This repository has been archived by the owner on Sep 11, 2023. It is now read-only.
-
Notifications
You must be signed in to change notification settings - Fork 119
/
maximum_likelihood_hmsm.py
689 lines (587 loc) Β· 31.1 KB
/
maximum_likelihood_hmsm.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
# This file is part of PyEMMA.
#
# Copyright (c) 2015, 2014 Computational Molecular Biology Group, Freie Universitaet Berlin (GER)
#
# PyEMMA is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from pyemma.util.annotators import alias, aliased, fix_docs
import numpy as _np
from pyemma.msm.models.hmsm import HMSM as _HMSM
from pyemma._base.estimator import Estimator as _Estimator
from pyemma.util import types as _types
from pyemma.util.units import TimeUnit
# TODO: currently, it's not possible to start with disconnected matrices.
@aliased
@fix_docs
class MaximumLikelihoodHMSM(_Estimator, _HMSM):
r"""Maximum likelihood estimator for a Hidden MSM given a MSM"""
__serialize_version = 0
__serialize_fields = ('_active_set', '_dtrajs_full', '_dtrajs_lagged', '_dtrajs_obs',
'_nstates_obs', '_nstates_obs_full',
'count_matrix', 'count_matrix_EM',
'hidden_state_probabilities', 'hidden_state_trajectories',
'_observable_set', '_observable_state_indexes',
'initial_count', 'initial_distribution',
'likelihood', 'likelihoods',
'timestep_traj', 'hmm',
)
def __init__(self, nstates=2, lag=1, stride=1, msm_init='largest-strong', reversible=True, stationary=False,
connectivity=None, mincount_connectivity='1/n', observe_nonempty=True, separate=None,
dt_traj='1 step', accuracy=1e-3, maxit=1000):
r"""Maximum likelihood estimator for a Hidden MSM given a MSM
Parameters
----------
nstates : int, optional, default=2
number of hidden states
lag : int, optional, default=1
lagtime to estimate the HMSM at
stride : str or int, default=1
stride between two lagged trajectories extracted from the input
trajectories. Given trajectory s[t], stride and lag will result
in trajectories
s[0], s[lag], s[2 lag], ...
s[stride], s[stride + lag], s[stride + 2 lag], ...
Setting stride = 1 will result in using all data (useful for maximum
likelihood estimator), while a Bayesian estimator requires a longer
stride in order to have statistically uncorrelated trajectories.
Setting stride = 'effective' uses the largest neglected timescale as
an estimate for the correlation time and sets the stride accordingly
msm_init : str or :class:`MSM <pyemma.msm.MSM>`
MSM object to initialize the estimation, or one of following keywords:
* 'largest-strong' or None (default) : Estimate MSM on the largest
strongly connected set and use spectral clustering to generate an
initial HMM
* 'all' : Estimate MSM(s) on the full state space to initialize the
HMM. This estimate maybe weakly connected or disconnected.
reversible : bool, optional, default = True
If true compute reversible MSM, else non-reversible MSM
stationary : bool, optional, default=False
If True, the initial distribution of hidden states is self-consistently computed as the stationary
distribution of the transition matrix. If False, it will be estimated from the starting states.
Only set this to true if you're sure that the observation trajectories are initiated from a global
equilibrium distribution.
connectivity : str, optional, default = None
Defines if the resulting HMM will be defined on all hidden states or on
a connected subset. Connectivity is defined by counting only
transitions with at least mincount_connectivity counts.
If a subset of states is used, all estimated quantities (transition
matrix, stationary distribution, etc) are only defined on this subset
and are correspondingly smaller than nstates.
Following modes are available:
* None or 'all' : The active set is the full set of states.
Estimation is done on all weakly connected subsets separately. The
resulting transition matrix may be disconnected.
* 'largest' : The active set is the largest reversibly connected set.
* 'populous' : The active set is the reversibly connected set with most counts.
mincount_connectivity : float or '1/n'
minimum number of counts to consider a connection between two states.
Counts lower than that will count zero in the connectivity check and
may thus separate the resulting transition matrix. The default
evaluates to 1/nstates.
separate : None or iterable of int
Force the given set of observed states to stay in a separate hidden state.
The remaining nstates-1 states will be assigned by a metastable decomposition.
observe_nonempty : bool
If True, will restricted the observed states to the states that have
at least one observation in the lagged input trajectories.
If an initial MSM is given, this option is ignored and the observed
subset is always identical to the active set of that MSM.
dt_traj : str, optional, default='1 step'
Description of the physical time corresponding to the trajectory time
step. May be used by analysis algorithms such as plotting tools to
pretty-print the axes. By default '1 step', i.e. there is no physical
time unit. Specify by a number, whitespace and unit. Permitted units
are (* is an arbitrary string):
| 'fs', 'femtosecond*'
| 'ps', 'picosecond*'
| 'ns', 'nanosecond*'
| 'us', 'microsecond*'
| 'ms', 'millisecond*'
| 's', 'second*'
accuracy : float, optional, default = 1e-3
convergence threshold for EM iteration. When two the likelihood does
not increase by more than accuracy, the iteration is stopped
successfully.
maxit : int, optional, default = 1000
stopping criterion for EM iteration. When so many iterations are
performed without reaching the requested accuracy, the iteration is
stopped without convergence (a warning is given)
"""
self.nstates = nstates
self.lag = lag
self.stride = stride
self.msm_init = msm_init
self.reversible = reversible
self.stationary = stationary
self.connectivity = connectivity
if mincount_connectivity == '1/n':
mincount_connectivity = 1.0/float(nstates)
self.mincount_connectivity = mincount_connectivity
self.separate = separate
self.observe_nonempty = observe_nonempty
self.dt_traj = dt_traj
self.accuracy = accuracy
self.maxit = maxit
@property
def dt_traj(self):
return self._dt_traj
@dt_traj.setter
def dt_traj(self, value):
self._dt_traj = value
self.timestep_traj = TimeUnit(value)
#TODO: store_data is mentioned but not implemented or used!
def _estimate(self, dtrajs):
import bhmm
# ensure right format
dtrajs = _types.ensure_dtraj_list(dtrajs)
# CHECK LAG
trajlengths = [_np.size(dtraj) for dtraj in dtrajs]
if self.lag >= _np.max(trajlengths):
raise ValueError('Illegal lag time ' + str(self.lag) + ' exceeds longest trajectory length')
if self.lag > _np.mean(trajlengths):
self.logger.warning('Lag time ' + str(self.lag) + ' is on the order of mean trajectory length '
+ str(_np.mean(trajlengths)) + '. It is recommended to fit four lag times in each '
+ 'trajectory. HMM might be inaccurate.')
# EVALUATE STRIDE
if self.stride == 'effective':
# by default use lag as stride (=lag sampling), because we currently have no better theory for deciding
# how many uncorrelated counts we can make
self.stride = self.lag
# get a quick estimate from the spectral radius of the non-reversible
from pyemma.msm import estimate_markov_model
msm_nr = estimate_markov_model(dtrajs, lag=self.lag, reversible=False, sparse=False,
connectivity='largest', dt_traj=self.timestep_traj)
# if we have more than nstates timescales in our MSM, we use the next (neglected) timescale as an
# estimate of the decorrelation time
if msm_nr.nstates > self.nstates:
# because we use non-reversible msm, we want to silence the ImaginaryEigenvalueWarning
import warnings
from msmtools.util.exceptions import ImaginaryEigenValueWarning
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=ImaginaryEigenValueWarning,
module='msmtools.analysis.dense.decomposition')
corrtime = max(1, msm_nr.timescales()[self.nstates - 1])
# use the smaller of these two pessimistic estimates
self.stride = int(min(self.lag, 2*corrtime))
# LAG AND STRIDE DATA
dtrajs_lagged_strided = bhmm.lag_observations(dtrajs, self.lag, stride=self.stride)
# OBSERVATION SET
if self.observe_nonempty:
observe_subset = 'nonempty'
else:
observe_subset = None
# INIT HMM
from bhmm import init_discrete_hmm
from pyemma.msm.estimators import MaximumLikelihoodMSM, OOMReweightedMSM
if self.msm_init=='largest-strong':
hmm_init = init_discrete_hmm(dtrajs_lagged_strided, self.nstates, lag=1,
reversible=self.reversible, stationary=True, regularize=True,
method='lcs-spectral', separate=self.separate)
elif self.msm_init=='all':
hmm_init = init_discrete_hmm(dtrajs_lagged_strided, self.nstates, lag=1,
reversible=self.reversible, stationary=True, regularize=True,
method='spectral', separate=self.separate)
elif isinstance(self.msm_init, (MaximumLikelihoodMSM, OOMReweightedMSM)): # initial MSM given.
from bhmm.init.discrete import init_discrete_hmm_spectral
p0, P0, pobs0 = init_discrete_hmm_spectral(self.msm_init.count_matrix_full, self.nstates,
reversible=self.reversible, stationary=True,
active_set=self.msm_init.active_set,
P=self.msm_init.transition_matrix, separate=self.separate)
hmm_init = bhmm.discrete_hmm(p0, P0, pobs0)
observe_subset = self.msm_init.active_set # override observe_subset.
else:
raise ValueError('Unknown MSM initialization option: ' + str(self.msm_init))
# ---------------------------------------------------------------------------------------
# Estimate discrete HMM
# ---------------------------------------------------------------------------------------
# run EM
from bhmm.estimators.maximum_likelihood import MaximumLikelihoodEstimator as _MaximumLikelihoodEstimator
hmm_est = _MaximumLikelihoodEstimator(dtrajs_lagged_strided, self.nstates, initial_model=hmm_init,
output='discrete', reversible=self.reversible, stationary=self.stationary,
accuracy=self.accuracy, maxit=self.maxit)
# run
hmm_est.fit()
# package in discrete HMM
self.hmm = bhmm.DiscreteHMM(hmm_est.hmm)
# get model parameters
self.initial_distribution = self.hmm.initial_distribution
transition_matrix = self.hmm.transition_matrix
observation_probabilities = self.hmm.output_probabilities
# get estimation parameters
self.likelihoods = hmm_est.likelihoods # Likelihood history
self.likelihood = self.likelihoods[-1]
self.hidden_state_probabilities = hmm_est.hidden_state_probabilities # gamma variables
self.hidden_state_trajectories = hmm_est.hmm.hidden_state_trajectories # Viterbi path
self.count_matrix = hmm_est.count_matrix # hidden count matrix
self.initial_count = hmm_est.initial_count # hidden init count
self._active_set = _np.arange(self.nstates)
# TODO: it can happen that we loose states due to striding. Should we lift the output probabilities afterwards?
# parametrize self
import msmtools.estimation as msmest
self._dtrajs_full = dtrajs
self._dtrajs_lagged = dtrajs_lagged_strided
self._nstates_obs_full = msmest.number_of_states(dtrajs)
self._nstates_obs = msmest.number_of_states(dtrajs_lagged_strided)
self._observable_set = _np.arange(self._nstates_obs)
self._dtrajs_obs = dtrajs
self.set_model_params(P=transition_matrix, pobs=observation_probabilities,
reversible=self.reversible, dt_model=self.timestep_traj.get_scaled(self.lag))
# TODO: perhaps remove connectivity and just rely on .submodel()?
# deal with connectivity
states_subset = None
if self.connectivity == 'largest':
states_subset = 'largest-strong'
elif self.connectivity == 'populous':
states_subset = 'populous-strong'
# return submodel (will return self if all None)
return self.submodel(states=states_subset, obs=observe_subset,
mincount_connectivity=self.mincount_connectivity,
inplace=True)
@property
def msm_init(self):
return self._msm_init
@msm_init.setter
def msm_init(self, value):
from pyemma.msm.estimators import MaximumLikelihoodMSM, OOMReweightedMSM
if (isinstance(value, (MaximumLikelihoodMSM, OOMReweightedMSM)) and not value._estimated):
raise ValueError('Given initial msm has not been estimated. Input was {}'.format(value))
self._msm_init = value
@property
def lagtime(self):
""" The lag time in steps """
return self.lag
@property
def nstates(self):
return self._nstates
@nstates.setter
def nstates(self, value):
# we override this setter here, because we want to avoid pyemma.msm.MSM class to overwrite our input parameter.
# caused bug #1266
if int(value) > 0 and value is not None:
self._nstates = value
@property
def nstates_obs(self):
r""" Number of states in discrete trajectories """
return self._nstates_obs
@property
def active_set(self):
"""
The active set of hidden states on which all hidden state computations are done
"""
if hasattr(self, '_active_set'):
return self._active_set
else:
return _np.arange(self.nstates) # all hidden states are active.
@property
def observable_set(self):
"""
The active set of states on which all computations and estimations will be done
"""
return self._observable_set
@property
@alias('dtrajs_full')
def discrete_trajectories_full(self):
"""
A list of integer arrays with the original trajectories.
"""
return self._dtrajs_full
@property
@alias('dtrajs_lagged')
def discrete_trajectories_lagged(self):
"""
Transformed original trajectories that are used as an input into the HMM estimation
"""
return self._dtrajs_lagged
@property
@alias('dtrajs_obs')
def discrete_trajectories_obs(self):
"""
A list of integer arrays with the discrete trajectories mapped to the observation mode used.
When using observe_active = True, the indexes will be given on the MSM active set. Frames that are not in the
observation set will be -1. When observe_active = False, this attribute is identical to
discrete_trajectories_full
"""
return self._dtrajs_obs
################################################################################
# Submodel functions using estimation information (counts)
################################################################################
def submodel(self, states=None, obs=None, mincount_connectivity='1/n', inplace=False):
"""Returns a HMM with restricted state space
Parameters
----------
states : None, str or int-array
Hidden states to restrict the model to. In addition to specifying
the subset, possible options are:
* None : all states - don't restrict
* 'populous-strong' : strongly connected subset with maximum counts
* 'populous-weak' : weakly connected subset with maximum counts
* 'largest-strong' : strongly connected subset with maximum size
* 'largest-weak' : weakly connected subset with maximum size
obs : None, str or int-array
Observed states to restrict the model to. In addition to specifying
an array with the state labels to be observed, possible options are:
* None : all states - don't restrict
* 'nonempty' : all states with at least one observation in the estimator
mincount_connectivity : float or '1/n'
minimum number of counts to consider a connection between two states.
Counts lower than that will count zero in the connectivity check and
may thus separate the resulting transition matrix. Default value:
1/nstates.
inplace : Bool
if True, submodel is estimated in-place, overwriting the original
estimator and possibly discarding information. Default value: False
Returns
-------
hmm : HMM
The restricted HMM.
"""
if states is None and obs is None and mincount_connectivity == 0:
return self
if states is None:
states = _np.arange(self.nstates)
if obs is None:
obs = _np.arange(self.nstates_obs)
if str(mincount_connectivity) == '1/n':
mincount_connectivity = 1.0/float(self.nstates)
# handle new connectivity
from bhmm.estimators import _tmatrix_disconnected
S = _tmatrix_disconnected.connected_sets(self.count_matrix,
mincount_connectivity=mincount_connectivity,
strong=True)
if inplace:
submodel_estimator = self
else:
from copy import deepcopy
submodel_estimator = deepcopy(self)
if len(S) > 1:
# keep only non-negligible transitions
C = _np.zeros(self.count_matrix.shape)
large = _np.where(self.count_matrix >= mincount_connectivity)
C[large] = self.count_matrix[large]
for s in S: # keep all (also small) transition counts within strongly connected subsets
C[_np.ix_(s, s)] = self.count_matrix[_np.ix_(s, s)]
# re-estimate transition matrix with disc.
P = _tmatrix_disconnected.estimate_P(C, reversible=self.reversible, mincount_connectivity=0)
pi = _tmatrix_disconnected.stationary_distribution(P, C)
else:
C = self.count_matrix
P = self.transition_matrix
pi = self.stationary_distribution
# determine substates
if isinstance(states, str):
from bhmm.estimators import _tmatrix_disconnected
strong = 'strong' in states
largest = 'largest' in states
S = _tmatrix_disconnected.connected_sets(self.count_matrix, mincount_connectivity=mincount_connectivity,
strong=strong)
if largest:
score = [len(s) for s in S]
else:
score = [self.count_matrix[_np.ix_(s, s)].sum() for s in S]
states = _np.array(S[_np.argmax(score)])
if states is not None: # sub-transition matrix
submodel_estimator._active_set = states
C = C[_np.ix_(states, states)].copy()
P = P[_np.ix_(states, states)].copy()
P /= P.sum(axis=1)[:, None]
pi = _tmatrix_disconnected.stationary_distribution(P, C)
submodel_estimator.initial_count = self.initial_count[states]
submodel_estimator.initial_distribution = self.initial_distribution[states] / self.initial_distribution[states].sum()
# determine observed states
if str(obs) == 'nonempty':
import msmtools.estimation as msmest
obs = _np.where(msmest.count_states(self.discrete_trajectories_lagged) > 0)[0]
if obs is not None:
# set observable set
submodel_estimator._observable_set = obs
submodel_estimator._nstates_obs = obs.size
# full2active mapping
_full2obs = -1 * _np.ones(self._nstates_obs_full, dtype=int)
_full2obs[obs] = _np.arange(len(obs), dtype=int)
# observable trajectories
submodel_estimator._dtrajs_obs = []
for dtraj in self.discrete_trajectories_full:
submodel_estimator._dtrajs_obs.append(_full2obs[dtraj])
# observation matrix
B = self.observation_probabilities[_np.ix_(states, obs)].copy()
B /= B.sum(axis=1)[:, None]
else:
B = self.observation_probabilities
# set quantities back.
submodel_estimator.update_model_params(P=P, pobs=B, pi=pi)
submodel_estimator.count_matrix_EM = self.count_matrix[_np.ix_(states, states)] # unchanged count matrix
submodel_estimator.count_matrix = C # count matrix consistent with P
return submodel_estimator
def submodel_largest(self, strong=True, mincount_connectivity='1/n'):
""" Returns the largest connected sub-HMM (convenience function)
Returns
-------
hmm : HMM
The restricted HMM.
"""
if strong:
return self.submodel(states='largest-strong', mincount_connectivity=mincount_connectivity)
else:
return self.submodel(states='largest-weak', mincount_connectivity=mincount_connectivity)
def submodel_populous(self, strong=True, mincount_connectivity='1/n'):
""" Returns the most populous connected sub-HMM (convenience function)
Returns
-------
hmm : HMM
The restricted HMM.
"""
if strong:
return self.submodel(states='populous-strong', mincount_connectivity=mincount_connectivity)
else:
return self.submodel(states='populous-weak', mincount_connectivity=mincount_connectivity)
def submodel_disconnect(self, mincount_connectivity='1/n'):
"""Disconnects sets of hidden states that are barely connected
Runs a connectivity check excluding all transition counts below
mincount_connectivity. The transition matrix and stationary distribution
will be re-estimated. Note that the resulting transition matrix
may have both strongly and weakly connected subsets.
Parameters
----------
mincount_connectivity : float or '1/n'
minimum number of counts to consider a connection between two states.
Counts lower than that will count zero in the connectivity check and
may thus separate the resulting transition matrix. The default
evaluates to 1/nstates.
Returns
-------
hmm : HMM
The restricted HMM.
"""
return self.submodel(mincount_connectivity=mincount_connectivity)
def trajectory_weights(self):
r"""Uses the HMSM to assign a probability weight to each trajectory frame.
This is a powerful function for the calculation of arbitrary observables in the trajectories one has
started the analysis with. The stationary probability of the MSM will be used to reweigh all states.
Returns a list of weight arrays, one for each trajectory, and with a number of elements equal to
trajectory frames. Given :math:`N` trajectories of lengths :math:`T_1` to :math:`T_N`, this function
returns corresponding weights:
.. math::
(w_{1,1}, ..., w_{1,T_1}), (w_{N,1}, ..., w_{N,T_N})
that are normalized to one:
.. math::
\sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} = 1
Suppose you are interested in computing the expectation value of a function :math:`a(x)`, where :math:`x`
are your input configurations. Use this function to compute the weights of all input configurations and
obtain the estimated expectation by:
.. math::
\langle a \rangle = \sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} a(x_{i,t})
Or if you are interested in computing the time-lagged correlation between functions :math:`a(x)` and
:math:`b(x)` you could do:
.. math::
\langle a(t) b(t+\tau) \rangle_t = \sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} a(x_{i,t}) a(x_{i,t+\tau})
Returns
-------
The normalized trajectory weights. Given :math:`N` trajectories of lengths :math:`T_1` to :math:`T_N`,
returns the corresponding weights:
.. math::
(w_{1,1}, ..., w_{1,T_1}), (w_{N,1}, ..., w_{N,T_N})
"""
# compute stationary distribution, expanded to full set
statdist = self.stationary_distribution_obs
statdist = _np.append(statdist, [-1]) # add a zero weight at index -1, to deal with unobserved states
# histogram observed states
import msmtools.dtraj as msmtraj
hist = 1.0 * msmtraj.count_states(self.discrete_trajectories_obs, ignore_negative=True)
# simply read off stationary distribution and accumulate total weight
W = []
wtot = 0.0
for dtraj in self.discrete_trajectories_obs:
w = statdist[dtraj] / hist[dtraj]
W.append(w)
wtot += _np.sum(w)
# normalize
for w in W:
w /= wtot
# done
return W
################################################################################
# Generation of trajectories and samples
################################################################################
@property
def observable_state_indexes(self):
"""
Ensures that the observable states are indexed and returns the indices
"""
try: # if we have this attribute, return it
return self._observable_state_indexes
except AttributeError: # didn't exist? then create it.
import pyemma.util.discrete_trajectories as dt
self._observable_state_indexes = dt.index_states(self.discrete_trajectories_obs)
return self._observable_state_indexes
# TODO: generate_traj. How should that be defined? Probably indexes of observable states, but should we specify
# hidden or observable states as start and stop states?
# TODO: sample_by_state. How should that be defined?
def sample_by_observation_probabilities(self, nsample):
r"""Generates samples according to the current observation probability distribution
Parameters
----------
nsample : int
Number of samples per distribution. If replace = False, the number of returned samples per state could be
smaller if less than nsample indexes are available for a state.
Returns
-------
indexes : length m list of ndarray( (nsample, 2) )
List of the sampled indices by distribution.
Each element is an index array with a number of rows equal to nsample, with rows consisting of a
tuple (i, t), where i is the index of the trajectory and t is the time index within the trajectory.
"""
import pyemma.util.discrete_trajectories as dt
return dt.sample_indexes_by_distribution(self.observable_state_indexes, self.observation_probabilities, nsample)
################################################################################
# Model Validation
################################################################################
def cktest(self, mlags=10, conf=0.95, err_est=False, n_jobs=None, show_progress=True):
""" Conducts a Chapman-Kolmogorow test.
Parameters
----------
mlags : int or int-array, default=10
multiples of lag times for testing the Model, e.g. range(10).
A single int will trigger a range, i.e. mlags=10 maps to
mlags=range(10). The setting None will choose mlags automatically
according to the longest available trajectory
conf : float, optional, default = 0.95
confidence interval
err_est : bool, default=False
compute errors also for all estimations (computationally expensive)
If False, only the prediction will get error bars, which is often
sufficient to validate a model.
n_jobs : int, default=None
how many jobs to use during calculation
show_progress : bool, default=True
Show progressbars for calculation?
Returns
-------
cktest : :class:`ChapmanKolmogorovValidator <pyemma.msm.ChapmanKolmogorovValidator>`
References
----------
This is an adaption of the Chapman-Kolmogorov Test described in detail
in [1]_ to Hidden MSMs as described in [2]_.
.. [1] Prinz, J H, H Wu, M Sarich, B Keller, M Senne, M Held, J D
Chodera, C Schuette and F Noe. 2011. Markov models of
molecular kinetics: Generation and validation. J Chem Phys
134: 174105
.. [2] F. Noe, H. Wu, J.-H. Prinz and N. Plattner: Projected and hidden
Markov models for calculating kinetics and metastable states of complex
molecules. J. Chem. Phys. 139, 184114 (2013)
"""
from pyemma.msm.estimators import ChapmanKolmogorovValidator
ck = ChapmanKolmogorovValidator(self, self, _np.eye(self.nstates),
mlags=mlags, conf=conf, err_est=err_est,
n_jobs=n_jobs, show_progress=show_progress)
ck.estimate(self._dtrajs_full)
return ck