def simulate_prior():
# Account for stick breaking asymmetry
mu_b, _ = compute_psi_cmoments(np.ones(K_true))
init_dynamics_distns = [
Gaussian(mu=np.array([-0, -0]), sigma=5 * np.eye(D_latent))
for _ in range(K)
]
dynamics_distns = make_dynamics_distns()
emission_distns = \
DiagonalRegression(D_obs, D_latent+1,
alpha_0=2.0, beta_0=2.0)
model = PGRecurrentSLDS(trans_params=dict(sigmasq_A=10., sigmasq_b=0.01),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
dynamics_distns=dynamics_distns,
emission_distns=emission_distns)
# Print the true parameters
np.set_printoptions(precision=2)
print("True W_markov:\n{}".format(model.trans_distn.A[:, :K_true]))
print("True W_input:\n{}".format(model.trans_distn.A[:, K_true:]))
return model
def __init__(self,
D_obs,
D_latent,
W=None,
sigmasq=None,
sigmasq_W_0=1.0,
mu_W_0=0.0,
alpha_0=3.0,
beta_0=2.0):
self.D_obs, self.D_latent = D_obs, D_latent
# The weights and variances are encapsulated in a DiagonalRegression class
self.regression = \
DiagonalRegression(
self.D_obs, self.D_latent,
mu_0=mu_W_0 * np.ones(self.D_latent),
Sigma_0=sigmasq_W_0 * np.eye(self.D_latent),
alpha_0=alpha_0, beta_0=beta_0,
A=W, sigmasq=sigmasq)
# Handle the mean separately since DiagonalRegression doesn't support affine :-/
self.mean = np.zeros(D_obs)
self.data_list = []
def make_rslds_parameters(C_init):
init_dynamics_distns = [
Gaussian(
mu=np.zeros(D_latent),
sigma=np.eye(D_latent),
nu_0=D_latent + 2, sigma_0=3. * np.eye(D_latent),
mu_0=np.zeros(D_latent), kappa_0=1.0,
)
for _ in range(args.K)]
dynamics_distns = [
Regression(
nu_0=D_latent + 2,
S_0=1e-4 * np.eye(D_latent),
M_0=np.hstack((np.eye(D_latent), np.zeros((D_latent, 1)))),
K_0=np.eye(D_latent + 1),
)
for _ in range(args.K)]
emission_distns = \
DiagonalRegression(args.D_obs, D_latent + 1,
A=C_init.copy(), sigmasq=np.ones(args.D_obs),
alpha_0=2.0, beta_0=2.0)
return init_dynamics_distns, dynamics_distns, emission_distns
def sample_slds_model():
mu_init = np.zeros(D_latent)
mu_init[0] = 2.0
sigma_init = 0.01 * np.eye(D_latent)
def random_rotation(n, theta):
rot = 0.99 * np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
out = np.zeros((n, n))
out[:2, :2] = rot
q = np.linalg.qr(np.random.randn(n, n))[0]
return q.dot(out).dot(q.T)
def random_dynamics(n):
A = np.random.randn(n,n)
A = A.dot(A.T)
U,S,V = np.linalg.svd(A)
A_stable = U.dot(np.diag(S/(1.1*np.max(S)))).dot(V.T)
# A_stable = U.dot(0.99 * np.eye(n)).dot(V.T)
return A_stable
ths = np.linspace(0, np.pi/8., K)
As = [random_rotation(D_latent, ths[k]) for k in range(K)]
# As = [random_dynamics(D_latent) for k in range(K)]
bs = [np.zeros((D_latent, 1))] + [.25 * np.random.randn(D_latent, 1) for k in range(K-1)]
C = np.random.randn(D_obs, D_latent)
d = np.zeros((D_obs, 1))
sigma_obs = 0.5 * np.ones(D_obs)
###################
# generate data #
###################
init_dynamics_distns = [Gaussian(mu=mu_init, sigma=sigma_init) for _ in range(K)]
dynamics_distns = [Regression(A=np.hstack((A, b)), sigma=0.01 * np.eye(D_latent)) for A,b in zip(As, bs)]
emission_distns = DiagonalRegression(D_obs, D_latent+1, A=np.hstack((C, d)), sigmasq=sigma_obs)
slds = HMMSLDS(
dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
init_dynamics_distns=init_dynamics_distns,
alpha=3., init_state_distn='uniform')
#### MANUALLY CREATE DATA
P = np.ones((K,K)) + 1 * np.eye(K)
P = P / np.sum(P,1,keepdims=True)
z = np.zeros(T//D, dtype=np.int32)
for t in range(1,T//D):
z[t] = np.random.choice(np.arange(K), p=P[z[t-1]])
z = np.repeat(z, D)
statesobj = slds._states_class(model=slds, T=z.size, stateseq=z, inputs=np.ones((z.size, 1)))
statesobj.generate_gaussian_states()
y = statesobj.data = statesobj.generate_obs()
x = statesobj.gaussian_states
slds.states_list.append(statesobj)
return z,x,y,slds
def make_rslds_parameters(C_init):
init_dynamics_distns = [
Gaussian(
mu=np.zeros(D_latent),
sigma=3 * np.eye(D_latent),
nu_0=D_latent + 2,
sigma_0=3. * np.eye(D_latent),
mu_0=np.zeros(D_latent),
kappa_0=1.0,
) for _ in range(K)
]
ths = np.random.uniform(np.pi / 30., 1.0, size=K)
As = [random_rotation(D_latent, th) for th in ths]
As = [np.hstack((A, np.ones((D_latent, 1)))) for A in As]
dynamics_distns = [
Regression(
A=As[k],
sigma=np.eye(D_latent),
nu_0=D_latent + 1000,
S_0=np.eye(D_latent),
M_0=np.hstack((np.eye(D_latent), np.zeros((D_latent, 1)))),
K_0=np.eye(D_latent + 1),
) for k in range(K)
]
if C_init is not None:
emission_distns = \
DiagonalRegression(D_obs, D_latent + 1,
A=C_init.copy(), sigmasq=np.ones(D_obs),
alpha_0=2.0, beta_0=2.0)
else:
emission_distns = \
DiagonalRegression(D_obs, D_latent + 1,
alpha_0=2.0, beta_0=2.0)
return init_dynamics_distns, dynamics_distns, emission_distns
def __init__(self, D_obs, D_latent,
W=None, sigmasq=None,
sigmasq_W_0=1.0, mu_W_0=0.0,
alpha_0=3.0, beta_0=2.0):
self.D_obs, self.D_latent = D_obs, D_latent
# The weights and variances are encapsulated in a DiagonalRegression class
self.regression = \
DiagonalRegression(
self.D_obs, self.D_latent,
mu_0=mu_W_0 * np.ones(self.D_latent),
Sigma_0=sigmasq_W_0 * np.eye(self.D_latent),
alpha_0=alpha_0, beta_0=beta_0,
A=W, sigmasq=sigmasq)
self.data_list = []
D_latent = 2
D_input = 0
T = 2000
# Simulate from an LDS with diagonal observation noise
truemodel = DefaultLDS(D_obs, D_latent, D_input, sigma_obs=0.1 * np.eye(D_obs))
inputs = np.random.randn(T, D_input)
data, stateseq = truemodel.generate(T, inputs=inputs)
# Fit with an LDS with diagonal observation noise
diag_model = LDS(dynamics_distn=Regression(
nu_0=D_latent + 2,
S_0=D_latent * np.eye(D_latent),
M_0=np.zeros((D_latent, D_latent + D_input)),
K_0=(D_latent + D_input) * np.eye(D_latent + D_input)),
emission_distn=DiagonalRegression(D_obs, D_latent + D_input))
diag_model.add_data(data, inputs=inputs)
# Also fit a model with a full covariance matrix
full_model = DefaultLDS(D_obs, D_latent, D_input)
full_model.add_data(data, inputs=inputs)
# Fit with Gibbs sampling
def update(model):
model.resample_model()
return model.log_likelihood()
N_steps = 100
diag_lls = [update(diag_model) for _ in progprint_xrange(N_steps)]
def simulate_nascar():
assert K_true == 4
def random_rotation(n, theta):
rot = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
out = np.zeros((n,n))
out[:2,:2] = rot
q = np.linalg.qr(np.random.randn(n,n))[0]
# q = np.eye(n)
return q.dot(out).dot(q.T)
As = [random_rotation(D_latent, np.pi/24.),
random_rotation(D_latent, np.pi/48.)]
# Set the center points for each system
centers = [np.array([+2.0, 0.]),
np.array([-2.0, 0.])]
bs = [-(A - np.eye(D_latent)).dot(center) for A, center in zip(As, centers)]
# Add a "right" state
As.append(np.eye(D_latent))
bs.append(np.array([+0.1, 0.]))
# Add a "right" state
As.append(np.eye(D_latent))
bs.append(np.array([-0.35, 0.]))
# Construct multinomial regression to divvy up the space #
w1, b1 = np.array([+1.0, 0.0]), np.array([-2.0]) # x + b > 0 -> x > -b
w2, b2 = np.array([-1.0, 0.0]), np.array([-2.0]) # -x + b > 0 -> x < b
w3, b3 = np.array([0.0, +1.0]), np.array([0.0]) # y > 0
reg_W = np.row_stack((w1, w2, w3))
reg_b = np.row_stack((b1, b2, b3))
# Scale the weights to make the transition boundary sharper
reg_scale = 100.
reg_b *= reg_scale
reg_W *= reg_scale
# Account for stick breaking asymmetry
mu_b, _ = compute_psi_cmoments(np.ones(K_true))
reg_b += mu_b[:,None]
# Make a recurrent SLDS with these params #
dynamics_distns = [
Regression(
A=np.column_stack((A,b)),
sigma=1e-4 * np.eye(D_latent),
nu_0=D_latent + 2,
S_0=1e-4 * np.eye(D_latent),
M_0=np.zeros((D_latent, D_latent + 1)),
K_0=np.eye(D_latent + 1),
)
for A,b in zip(As, bs)]
init_dynamics_distns = [
Gaussian(
mu=np.array([0.0, 1.0]),
sigma=1e-3 * np.eye(D_latent))
for _ in range(K_true)]
C = np.hstack((npr.randn(args.D_obs, D_latent), np.zeros((args.D_obs, 1))))
emission_distns = \
DiagonalRegression(args.D_obs, D_latent+1,
A=C, sigmasq=1e-5 *np.ones(args.D_obs),
alpha_0=2.0, beta_0=2.0)
model = PGRecurrentSLDS(
trans_params=dict(A=np.hstack((np.zeros((K_true-1, K_true)), reg_W)), b=reg_b,
sigmasq_A=100., sigmasq_b=100.),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
dynamics_distns=dynamics_distns,
emission_distns=emission_distns)
# Sample from the model
inputs = np.ones((args.T, 1))
y, x, z = model.generate(T=args.T, inputs=inputs)
# Maks off some data
mask = np.ones((args.T, args.D_obs), dtype=bool)
mask[args.mask_start:args.mask_stop] = False
return model, inputs, z, x, y, mask
def make_roslds_mtpl(V, I_inj_values, V_compartment, K=3, D_latent=2, sigmasq_value=1e-4, penalty=.05):
"""
:param V: the (T,) array of voltage observations
:param K: the number of discrete states (integer)
:param D_latent: the dimension of the continuous latent states
"""
assert V.ndim == 1, "V must be a shape (T,) array of voltage observations"
T = V.shape[0]
D_obs = 2
directory = './results/'
# set initial plane
if K > 1:
reg_W, reg_b = make_initial_plane(K)
# Scale the weights to make the transition boundary sharper
reg_scale = 100.
reg_b *= reg_scale
reg_W *= reg_scale
# Create the model components
# (initial state dist, dynamics dist, emissions dist)
init_dynamics_distns = [
Gaussian(
mu=np.zeros(D_latent),
sigma=np.eye(D_latent),
nu_0=D_latent + 2, sigma_0=3 * np.eye(D_latent),
mu_0=np.zeros(D_latent), kappa_0=1.0,
)
for _ in range(K)]
dynamics_distns = [
Regression(
nu_0=D_latent + 6,#4,
S_0=1e-4 * np.eye(D_latent),
M_0=np.hstack((np.eye(D_latent), np.zeros((D_latent, 3)))),#2)))),
K_0=np.eye(D_latent + 3),#2),
affine=False
)
for _ in range(K)]
# Constrain the emission matrix to have C = [[1, 0, ..., 0]]
# and small sigmasq
# C = np.hstack((np.eye(D_obs), np.zeros((D_obs, 2))))
C = np.hstack((np.eye(D_obs), np.zeros((D_latent, 3))))#2))))
#sigmasq = np.concatenate((np.array([1e-4]), np.ones(D_obs-1)))
sigmasq = np.array([sigmasq_value, penalty])
emission_distns = \
DiagonalRegression(D_obs, D_latent+3,#+2,
A=C, sigmasq=sigmasq)
# Construct the full model
if K == 1:
rslds = PGRecurrentOnlySLDS(
trans_params=dict(sigmasq_A=10000., sigmasq_b=10000.),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
fixed_emission=True)
else:
rslds = PGRecurrentOnlySLDS(
trans_params=dict(A=np.hstack((np.zeros((K-1, K)), reg_W)), b=reg_b, sigmasq_A=10000., sigmasq_b=10000.),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
fixed_emission=True)
# Initialize the continuous states to be V and its gradient
assert D_latent == 2
from scipy.ndimage import gaussian_filter1d
from sklearn.cluster import KMeans
#dV = gaussian_filter1d(np.gradient(V), 1)
#nconvolve = 0
#nconvolve =500#100
#dV =np.convolve(np.gradient(V), np.ones((nconvolve,))/nconvolve, mode='same')
V_tmp = V.copy()
v_thre = 0#3.3 (good)#3#3.5#4#3.5#3#2.5#2.2
V_tmp[V_tmp<v_thre] = 0
print('NEW INITIALIZATION!', v_thre)
#dV = gaussian_filter1d(np.gradient(V_tmp), 1)
dV = gaussian_filter1d(np.gradient(V_tmp), 10)
print('convolue dV')
#x_init = np.column_stack((V, dV))
x_init = np.column_stack((V_tmp, dV))
x_init = (x_init - np.mean(x_init, axis=0)) / np.std(x_init, axis=0)
# Initialize the discrete states by clustering x_init
km = KMeans(K).fit(x_init)
z_init = km.labels_
# Plot the
#'''
plt.close('all')
plt.figure()
plt.subplot(211)
plt.plot(x_init[:10000,:])
# plt.plot(Vs_true[:,j],'r')
plt.subplot(212)
plt.plot(z_init[:10000])
#plt.show()
plt.savefig(directory+'-init-penalized.png')
#plt.savefig('nconvolve'+str(nconvolve)+'-init-penalized.png')
#'''
# Provide an array of ones for the bias (affine term)
assert I_inj_values.shape == (T,)
data = np.column_stack((V, np.zeros(T,))) # pseudo obs
# add voltage effect on rslds (V_compartments)
inputs = np.column_stack((np.ones((T, 1)), I_inj_values, V_compartment))
#inputs = np.column_stack((np.ones((T, 1)), I_inj_values))
mask = np.ones((T, D_obs), dtype=bool)
rslds.add_data(data, mask=mask, inputs=inputs,
stateseq=z_init, gaussian_states=x_init)
return rslds
def make_roslds(V, I_inj_values, not_noisy=True, K=6, D_latent=2, sigmasq_value=1e-4, penalty=.05):
"""
:param V: the (T,) array of voltage observations
:param K: the number of discrete states (integer)
:param D_latent: the dimension of the continuous latent states
"""
assert V.ndim == 1, "V must be a shape (T,) array of voltage observations"
T = V.shape[0]
D_obs = 2
'''
# initialization
w1, b1 = np.array([+1.0, 0.0]), np.array([0.0]) # x >0
w2, b2 = np.array([0.0, +1.0]), np.array([0.0]) # y > 0
reg_W = np.row_stack((w1, w2))
reg_b = np.row_stack((b1, b2))
'''
reg_W, reg_b = make_initial_plane(K)
# Scale the weights to make the transition boundary sharper
reg_scale = 100.
reg_b *= reg_scale
reg_W *= reg_scale
# Create the model components
# (initial state dist, dynamics dist, emissions dist)
init_dynamics_distns = [Gaussian(mu=np.zeros(D_latent),
sigma=np.eye(D_latent),
nu_0=D_latent + 2, sigma_0=3 * np.eye(D_latent),
mu_0=np.zeros(D_latent), kappa_0=1.0,
) for _ in range(K)]
dynamics_distns = [Regression( nu_0=D_latent + 4,
S_0=1e-4 * np.eye(D_latent),
M_0=np.hstack((np.eye(D_latent), np.zeros((D_latent, 2)))),
K_0=np.eye(D_latent + 2),
affine=False
) for _ in range(K)]
# Constrain the emission matrix to have C = [[1, 0, ..., 0]]
# and small sigmasq
# C = np.hstack((np.eye(D_obs), np.zeros((D_obs, 2))))
C = np.hstack((np.eye(D_obs), np.zeros((D_latent, 2))))
#sigmasq = np.concatenate((np.array([1e-4]), np.ones(D_obs-1)))
sigmasq = np.array([sigmasq_value, penalty])
emission_distns = DiagonalRegression(D_obs, D_latent+2, A=C, sigmasq=sigmasq)
# Construct the full model
if K == 1:
rslds = PGRecurrentOnlySLDS(trans_params=dict(sigmasq_A=10000., sigmasq_b=10000.),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
fixed_emission=True)
else:
rslds = PGRecurrentOnlySLDS(trans_params=dict(A=np.hstack((np.zeros((K-1, K)), reg_W)), b=reg_b, sigmasq_A=10000., sigmasq_b=10000.), init_state_distn='uniform', init_dynamics_distns=init_dynamics_distns, dynamics_distns=dynamics_distns, emission_distns=emission_distns, fixed_emission=True)
# Initialize the continuous states to be V and its gradient
assert D_latent == 2
if not_noisy:
dV = gaussian_filter1d(np.gradient(V), 1)
else:
nconvolve =10000
dV =np.convolve(np.gradient(V), np.ones((nconvolve,))/nconvolve, mode='same')
x_init = np.column_stack((V, dV))
x_init = (x_init - np.mean(x_init, axis=0)) / np.std(x_init, axis=0)
# Initialize the discrete states by clustering x_init
km = KMeans(K).fit(x_init)
z_init = km.labels_
# Provide an array of ones for the bias (affine term)
assert I_inj_values.shape == (T,)
data = np.column_stack((V, np.zeros(T,))) # pseudo obs
inputs = np.column_stack((np.ones((T, 1)), I_inj_values))
mask = np.ones((T, D_obs), dtype=bool)
rslds.add_data(data, mask=mask, inputs=inputs,
stateseq=z_init, gaussian_states=x_init)
return rslds
# Make rSLDS parameters
init_dynamics_distns = [
Gaussian(
mu=np.zeros(D_latent),
sigma=np.eye(D_latent),
nu_0=D_latent + 2, sigma_0=3. * np.eye(D_latent),
mu_0=np.zeros(D_latent), kappa_0=1.0,
)
for _ in range(K)]
# Create hierarchical dynamics model
hierarchical_dynamics_distn = \
TreeStructuredHierarchicalDynamics(tree, 0.1 * np.eye(D_latent), 3 * np.eye(D_latent + 1))
emission_distns = \
DiagonalRegression(D_obs, D_latent + 1,
alpha_0=2.0, beta_0=2.0)
model = TreeStructuredPGRecurrentSLDS(
trans_params=dict(sigmasq_A=10., sigmasq_b=0.01),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
hierarchical_dynamics_distn=hierarchical_dynamics_distn,
emission_distns=emission_distns)
plt.figure(figsize=(12, 12))
ax = plt.subplot(3, 4, 2)
plot_dynamics(hierarchical_dynamics_distn.As[0], 0, ax=ax)
ax = plt.subplot(3, 4, 4+1)
plot_dynamics(hierarchical_dynamics_distn.As[1], 1, ax=ax)
ax = plt.subplot(3, 4, 4 + 2)
plot_dynamics(hierarchical_dynamics_distn.As[4], 4, ax=ax)
],
dynamics_distns=[
Regression(
A=np.hstack(
(np.eye(D_latent), np.zeros((D_latent, D_input)))),
sigma=np.eye(D_latent),
nu_0=D_latent + 3,
S_0=D_latent * np.eye(D_latent),
M_0=np.hstack(
(np.eye(D_latent), np.zeros((D_latent, D_input)))),
K_0=D_latent * np.eye(D_latent + D_input),
) for _ in range(Kmax)
],
emission_distns=DiagonalRegression(
D_obs,
D_latent + D_input,
alpha_0=2.0,
beta_0=1.0,
),
alpha=3.,
init_state_distn='uniform')
model.add_data(data, inputs=np.ones((T, D_input)))
model.resample_states()
for _ in progprint_xrange(0):
model.resample_model()
model.states_list[0]._init_mf_from_gibbs()
####################
# run mean field #
####################
]
C = np.random.randn(D_obs, D_latent)
sigma_obs = 0.5 * np.ones(D_obs)
#%%
###################
# generate data #
###################
# K: x_0 ~ Normal(mu_init, sigma_init)
init_dynamics_distns = [
Gaussian(mu=mu_init, sigma=sigma_init) for _ in range(K)
]
# K : x_t ~ Normal( A_{z=k} x_t + b_{z=K}, I)
dynamics_distns = [Regression(A=A, sigma=np.eye(D_latent)) for A in As]
#K: y_t | x_t ~ Normal (C_{z=k} x_t + d_z{k=K}, diag(Sigma_obs))
emission_distns = DiagonalRegression(D_obs, D_latent, A=C, sigmasq=sigma_obs)
truemodel = HMMSLDS(dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
init_dynamics_distns=init_dynamics_distns,
alpha=3.,
init_state_distn='uniform')
#%%
# Manually create the states object with the mask
T = 1000
# get z is T x 1
stateseq = np.repeat(np.arange(T // 100) % 2, 100).astype(np.int32)
statesobj = truemodel._states_class(model=truemodel,
T=stateseq.size,
stateseq=stateseq)
def trainModel(fileName, unit_trial, K=8, xDim=5):
# unit_trial -- training data
# randomization
np.random.seed()
numTrial, numUnit, numTime = unit_trial.shape
# factor analysis for initialization
factor_unit_trial = unit_trial.transpose([0, 2, 1])
factor_unit_trial = factor_unit_trial.reshape([-1, factor_unit_trial.shape[2]])
yDim = numUnit
inputDim = 1 # some constants
inputs = np.ones((numTime, inputDim))
estimator = factan(n_components=xDim, tol=0.00001, copy=True,
max_iter=10000, noise_variance_init=None,
svd_method='randomized', iterated_power=3,
random_state=None)
estimator.fit(factor_unit_trial)
C_init = estimator.components_.T
D_init = estimator.mean_.reshape([-1, 1])
# SLDS fit
init_dynamics_distns = [Gaussian(nu_0=xDim+3,
sigma_0=3.*np.eye(xDim),
mu_0=np.zeros(xDim),
kappa_0=0.01)
for _ in range(K)]
dynamics_distns = [Regression(nu_0=xDim + 1,
S_0=xDim * np.eye(xDim),
M_0=np.hstack((.99 * np.eye(xDim), np.zeros((xDim, inputDim)))),
K_0=xDim * np.eye(xDim + inputDim))
for _ in range(K)]
As = [np.eye(xDim) for _ in range(K)]
if inputDim > 0:
As = [np.hstack((A, np.zeros((xDim, inputDim))))
for A in As]
for dd, A in zip(dynamics_distns, As):
dd.A = A
sigma_statess = [np.eye(xDim) for _ in range(K)]
for dd, sigma in zip(dynamics_distns, sigma_statess):
dd.sigma = sigma
emission_distns = [DiagonalRegression(yDim, xDim + inputDim,
mu_0=None, Sigma_0=None,
alpha_0=3.0, beta_0=2.0,
A=np.hstack((C_init.copy(), D_init.copy())),
sigmasq=None, niter=1)
for _ in range(K)]
train_model = HMMSLDS(
init_dynamics_distns= init_dynamics_distns,
dynamics_distns= dynamics_distns,
emission_distns= emission_distns,
alpha=3., init_state_distn='uniform')
# Adding training data
for trial in range(numTrial):
train_model.add_data(unit_trial[trial].T, inputs=inputs)
print("Initializing with Gibbs")
N_gibbs_samples = 2000
def initialize(model):
model.resample_model()
return model.log_likelihood()
gibbs_lls = [initialize(train_model) for _ in progprint_xrange(N_gibbs_samples)]
print("Fitting with VBEM")
N_vbem_iters = 100
def update(model):
model.VBEM_step()
return model.log_likelihood()
train_model._init_mf_from_gibbs()
vbem_lls = [update(train_model) for _ in progprint_xrange(N_vbem_iters)]
np.save(fileName + '_gibbs_lls', gibbs_lls)
np.save(fileName + '_vbem_lls', vbem_lls)
np.save(fileName + '_train_model', train_model)
return train_model
mask = np.ones_like(data, dtype=bool)
chunksz = 100
for i, offset in enumerate(range(0, T, chunksz)):
j = i % (D_obs + 1)
if j < D_obs:
mask[offset:min(offset + chunksz, T), j] = False
if j == D_obs:
mask[offset:min(offset + chunksz, T), :] = False
# Fit with another LDS
model = LDS(dynamics_distn=Regression(nu_0=D_latent + 3,
S_0=D_latent * np.eye(D_latent),
M_0=np.zeros((D_latent, D_latent)),
K_0=D_latent * np.eye(D_latent)),
emission_distn=DiagonalRegression(D_obs,
D_latent,
alpha_0=2.0,
beta_0=1.0))
model.add_data(data=data, mask=mask)
# Fit the model
N_samples = 500
sigma_obs_smpls = []
def gibbs_update(model):
model.resample_model()
sigma_obs_smpls.append(model.sigma_obs_flat)
return model.log_likelihood()
def em_update(model):
def simulate_nascar():
assert K_true == 4
As = [
random_rotation(D_latent, np.pi / 24.),
random_rotation(D_latent, np.pi / 48.)
]
# Set the center points for each system
centers = [np.array([+2.0, 0.]), np.array([-2.0, 0.])]
bs = [
-(A - np.eye(D_latent)).dot(center) for A, center in zip(As, centers)
]
# Add a "right" state
As.append(np.eye(D_latent))
bs.append(np.array([+0.1, 0.]))
# Add a "right" state
As.append(np.eye(D_latent))
bs.append(np.array([-0.25, 0.]))
# Construct multinomial regression to divvy up the space
w1, b1 = np.array([+1.0, 0.0]), np.array([-2.0]) # x + b > 0 -> x > -b
w2, b2 = np.array([-1.0, 0.0]), np.array([-2.0]) # -x + b > 0 -> x < b
w3, b3 = np.array([0.0, +1.0]), np.array([0.0]) # y > 0
w4, b4 = np.array([0.0, -1.0]), np.array([0.0]) # y < 0
reg_W = np.column_stack((100 * w1, 100 * w2, 10 * w3, 10 * w4))
reg_b = np.concatenate((100 * b1, 100 * b2, 10 * b3, 10 * b4))
# Make a recurrent SLDS with these params #
dynamics_distns = [
Regression(
A=np.column_stack((A, b)),
sigma=1e-4 * np.eye(D_latent),
nu_0=D_latent + 2,
S_0=1e-4 * np.eye(D_latent),
M_0=np.zeros((D_latent, D_latent + 1)),
K_0=np.eye(D_latent + 1),
) for A, b in zip(As, bs)
]
init_dynamics_distns = [
Gaussian(mu=np.array([0.0, 1.0]), sigma=1e-3 * np.eye(D_latent))
for _ in range(K)
]
C = np.hstack((npr.randn(D_obs, D_latent), np.zeros((D_obs, 1))))
emission_distns = \
DiagonalRegression(D_obs, D_latent+1,
A=C, sigmasq=1e-5 *np.ones(D_obs),
alpha_0=2.0, beta_0=2.0)
model = SoftmaxRecurrentOnlySLDS(trans_params=dict(W=reg_W, b=reg_b),
init_state_distn='uniform',
init_dynamics_distns=init_dynamics_distns,
dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
alpha=3.)
#########################
# Sample from the model #
#########################
inputs = np.ones((T, 1))
y, x, z = model.generate(T=T, inputs=inputs)
# Maks off some data
if mask_start == mask_stop:
mask = None
else:
mask = np.ones((T, D_obs), dtype=bool)
mask[mask_start:mask_stop] = False
# Print the true parameters
np.set_printoptions(precision=2)
print("True W:\n{}".format(model.trans_distn.W))
print("True logpi:\n{}".format(model.trans_distn.logpi))
return model, inputs, z, x, y, mask
