pyemma.msm.timescales_msm¶

pyemma.msm.timescales_msm(dtrajs, lags=None, nits=None, reversible=True, connected=True, weights='empirical', errors=None, nsamples=50, n_jobs=1, show_progress=True)¶

Implied timescales from Markov state models estimated at a series of lag times.

Parameters:	dtrajs (array-like or list of array-likes) – discrete trajectories lags (array-like of integers, optional) – integer lag times at which the implied timescales will be calculated nits (int, optional) – number of implied timescales to be computed. Will compute less if the number of states are smaller. If None, the number of timescales will be automatically determined. reversible (boolean, optional) – Estimate transition matrix reversibly (True) or nonreversibly (False) connected (boolean, optional) – If true compute the connected set before transition matrix estimation at each lag separately weights (str, optional) – can be used to re-weight non-equilibrium data to equilibrium. Must be one of the following: ‘empirical’: Each trajectory frame counts as one. (default) ‘oom’: Each transition is re-weighted using OOM theory, see [5]. errors (None \| 'bayes', optional) – Specifies whether to compute statistical uncertainties (by default not), an which algorithm to use if yes. Currently the only option is: ‘bayes’ for Bayesian sampling of the posterior Attention: * The Bayes mode will use an estimate for the effective count matrix that may produce somewhat different estimates than the ‘sliding window’ estimate used with `errors=None` by default. Computing errors can be// slow if the MSM has many states. There are still unsolved theoretical problems in the computation of effective count matrices, and therefore the uncertainty interval and the maximum likelihood estimator can be inconsistent. Use this as a rough guess for statistical uncertainties. nsamples (int, optional) – The number of approximately independent transition matrix samples generated for each lag time for uncertainty quantification. Only used if errors is not None. n_jobs (int, optional) – how many subprocesses to start to estimate the models for each lag time.
Returns:	itsobj
Return type:	`ImpliedTimescales` object

Example

>>> from pyemma import msm
>>> dtraj = [0,1,1,2,2,2,1,2,2,2,1,0,0,1,1,1,2,2,1,1,2,1,1,0,0,0,1,1,2,2,1]   # mini-trajectory
>>> ts = msm.its(dtraj, [1,2,3,4,5], show_progress=False)
>>> print(ts.timescales)  
[[ 1.5...  0.2...]
 [ 3.1...  1.0...]
 [ 2.03...  1.02...]
 [ 4.63...  3.42...]
 [ 5.13...  2.59...]]

See also

ImpliedTimescales(): The object returned by this function.
pyemma.plots.plot_implied_timescales(): Implied timescales plotting function. Just call it with the ImpliedTimescales object produced by this function as an argument.

class pyemma.msm.estimators.implied_timescales.ImpliedTimescales(estimator, lags=None, nits=None, n_jobs=1, show_progress=True)¶

Implied timescales for a series of lag times.

Parameters:

estimator (Estimator) – Estimator to be used for estimating timescales at each lag time.
lags (array-like with integers or None, optional) – integer lag times at which the implied timescales will be calculated. If set to None (default) as list of lagtimes will be automatically generated.
nits (int, optional) – maximum number of implied timescales to be computed and stored. If less timescales are available, nits will be set to a smaller value during estimation. None means the number of timescales will be automatically determined.
n_jobs (int, optional) – how many subprocesses to start to estimate the models for each lag time.

Methods

estimate(X, **params)

param X:	discrete trajectories

fit(X) Estimates parameters - for compatibility with sklearn.

get_params([deep]) Get parameters for this estimator.

get_sample_conf([conf, process]) Returns the confidence interval that contains alpha % of the sample data

get_sample_mean([process]) Returns the sample means of implied timescales.

get_sample_std([process]) Returns the standard error of implied timescales.

get_timescales([process]) Returns the implied timescale estimates

register_progress_callback(call_back[, stage]) Registers the progress reporter.

set_params(**params) Set the parameters of this estimator.

Attributes

`estimators`	Returns the estimators for all lagtimes.
`fraction_of_frames`	Returns the fraction of frames used to compute the count matrix at each lag time.
`lags`	Return the list of lag times for which timescales were computed.
`lagtimes`	Return the list of lag times for which timescales were computed.
`logger`	The logger for this class instance
`model`	The model estimated by this Estimator
`models`	Returns the models for all lagtimes.
`n_jobs`	Returns number of jobs/threads to use during assignment of data.
`name`	The name of this instance
`nits`	Return the number of timescales.
`number_of_timescales`	Return the number of timescales.
`sample_mean`	Returns the sample means of implied timescales.
`sample_std`	Returns the standard error of implied timescales.
`samples_available`	Returns True if samples are available and thus sample
`show_progress`	whether to show the progress of heavy calculations on this object.
`timescales`	Returns the implied timescale estimates

estimate(X, **params)¶

Parameters:

X (lists of integer arrays) – discrete trajectories
estimator (Estimator) – Estimator to be used for estimating timescales at each lag time.
lags (array-like with integers or None, optional) – integer lag times at which the implied timescales will be calculated. If set to None (default) as list of lagtimes will be automatically generated.
nits (int, optional) – maximum number of implied timescales to be computed and stored. If less timescales are available, nits will be set to a smaller value during estimation. None means the number of timescales will be automatically determined.
n_jobs (int, optional) – how many subprocesses to start to estimate the models for each lag time.

estimators¶: Returns the estimators for all lagtimes.

fit(X)¶

Estimates parameters - for compatibility with sklearn.

Parameters:	X (object) – A reference to the data from which the model will be estimated
Returns:	estimator – The estimator (self) with estimated model.
Return type:	object

fraction_of_frames¶

Returns the fraction of frames used to compute the count matrix at each lag time. .. rubric:: Notes

In a list of discrete trajectories with varying lengths, the estimation at longer lag times will mean discarding some trajectories for which not even one count can be computed. This function returns the fraction of frames that was actually used in computing the count matrix.

Be aware: this fraction refers to the full count matrix, and not that of the largest connected set. Hence, the output is not necessarily the active fraction. For that, use the activte_count_fraction function of the pyemma.msm.MaximumLikelihoodMSM class object or for HMM respectively.

get_params(deep=True)¶

Get parameters for this estimator.

Parameters:	deep (boolean, optional) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params – Parameter names mapped to their values.
Return type:	mapping of string to any

get_sample_conf(conf=0.95, process=None)¶

Returns the confidence interval that contains alpha % of the sample data

etc.

Parameters:

conf (float, default = 0.95) –

the confidence interval. Use:

conf = 0.6827 for 1-sigma confidence interval
conf = 0.9545 for 2-sigma confidence interval
conf = 0.9973 for 3-sigma confidence interval

Returns:

(L,R) – lower and upper timescales bounding the confidence interval

if process is None, will return two (l x k) arrays, where l is the number of lag times and k is the number of computed timescales.
if process is an integer, will return two (l)-arrays with the selected process time scale for every lag time

Return type: (float[],float[]) or (float[][],float[][])

get_sample_mean(process=None)¶

Returns the sample means of implied timescales. Only available if underlying estimator produces samples.

Parameters:	process (int or None, default = None) – index in [0:n-1] referring to the process whose timescale will be returned. By default, process = None and all computed process timescales will be returned.
Returns:	if process is None, will return a (l x k) array, where l is the number of lag times and k is the number of computed timescales. if process is an integer, will return a (l) array with the selected process time scale for every lag time

get_sample_std(process=None)¶

Returns the standard error of implied timescales. Only available if underlying estimator produces samples.

Parameters:	process (int or None, default = None) – index in [0:n-1] referring to the process whose timescale will be returned. By default, process = None and all computed process timescales will be returned.
Returns:	if process is None, will return a (l x k) array, where l is the number of lag times and k is the number of computed timescales. if process is an integer, will return a (l) array with the selected process time scale for every lag time

get_timescales(process=None)¶

Returns the implied timescale estimates

Parameters:	process (int or None, default = None) – index in [0:n-1] referring to the process whose timescale will be returned. By default, process = None and all computed process timescales will be returned.
Returns:	if process is None, will return a (l x k) array, where l is the number of lag times and k is the number of computed timescales. if process is an integer, will return a (l) array with the selected process time scale for every lag time

lags¶: Return the list of lag times for which timescales were computed.

lagtimes¶: Return the list of lag times for which timescales were computed.

logger¶: The logger for this class instance

model¶: The model estimated by this Estimator

models¶: Returns the models for all lagtimes.

n_jobs¶

Returns number of jobs/threads to use during assignment of data.

Returns:
Return type:	If None it will return number of processors /or cores or the setting of ‘OMP_NUM_THREADS’ env variable.

Notes

By setting the environment variable ‘OMP_NUM_THREADS’ to an integer, one will override the default argument of n_jobs (currently None).

name¶: The name of this instance

nits¶: Return the number of timescales.

number_of_timescales¶: Return the number of timescales.

register_progress_callback(call_back, stage=0)¶

Registers the progress reporter.

Parameters:	call_back (function) – This function will be called with the following arguments: stage (int) instance of pyemma.utils.progressbar.ProgressBar optional args and named keywords (kw), for future changes stage* (int, optional, default=0) – The stage you want the given call back function to be fired.

sample_mean¶

Returns the sample means of implied timescales. Need to generate the samples first, e.g. by calling bootstrap

Returns:	timescales – mean timescales for all processes and lag times. l is the number of lag times and k is the number of computed timescales.
Return type:	ndarray((l x k), dtype=float)

sample_std¶

Returns the standard error of implied timescales. Only available if underlying estimator produces samples.

Returns:	timescales – standard deviations of timescales for all processes and lag times. l is the number of lag times and k is the number of computed timescales.
Return type:	ndarray((l x k), dtype=float)

samples_available¶: Returns True if samples are available and thus sample means, standard errors and confidence intervals can be obtained

set_params(**params)¶: Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object. :returns: :rtype: self

show_progress¶: whether to show the progress of heavy calculations on this object.

timescales¶

Returns the implied timescale estimates

Returns:	timescales – timescales for all processes and lag times. l is the number of lag times and k is the number of computed timescales.
Return type:	ndarray((l x k), dtype=float)

References

Implied timescales as a lagtime-selection and MSM-validation approach were suggested in [1]. Error estimation is done either using moving block bootstrapping [2] or a Bayesian analysis using Metropolis-Hastings Monte Carlo sampling of the posterior. Nonreversible Bayesian sampling is done by independently sampling Dirichtlet distributions of the transition matrix rows. A Monte Carlo method for sampling reversible MSMs was introduced in [3]. Here we employ a much more efficient algorithm introduced in [4].

[1]	Swope, W. C. and J. W. Pitera and F. Suits: Describing protein folding kinetics by molecular dynamics simulations: 1. Theory. J. Phys. Chem. B 108: 6571-6581 (2004)

[2]	Kuensch, H. R.: The jackknife and the bootstrap for general stationary observations. Ann. Stat. 17, 1217-1241 (1989)

[3]	Noe, F.: Probability Distributions of Molecular Observables computed from Markov Models. J. Chem. Phys. 128, 244103 (2008)

[4]	Trendelkamp-Schroer, B, H. Wu, F. Paul and F. Noe: Estimation and uncertainty of reversible Markov models. http://arxiv.org/abs/1507.05990

[5]	Nueske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C. and Noe, F.: Markov State Models from short non-Equilibrium Simulations - Analysis and Correction of Estimation Bias J. Chem. Phys. (submitted) (2017)