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['Q'] = np.array([[0.1,0.05,0],[0.05,0.1,0.05],[0,0.05,0.1]])
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 = BasicLinearModel(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['Q'] = np.identity(self.ds)
est_params['H'] = np.identity(self.do)
est_params['R'] = np.identity(self.do)
est_model = BasicLinearModel(self.ds, self.do, prior, est_params)
self.est_model = est_model
# Set MCMC parameters
self.num_iter = 200
self.num_burn = int(self.num_iter/5)
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['Q'] = np.array([[0.1, 0.05, 0], [0.05, 0.1, 0.05],
[0, 0.05, 0.1]])
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 = BasicLinearModel(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['Q'] = np.identity(self.ds)
est_params['H'] = np.identity(self.do)
est_params['R'] = np.identity(self.do)
est_model = BasicLinearModel(self.ds, self.do, prior, est_params)
self.est_model = est_model
# Set MCMC parameters
self.num_iter = 200
self.num_burn = int(self.num_iter / 5)
def setUp(self):
# Basic parameters
self.K = 10
self.ds = 2
self.do = 1
# System matrices
params = dict()
params['F'] = np.array([[0.9,0.81],[0,0.9]])
params['Q'] = np.array([[1,0],[0,1]])
params['H'] = np.array([[1,0]])
params['R'] = np.array([[1]])
# Create model
prior = GaussianDensity(np.array([0,0]), np.array([[100,0],[0,100]]))
self.model = BasicLinearModel(self.ds, self.do, prior, params)
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 algoparams = dict()
from learners_mcmc import MCMCLearnerForBasicModelWithMNIWPrior
plt.close('all')
K = 10
ds = 2
do = 1
params = dict()
params['F'] = np.array([[0.9,0.81],[0,0.9]])
params['Q'] = np.array([[1,0],[0,1]])
params['H'] = np.array([[1,0]])
params['R'] = np.array([[1]])
prior = GaussianDensity(np.array([0,0]), np.array([[100,0],[0,100]]))
model = BasicLinearModel(ds, do, prior, params)
np.random.seed(0)
state, observ = model.simulate_data(K)
fig = plt.figure()
for dd in range(ds):
ax = fig.add_subplot(ds,1,dd+1)
ax.plot(state[:,dd])
fig = plt.figure()
for dd in range(do):
ax = fig.add_subplot(do,1,dd+1)
ax.plot(observ[:,dd])
hyperparams['rPsi0'] = np.identity(ds)
hyperparams['Psi0'] = hyperparams['nu0'] * hyperparams['rPsi0']
hyperparams['alpha'] = 1
hyperparams['M0'] = np.zeros((ds, ds))
hyperparams['V0'] = 100 * np.identity(ds)
hyperparams['a0'] = 1
hyperparams['b0'] = hyperparams['a0'] * 0.1
algoparams = dict()
algoparams['rotate'] = 1E-2
algoparams['perturb'] = 1E-6
# Learning
if model_type == 'basic':
est_model = BasicLinearModel(ds, do, prior, est_params)
learner = MCMCLearnerB(est_model,
observ,
hyperparams,
algoparams=algoparams,
verbose=True)
for ii in range(num_iter):
print("Running iteration {} of {}.".format(ii + 1, num_iter))
learner.sample_transition()
learner.sample_observation_diagonal_covariance()
learner.sample_state_trajectory()
learner.save_link()
elif model_type == 'degenerate':
plt.close('all')
filename = './results/toy-mcmc-basic.p'
K = 200
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]]) #0.9*np.identity(ds)#
params['Q'] = np.array([[0.1, 0.05, 0], [0.05, 0.1, 0.05], [0, 0.05, 0.1]])
params['H'] = np.identity(do) #np.array([[1,0,0],[0,1,0]])#
params['R'] = 0.1 * np.identity(do) #np.array([[1]])
prior = GaussianDensity(np.zeros(ds), 100 * np.identity(ds))
model = BasicLinearModel(ds, do, prior, params)
np.random.seed(1)
state, observ = model.simulate_data(K)
est_params = deepcopy(params)
est_params['F'] = 0.5 * np.identity(ds)
est_params['Q'] = np.identity(ds)
est_params['R'] = np.identity(do)
est_model = BasicLinearModel(ds, do, prior, est_params)
hyperparams = dict()
hyperparams['nu0'] = ds - 1
hyperparams['Psi0'] = hyperparams['nu0'] * 0.1 * np.identity(ds)
hyperparams['M0'] = np.zeros((ds, ds))
hyperparams['V0'] = np.identity(ds)
