def __init__(
self,
n_states,
n_features,
n_experiments=5,
n_hotstart_sequences=10,
params="tmcqab",
n_em_iter=10,
n_hotstart=5,
backend="FirstOpt",
):
self.n_states = n_states
self.n_experiments = n_experiments
self.n_features = n_features
self.n_hotstart = n_hotstart
self.n_hotstart_sequences = n_hotstart_sequences
self.n_em_iter = n_em_iter
self.params = params
self.eps = 0.2
self._As_ = None
self._bs_ = None
self._Qs_ = None
self._covars_ = None
self._means_ = None
self._transmat_ = None
self._populations_ = None
self.solver = MetastableSwitchingLDSSolver(self.n_states, self.n_features)
self.inferrer = MetastableSLDSCPUImpl(self.n_states, self.n_features, precision="mixed")
class MetastableSwitchingLDS(object):
"""
The Metastable Switching Linear Dynamical System (mslds) models
within-state dynamics of metastable states by a linear dynamical
system. The model is a Markov jump process between different linear
dynamical systems.
Parameters
----------
n_states : int
The number of hidden states.
n_experiments : int
Number of time the EM algorithm will be run with different
random seeds.
n_features : int
Dimensionality of the space.
n_hotstart : {int}
Number of EM iterations for HMM hot-starting of mslds learning.
n_em_iter : int, optional
Number of iterations to perform during training
params : string, optional, default
Controls which parameters are updated in the training process.
backet: string
Either FirstOpt or cvxopt
"""
def __init__(
self,
n_states,
n_features,
n_experiments=5,
n_hotstart_sequences=10,
params="tmcqab",
n_em_iter=10,
n_hotstart=5,
backend="FirstOpt",
):
self.n_states = n_states
self.n_experiments = n_experiments
self.n_features = n_features
self.n_hotstart = n_hotstart
self.n_hotstart_sequences = n_hotstart_sequences
self.n_em_iter = n_em_iter
self.params = params
self.eps = 0.2
self._As_ = None
self._bs_ = None
self._Qs_ = None
self._covars_ = None
self._means_ = None
self._transmat_ = None
self._populations_ = None
self.solver = MetastableSwitchingLDSSolver(self.n_states, self.n_features)
self.inferrer = MetastableSLDSCPUImpl(self.n_states, self.n_features, precision="mixed")
def _init(self, sequences):
"""Initialize the state, prior to fitting (hot starting)
"""
sequences = [ensure_type(s, dtype=np.float32, ndim=2, name="s") for s in sequences]
self.inferrer._sequences = sequences
small_dataset = np.vstack(sequences[0 : min(len(sequences), self.n_hotstart_sequences)])
# Initialize means
with warnings.catch_warnings():
warnings.simplefilter("ignore")
self.means_ = cluster.KMeans(n_clusters=self.n_states).fit(small_dataset).cluster_centers_
# Initialize covariances
cv = np.cov(small_dataset.T)
self.covars_ = distribute_covar_matrix_to_match_covariance_type(cv, "full", self.n_states)
self.covars_[self.covars_ == 0] = 1e-5
# Stabilize eigenvalues of matrix
for i in range(self.n_states):
self.covars_[i] = self.covars_[i] + 1e-5 * np.eye(self.n_features)
# Initialize transmat
transmat_ = np.empty((self.n_states, self.n_states))
transmat_.fill(1.0 / self.n_states)
self.transmat_ = transmat_
self.populations_ = np.ones(self.n_states) / self.n_states
# Initialize As
self.As_ = np.zeros((self.n_states, self.n_features, self.n_features))
self.bs_ = np.zeros((self.n_states, self.n_features))
for i in range(self.n_states):
A = self.As_[i]
mean = self.means_[i]
self.bs_[i] = np.dot(np.eye(self.n_features) - A, mean)
# Initialize means
# Initialize local covariances
self.Qs_ = np.zeros((self.n_states, self.n_features, self.n_features))
for i in range(self.n_states):
self.Qs_[i] = self.eps * self.covars_[i]
def sample(self, n_samples, init_state=None, init_obs=None):
"""Sample a trajectory from model distribution
"""
# Allocate Memory
obs = np.zeros((n_samples, self.n_features))
hidden_state = np.zeros(n_samples, dtype=int)
# set the initial values of the sequences
if init_state is None:
# Sample Start conditions
hidden_state[0] = categorical(self.populations_)
else:
hidden_state[0] = init_state
if init_obs is None:
obs[0] = multivariate_normal(self.means_[hidden_state[0]], self.covars_[hidden_state[0]])
else:
obs[0] = init_obs
# Perform time updates
import pdb, traceback, sys
try:
for t in range(n_samples - 1):
s = hidden_state[t]
A = self.As_[s]
b = self.bs_[s]
Q = self.Qs_[s]
obs[t + 1] = multivariate_normal(np.dot(A, obs[t]) + b, Q)
hidden_state[t + 1] = categorical(self.transmat_[s])
except:
type, value, tb = sys.exc_info()
traceback.print_exc()
pdb.post_mortem(tb)
return obs, hidden_state
def score(self, data):
"""Log-likelihood of sequences under the model
"""
sequences = [ensure_type(s, dtype=np.float32, ndim=2, name="s") for s in data]
self.inferrer._sequences = data
logprob, _ = self.inferrer.do_mslds_estep()
return logprob
def print_parameters(self, phase="", logprob=None, print_status=True):
if not print_status:
return
display_string = (
"""
######################################################
Current Mslds Parameters. Phase: %s
######################################################
"""
% phase
)
display_string += "self.transmat:\n" + str(self.transmat_) + "\n"
for i in range(self.n_states):
display_string += (
"""
++++++++++++++++++++++++ State %d++++++++++++++\n
"""
% i
)
display_string += (
("\nself.As[%d]:\n" % i + str(self.As_[i]) + "\n")
+ ("self.Qs[%d]:\n" % i + str(self.Qs_[i]) + "\n")
+ ("self.bs[%d]:\n" % i + str(self.bs_[i]) + "\n")
+ ("self.means[%d]:\n" % i + str(self.means_[i]) + "\n")
+ ("self.covars[%d]:\n" % i + str(self.covars_[i]) + "\n")
)
if logprob != None:
display_string += "\nLog-probability of model: %f\n" % logprob
display_string = bcolors.WARNING + display_string + bcolors.ENDC
print(display_string)
def fit(self, data, gamma=0.5, print_status=False, tol=1e-1, verbose=False, N_iter=400):
"""Estimate model parameters.
"""
self._init(data)
best_fit = {"params": {}, "loglikelihood": -np.inf}
fit_logprob = []
for i in range(self.n_hotstart):
print("Starting hotstart M-step %d" % i)
curr_logprob, stats = self.inferrer.do_hmm_estep()
self.transmat_, self.means_, self.covars_ = self.solver.do_hmm_mstep(stats)
self.print_parameters(
phase="HMM Pretraining Step " + str(i), logprob=curr_logprob, print_status=print_status
)
# Move this inwards later for neatness
for i in range(self.n_states):
D = np.copy(self.covars_[i])
Q = gamma * D
self.Qs_[i] = Q
As = []
for i in range(self.n_states):
A = np.eye(self.n_features)
As.append(A)
self.As_ = As
bs = []
for i in range(self.n_states):
b = self.means_[i]
bs.append(b)
self.bs_ = bs
for i in range(self.n_em_iter):
print("Starting M-step %d" % i)
curr_logprob, stats = self.inferrer.do_mslds_estep()
fit_logprob.append(curr_logprob)
# self.transmat_, self.As_, self.Qs_, self.bs_ \
_, self.As_, self.Qs_, self.bs_ = self.solver.do_mstep(
self.As_,
self.Qs_,
self.bs_,
self.means_,
self.covars_,
stats,
gamma=gamma,
tol=tol,
verbose=verbose,
N_iter=N_iter,
)
self.print_parameters(phase="Learning Step " + str(i), logprob=curr_logprob, print_status=print_status)
disp_string = "logprob: %f" % curr_logprob
disp_string = bcolors.WARNING + disp_string + bcolors.ENDC
print(disp_string)
return self
def compute_metastable_wells(self):
"""Compute the metastable wells according to the formula
x_i = (I - A)^{-1}b
Output: wells
"""
wells = np.zeros((self.n_states, self.n_features))
for i in range(self.n_states):
wells[i] = np.dot(np.linalg.inv(np.eye(self.n_features) - self.As_[i]), self.bs_[i])
return wells
def compute_process_covariances(self, N=10000):
"""Compute the emergent complexity D_i of metastable state i by
solving the fixed point equation Q_i + A_i D_i A_i.T = D_i
for D_i
Can this be deleted?
"""
covs = np.zeros((self.n_states, self.n_features, self.n_features))
for k in range(self.n_states):
A = self.As_[k]
Q = self.Qs_[k]
V = iter_vars(A, Q, N)
covs[k] = V
return covs
# Boilerplate setters and getters
@property
def As_(self):
return self._As_
@As_.setter
def As_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._As_ = value
self.inferrer.As_ = value
@property
def Qs_(self):
return self._Qs_
@Qs_.setter
def Qs_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._Qs_ = value
self.inferrer.Qs_ = value
@property
def bs_(self):
return self._bs_
@bs_.setter
def bs_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._bs_ = value
self.inferrer.bs_ = value
@property
def means_(self):
return self._means_
@means_.setter
def means_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._means_ = value
self.inferrer.means_ = value
@property
def covars_(self):
return self._covars_
@covars_.setter
def covars_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._covars_ = value
self.inferrer.covars_ = value
@property
def transmat_(self):
return self._transmat_
@transmat_.setter
def transmat_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._transmat_ = value
self.inferrer.transmat_ = value
@property
def populations_(self):
return self._populations_
@populations_.setter
def populations_(self, value):
value = np.asarray(value, order="c", dtype=np.float32)
self._populations_ = value
self.inferrer.startprob_ = value