def make_synthetic_data():
mu_init = np.zeros(D)
# mu_init[0] = 1.0
sigma_init = 0.5*np.eye(D)
A = np.eye(D)
# A[:2,:2] = \
# 0.99*np.array([[np.cos(np.pi/24), -np.sin(np.pi/24)],
# [np.sin(np.pi/24), np.cos(np.pi/24)]])
sigma_states = 0.1*np.eye(D)
# C = np.hstack((np.ones((K-1, 1)), np.zeros((K-1, D-1))))
C = 0. * np.random.randn(K-1, D)
truemodel = MultinomialLDS(K, D,
init_dynamics_distn=Gaussian(mu=mu_init,sigma=sigma_init),
dynamics_distn=AutoRegression(A=A,sigma=sigma_states),
C=C
)
data_list = []
Xs = []
for i in xrange(Ndata):
data = truemodel.generate(T=T, N=N)
data_list.append(data)
Xs.append(data["x"])
return data_list, Xs
def make_synthetic_data():
mu_init = np.zeros(D)
# mu_init[0] = 1.0
sigma_init = 0.5 * np.eye(D)
A = np.eye(D)
# A[:2,:2] = \
# 0.99*np.array([[np.cos(np.pi/24), -np.sin(np.pi/24)],
# [np.sin(np.pi/24), np.cos(np.pi/24)]])
sigma_states = 0.1 * np.eye(D)
# C = np.hstack((np.ones((K-1, 1)), np.zeros((K-1, D-1))))
C = 0. * np.random.randn(K - 1, D)
truemodel = MultinomialLDS(K,
D,
init_dynamics_distn=Gaussian(mu=mu_init,
sigma=sigma_init),
dynamics_distn=AutoRegression(
A=A, sigma=sigma_states),
C=C)
data_list = []
Xs = []
for i in xrange(Ndata):
data = truemodel.generate(T=T, N=N)
data_list.append(data)
Xs.append(data["x"])
return data_list, Xs
sigma_states = 0.1 * np.eye(D)
K = 3
# C = np.hstack((np.ones((K-1, 1)), np.zeros((K-1, D-1))))
C = np.random.randn(K - 1, D)
###################
# generate data #
###################
model = MultinomialLDS(K,
D,
init_dynamics_distn=Gaussian(mu=mu_init,
sigma=sigma_init),
dynamics_distn=AutoRegression(A=A, sigma=sigma_states),
C=C)
data = model.generate(T=T, N=N, keep=False)
# data["x"] = np.hstack([np.zeros((T,K-1)), np.ones((T,1))])
# Estimate the held out likelihood using Monte Carlo
M = 10000
hll_mc, std_mc = model._mc_heldout_log_likelihood(data["x"], M=M)
# Estimate the held out log likelihood
# hll_info, std_info = model._info_form_heldout_log_likelihood(data["x"], M=M)
hll_dist, std_dist = model._distn_form_heldout_log_likelihood(data["x"], M=M)
print("MC. Model: ", hll_mc, " +- ", std_mc)
# print "AN. Model (info): ", hll_info, " +- ", std_info
print("AN. Model (dist): ", hll_dist, " +- ", std_dist)
[np.sin(np.pi/24), np.cos(np.pi/24)]])
sigma_states = 0.1*np.eye(D)
K = 3
# C = np.hstack((np.ones((K-1, 1)), np.zeros((K-1, D-1))))
C = np.random.randn(K-1, D)
###################
# generate data #
###################
model = MultinomialLDS(K, D,
init_dynamics_distn=Gaussian(mu=mu_init,sigma=sigma_init),
dynamics_distn=AutoRegression(A=A,sigma=sigma_states),
C=C
)
data = model.generate(T=T, N=N, keep=False)
# data["x"] = np.hstack([np.zeros((T,K-1)), np.ones((T,1))])
# Estimate the held out likelihood using Monte Carlo
M = 10000
hll_mc, std_mc = model._mc_heldout_log_likelihood(data["x"], M=M)
# Estimate the held out log likelihood
# hll_info, std_info = model._info_form_heldout_log_likelihood(data["x"], M=M)
hll_dist, std_dist = model._distn_form_heldout_log_likelihood(data["x"], M=M)
print("MC. Model: ", hll_mc, " +- ", std_mc)
# print "AN. Model (info): ", hll_info, " +- ", std_info
print("AN. Model (dist): ", hll_dist, " +- ", std_dist)
C = np.random.randn(K - 1, D)
sigma_obs = 0.01 * np.eye(K)
###################
# generate data #
###################
truemodel = MultinomialLDS(K,
D,
init_dynamics_distn=Gaussian(mu=mu_init,
sigma=sigma_init),
dynamics_distn=AutoRegression(A=A,
sigma=sigma_states),
C=C)
data = truemodel.generate(T=T)
###################
# inference #
###################
testmodel = MultinomialLDS(K,
D,
init_dynamics_distn=Gaussian(mu_0=mu_init,
sigma_0=sigma_init,
kappa_0=1.0,
nu_0=3.0),
dynamics_distn=AutoRegression(nu_0=D + 1,
S_0=np.eye(D),
M_0=np.zeros((D, D)),
K_0=np.eye(D)),
sigma_C=1)
K = 4
# C = np.hstack((np.ones((K-1, 1)), np.zeros((K-1, D-1))))
C = np.random.randn(K-1, D)
sigma_obs = 0.01 * np.eye(K)
###################
# generate data #
###################
truemodel = MultinomialLDS(K, D,
init_dynamics_distn=Gaussian(mu=mu_init,sigma=sigma_init),
dynamics_distn=AutoRegression(A=A,sigma=sigma_states),
C=C
)
data = truemodel.generate(T=T)
###################
# inference #
###################
testmodel = MultinomialLDS(K, D,
init_dynamics_distn=Gaussian(mu_0=mu_init, sigma_0=sigma_init, kappa_0=1.0, nu_0=3.0),
dynamics_distn=AutoRegression(nu_0=D+1,S_0=np.eye(D),M_0=np.zeros((D,D)),K_0=np.eye(D)),
sigma_C=1
)
testmodel.add_data(data["x"])
testdata = testmodel.data_list[0]
N_samples = 100
