagonal observation covariance
matrix with inverse-gamma prior
"""
# Calculate sufficient statistics using current state trajectory
suffStats = smp.evaluate_transition_sufficient_statistics(self.state)
# Update hyperparameters
Qs = self.model.parameters['Q']
Qs /= Qs[0, 0]
a, b = smp.hyperparam_update_ncvm_ig_transition_variance(
suffStats, self.model.parameters['F'], Qs, self.hyperparams['a0'],
self.hyperparams['b0']
) # This uses the same hyperparameters as the observation variance because I'm lazy and want to go to bed.
# Sample new parameter
s = stats.invgamma.rvs(a, scale=b)
self.model.parameters['Q'] = s * Qs
# self.flt and self.lhood are no longer up-to-date
self.filter_current = False