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 fit_lds_model(Xs, Xtest, D, N_samples=100):
model = MultinomialLDS(K,
D,
init_dynamics_distn=GaussianFixed(mu=np.zeros(D),
sigma=1 *
np.eye(D)),
dynamics_distn=AutoRegression(nu_0=D + 1,
S_0=1 * np.eye(D),
M_0=np.zeros((D, D)),
K_0=1 * np.eye(D)),
sigma_C=0.01)
for X in Xs:
model.add_data(X)
model.resample_parameters()
init_results = (0, model, model.log_likelihood(),
model.heldout_log_likelihood(Xtest, M=1),
model.predictive_log_likelihood(Xtest, M=1000))
def resample():
tic = time.time()
model.resample_model()
toc = time.time() - tic
return toc, None, model.log_likelihood(), \
model.heldout_log_likelihood(Xtest, M=1), \
model.predictive_log_likelihood(Xtest, M=1000)
times, samples, lls, test_lls, pred_lls = \
map(np.array, zip(*([init_results] + [resample() for _ in progprint_xrange(N_samples)])))
timestamps = np.cumsum(times)
return Results(lls, test_lls, pred_lls, samples, timestamps)
def fit_lds_model(Xs, Xtest, D, N_samples=100):
Nx = len(Xs)
assert len(Xtest) == Nx
mus = [X.sum(0) + 0.1 for X in Xs]
mus = [mu / mu.sum() for mu in mus]
# mus = [np.ones(K)/float(K) for _ in Xs]
models = [
MultinomialLDS(K,
D,
init_dynamics_distn=GaussianFixed(mu=np.zeros(D),
sigma=1 * np.eye(D)),
dynamics_distn=AutoRegression(nu_0=D + 1,
S_0=1 * np.eye(D),
M_0=np.zeros((D, D)),
K_0=1 * np.eye(D)),
sigma_C=1.,
mu_pi=mus[i]) for i in xrange(Nx)
]
for X, model in zip(Xs, models):
model.add_data(X)
[model.resample_parameters() for model in models]
def compute_pred_ll():
pred_ll = 0
for Xt, model in zip(Xtest, models):
pred_ll += model.predictive_log_likelihood(Xt, M=1)[0]
return pred_ll
init_results = (0, models, np.nan, np.nan, compute_pred_ll())
def resample():
tic = time.time()
[model.resample_model() for model in models]
toc = time.time() - tic
return toc, None, np.nan, np.nan, compute_pred_ll()
times, samples, lls, test_lls, pred_lls = \
map(np.array, zip(*([init_results] +
[resample() for _ in progprint_xrange(N_samples, perline=5)])))
timestamps = np.cumsum(times)
return Results(lls, test_lls, pred_lls, samples, timestamps)
def fit_lds_model(Xs, Xtest, D, N_samples=100):
Nx = len(Xs)
assert len(Xtest) == Nx
model = MultinomialLDS(K,
D,
init_dynamics_distn=GaussianFixed(mu=np.zeros(D),
sigma=1 *
np.eye(D)),
dynamics_distn=AutoRegression(nu_0=D + 1,
S_0=1 * np.eye(D),
M_0=np.zeros((D, D)),
K_0=1 * np.eye(D)),
sigma_C=1.)
for X in Xs:
model.add_data(X)
model.resample_parameters()
compute_pred_ll = lambda: sum([
model.predictive_log_likelihood(Xt, data_index=i, M=10)[0]
for i, Xt in enumerate(Xtest)
])
init_results = (
0,
None,
model.log_likelihood(),
# model.heldout_log_likelihood(Xtest, M=1),
np.nan,
compute_pred_ll())
def resample():
tic = time.time()
model.resample_model()
toc = time.time() - tic
return toc, None, model.log_likelihood(), \
np.nan,\
compute_pred_ll()
times, samples, lls, test_lls, pred_lls = \
list(map(np.array, list(zip(*([init_results] +
[resample() for _ in progprint_xrange(N_samples, perline=5)])))))
timestamps = np.cumsum(times)
return Results(lls, test_lls, pred_lls, samples, timestamps)
def fit_lds_model(Xs, Xtest, N_samples=100):
model = MultinomialLDS(K,
D,
init_dynamics_distn=Gaussian(mu_0=np.zeros(D),
sigma_0=np.eye(D),
kappa_0=1.0,
nu_0=D + 1.0),
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)
for X in Xs:
model.add_data(X)
data = model.data_list[0]
samples = []
lls = []
test_lls = []
mc_test_lls = []
pis = []
psis = []
zs = []
timestamps = [time.time()]
for smpl in progprint_xrange(N_samples):
model.resample_model()
timestamps.append(time.time())
samples.append(model.copy_sample())
# TODO: Use log_likelihood() to marginalize over z
lls.append(model.log_likelihood())
# test_lls.append(model.heldout_log_likelihood(Xtest, M=50)[0])
mc_test_lls.append(model._mc_heldout_log_likelihood(Xtest, M=1)[0])
pis.append(model.pi(data))
psis.append(model.psi(data))
zs.append(data["states"].stateseq)
lls = np.array(lls)
test_lls = np.array(test_lls)
pis = np.array(pis)
psis = np.array(psis)
zs = np.array(zs)
timestamps = np.array(timestamps)
timestamps -= timestamps[0]
return model, lls, test_lls, mc_test_lls, pis, psis, zs, timestamps
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)
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
np.cos(np.pi / 24)]])
sigma_states = 0.0001 * np.eye(D)
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),