def setUp(self):
# Basic parameters
self.K = 100
self.ds = 3
self.do = 3
# System matrices
params = dict()
params['F'] = np.array([[0.9, 0.8, 0.7], [0, 0.9, 0.8], [0, 0, 0.7]])
params['rank'] = np.array([2])
params['vec'] = (1. / np.sqrt(3)) * np.array([[1, 1], [1, 1], [1, -1]])
params['val'] = np.array([1. / 5, 1. / 2])
params['H'] = np.identity(self.do)
params['R'] = 0.1 * np.identity(self.do)
self.params = params
# Create model
prior = GaussianDensity(np.zeros(self.ds), np.identity(self.ds))
self.model = DegenerateLinearModel(self.ds, self.do, prior,
self.params)
# Simulate data
np.random.seed(1)
self.state, self.observ = self.model.simulate_data(self.K)
# Create initial estimated model
est_params = dict()
est_params['F'] = 0.5 * np.identity(self.ds)
est_params['rank'] = np.array([2])
est_params['vec'] = np.array([[1.0, 0.0], [0.0, 1.0], [0.0, 0.0]])
est_params['val'] = np.array([1, 1])
est_params['H'] = np.identity(self.do)
est_params['R'] = np.identity(self.do)
est_model = DegenerateLinearModel(self.ds, self.do, prior, est_params)
self.est_model = est_model
# Set MCMC parameters
self.num_iter = 2000
self.num_burn = int(self.num_iter / 5)
class DegenerateModelLearningTestCase(unittest.TestCase):
def setUp(self):
# Basic parameters
self.K = 100
self.ds = 3
self.do = 3
# System matrices
params = dict()
params['F'] = np.array([[0.9,0.8,0.7],[0,0.9,0.8],[0,0,0.7]])
params['rank'] = np.array([2])
params['vec'] = (1./np.sqrt(3))*np.array([[1,1],[1,1],[1,-1]])
params['val'] = np.array([1./5,1./2])
params['H'] = np.identity(self.do)
params['R'] = 0.1*np.identity(self.do)
self.params = params
# Create model
prior = GaussianDensity(np.zeros(self.ds), np.identity(self.ds))
self.model = DegenerateLinearModel(self.ds, self.do, prior,
self.params)
# Simulate data
np.random.seed(1)
self.state, self.observ = self.model.simulate_data(self.K)
# Create initial estimated model
est_params = dict()
est_params['F'] = 0.5*np.identity(self.ds)
est_params['rank'] = np.array([2])
est_params['vec'] = np.array([[1.0,0.0],[0.0,1.0],[0.0,0.0]])
est_params['val'] = np.array([1,1])
est_params['H'] = np.identity(self.do)
est_params['R'] = np.identity(self.do)
est_model = DegenerateLinearModel(self.ds, self.do, prior, est_params)
self.est_model = est_model
# Set MCMC parameters
self.num_iter = 2000
self.num_burn = int(self.num_iter/5)
num_burn = int(num_iter/2)
ds = 4
do = 4
params = dict()
params['F'] = np.array([[0.95,0.8,0.8,0.0],[0,0.95,-0.5,0.1],[0,0,1.6,-0.8],[0.0,0.0,1.0,0.0]])
params['rank'] = np.array([2])
params['val'] = np.array([1.5,0.5])
params['vec'] = np.array([[0.5,0.5,0.5,0.5],[1.0/np.sqrt(2),-1.0/np.sqrt(2),0.0,0.0]]).T
params['Q'] = np.dot(params['vec'], np.dot(np.diag(params['val']), params['vec'].T))
params['H'] = np.identity(do)
params['R'] = 0.03*np.identity(do)
prior = GaussianDensity(np.zeros(ds), 10*np.identity(ds))
model = DegenerateLinearModel(ds, do, prior, params)
state, observ = model.simulate_data(K)
# Draw it
fig, axs = plt.subplots(nrows=ds,ncols=1)
for dd in range(ds):
axs[dd].plot(observ[:,dd])
# Save the data
fh = open(test_data_file, 'wb')
pickle.dump([model, state, observ], fh)
fh.close()
est_params = deepcopy(params)
est_params['F'] = 0.5*np.identity(ds)
est_params['rank'] = np.array([4])
def smc_reduce_rank(self, rank):
"""
The main step of the algorithm. Use the previous approximation to
'propose' parameters for a reduced rank mode, and weight them
correctly.
"""
# Create a new SMC approximation
if rank in self.approx.keys():
raise ValueError("Already done that one")
if rank + 1 not in self.approx.keys():
raise ValueError("Need to do rank {} first.".format(rank + 1))
self.approx[rank] = DegenerateModelSMCApproximation(
self.num_samples, self.ds, rank)
# Create space to store the state trajectories
self.state[rank] = np.zeros(
(self.num_samples, self.num_rejuv, self.K, self.ds))
# Create a store for the filter results for RM in the next iteration
filters = []
# Resampling
w = self.approx[rank + 1].weight.copy()
w -= np.max(w)
w = np.exp(w)
w /= np.sum(w)
ancestors = np.random.choice(self.num_samples,
size=self.num_samples,
replace=True,
p=w)
self.approx[rank].ancestor = ancestors
# Loop through samples
for nn in range(self.num_samples):
if self.verbose:
print("Sample number {}.".format(nn + 1))
# Create model object
ai = ancestors[nn]
parameters = {
'F': self.approx[rank + 1].F[ai, :, :].copy(),
'rank': [rank + 1],
'val': self.approx[rank + 1].val[ai, :].copy(),
'vec': self.approx[rank + 1].vec[ai, :, :].copy(),
'H': self.H,
'R': self.approx[rank + 1].Rs[ai].copy() * np.identity(self.do)
}
model = DegenerateLinearModel(self.ds, self.do,
self.initial_state_prior, parameters)
# Resample-move with Gibbs sampling to improve diversity
if (self.filters is not None) and (self.num_rejuv > 0):
flt = self.filters[ai]
for ii in range(self.num_rejuv):
state = model.backward_simulation(flt)
model = sample_transition_within_subspace(
model, state, self.hyperparams)
model = sample_observation_diagonal_covariance(
model, state, self.observ, self.hyperparams)
flt, _, old_lhood = model.kalman_filter(self.observ)
self.state[rank][nn, ii, :, :] = state
old_prior = transition_prior(rank, model.parameters['val'],
model.parameters['vec'],
model.parameters['F'],
self.hyperparams)
else:
old_prior = self.approx[rank + 1].prior[ai]
old_lhood = self.approx[rank + 1].lhood[ai]
# Remove smallest eigenvalue/vector pair
remVal, remVec = model.remove_min_eigen_value_vector()
# Probabilities for new model
prior = transition_prior(rank, model.parameters['val'],
model.parameters['vec'],
model.parameters['F'], self.hyperparams)
flt, _, lhood = model.kalman_filter(self.observ)
exten = extended_density(remVal, remVec, model.parameters['val'])
# Jacobian of transformation
jac = - np.log(2) \
- np.sum(np.log(model.parameters['val'])) \
+ (self.ds - rank - 1)*np.log(remVal) \
+ np.sum(np.log(model.parameters['val']-remVal))
# Calculate weight
weight = + prior \
+ lhood \
- old_prior \
- old_lhood \
- jac \
+ exten
# print(lhood-old_lhood)
# print(prior-old_prior)
# print(exten)
# print(jac)
if self.verbose:
print("Particle log-weight: {}".format(weight))
# Store everything
filters.append(flt)
self.approx[rank].prior[nn] = prior
self.approx[rank].lhood[nn] = lhood
self.approx[rank].weight[nn] = weight
self.approx[rank].F[nn, :, :] = model.parameters['F'].copy()
self.approx[rank].val[nn] = model.parameters['val'].copy()
self.approx[rank].vec[nn] = model.parameters['vec'].copy()
self.approx[rank].Rs[nn] = model.parameters['R'][0][0]
# End of particle loop
# Save the filter results for later
self.filters = filters
if self.verbose:
print("For rank {}, effective sample size: {}".format(
rank, effective_sample_size(self.approx[rank].weight)))
filename = './results/toy-mcmc-degenerate.p' K = 100 ds = 3 do = 3 params = dict() params['F'] = np.array([[0.9, 0.8, 0.7], [0, 0.9, 0.8], [0, 0, 0.7]]) params['rank'] = np.array([2]) params['vec'] = (1. / np.sqrt(3)) * np.array([[1, 1], [1, 1], [1, -1]]) params['val'] = np.array([1. / 5, 1. / 2]) params['H'] = np.identity(do) params['R'] = 0.1 * np.identity(do) prior = GaussianDensity(np.zeros(ds), 100 * np.identity(ds)) model = DegenerateLinearModel(ds, do, prior, params) np.random.seed(0) state, observ = model.simulate_data(K) est_params = deepcopy(params) est_params['F'] = 0.5 * np.identity(ds) est_params['rank'] = np.array([2]) est_params['vec'] = np.array([[1, 0], [0, 1], [0, 0]]) est_params['val'] = np.array([1, 1]) est_params['R'] = np.identity(do) est_model = DegenerateLinearModel(ds, do, prior, est_params) hyperparams = dict() hyperparams['nu0'] = params['rank'] hyperparams['rPsi0'] = np.identity(ds)
def smc_reduce_rank(self, rank):
"""
The main step of the algorithm. Use the previous approximation to
'propose' parameters for a reduced rank mode, and weight them
correctly.
"""
# Create a new SMC approximation
if rank in self.approx.keys():
raise ValueError("Already done that one")
if rank+1 not in self.approx.keys():
raise ValueError("Need to do rank {} first.".format(rank+1))
self.approx[rank] = DegenerateModelSMCApproximation(self.num_samples,
self.ds, rank)
# Create space to store the state trajectories
self.state[rank] = np.zeros((self.num_samples,
self.num_rejuv,
self.K,
self.ds))
# Create a store for the filter results for RM in the next iteration
filters = []
# Resampling
w = self.approx[rank+1].weight.copy()
w -= np.max(w)
w = np.exp(w)
w /= np.sum(w)
ancestors = np.random.choice(self.num_samples,
size=self.num_samples,
replace=True,
p=w)
self.approx[rank].ancestor = ancestors
# Loop through samples
for nn in range(self.num_samples):
if self.verbose:
print("Sample number {}.".format(nn+1))
# Create model object
ai = ancestors[nn]
parameters = {
'F': self.approx[rank+1].F[ai,:,:].copy(),
'rank': [rank+1],
'val': self.approx[rank+1].val[ai,:].copy(),
'vec': self.approx[rank+1].vec[ai,:,:].copy(),
'H': self.H,
'R': self.approx[rank+1].Rs[ai].copy()*np.identity(self.do)
}
model = DegenerateLinearModel(self.ds,
self.do,
self.initial_state_prior,
parameters)
# Resample-move with Gibbs sampling to improve diversity
if (self.filters is not None) and (self.num_rejuv > 0):
flt = self.filters[ai]
for ii in range(self.num_rejuv):
state = model.backward_simulation(flt)
model = sample_transition_within_subspace(model, state,
self.hyperparams)
model = sample_observation_diagonal_covariance(
model,
state,
self.observ,
self.hyperparams)
flt,_,old_lhood = model.kalman_filter(self.observ)
self.state[rank][nn,ii,:,:] = state
old_prior = transition_prior(rank,
model.parameters['val'],
model.parameters['vec'],
model.parameters['F'],
self.hyperparams)
else:
old_prior = self.approx[rank+1].prior[ai]
old_lhood = self.approx[rank+1].lhood[ai]
# Remove smallest eigenvalue/vector pair
remVal, remVec = model.remove_min_eigen_value_vector()
# Probabilities for new model
prior = transition_prior(rank,
model.parameters['val'],
model.parameters['vec'],
model.parameters['F'],
self.hyperparams)
flt,_,lhood = model.kalman_filter(self.observ)
exten = extended_density(remVal, remVec, model.parameters['val'])
# Jacobian of transformation
jac = - np.log(2) \
- np.sum(np.log(model.parameters['val'])) \
+ (self.ds - rank - 1)*np.log(remVal) \
+ np.sum(np.log(model.parameters['val']-remVal))
# Calculate weight
weight = + prior \
+ lhood \
- old_prior \
- old_lhood \
- jac \
+ exten
# print(lhood-old_lhood)
# print(prior-old_prior)
# print(exten)
# print(jac)
if self.verbose:
print("Particle log-weight: {}".format(weight))
# Store everything
filters.append(flt)
self.approx[rank].prior[nn] = prior
self.approx[rank].lhood[nn] = lhood
self.approx[rank].weight[nn] = weight
self.approx[rank].F[nn,:,:] = model.parameters['F'].copy()
self.approx[rank].val[nn] = model.parameters['val'].copy()
self.approx[rank].vec[nn] = model.parameters['vec'].copy()
self.approx[rank].Rs[nn] = model.parameters['R'][0][0]
# End of particle loop
# Save the filter results for later
self.filters = filters
if self.verbose:
print("For rank {}, effective sample size: {}".format(rank,
effective_sample_size(self.approx[rank].weight)))
est_params['F'] = np.vstack((np.hstack((Imat,Imat)), np.hstack((Zmat,Imat)))) est_params['Q'] = 0.001*np.vstack((np.hstack((Imat/3.0,Imat/2.0)), np.hstack((Imat/2.0,Imat/1.0)))) est_params['val'], est_params['vec'] = la.eigh(est_params['Q']) est_params['rank'] = np.array([ds]) #val,vec = la.eigh(est_params['Q']) #est_params['val'] = val[:1] #est_params['vec'] = vec[:,:1] #est_params['rank'] = np.array([1]) est_params['H'] = np.hstack((np.identity(d),np.zeros((d,d)))) est_params['R'] = 0.001*np.identity(d) prior = GaussianDensity(np.zeros(ds), 1000*np.identity(ds)) est_degenerate_model = DegenerateLinearModel(ds, do, prior, est_params) est_basic_model = BasicLinearModel(ds, do, prior, est_params) est_naive_model = BasicLinearModel(ds, do, prior, est_params) # Hyperparameters hyperparams = dict() hyperparams['nu0'] = ds hyperparams['rPsi0'] = 0.001*np.identity(ds) hyperparams['Psi0'] = ds*hyperparams['rPsi0'] hyperparams['M0'] = np.zeros((ds,ds)) hyperparams['V0'] = 1E2*np.identity(ds) hyperparams['alpha'] = 0.01 hyperparams['a0'] = 1 hyperparams['b0'] = 0.001 # Algorithm parameters
