pactools.dar_model.DAR

class pactools.dar_model.DAR(ordar=1, ordriv=0, criterion=None, normalize=True, ortho=True, center=True, iter_gain=10, eps_gain=0.0001, progress_bar=False, use_driver_phase=False, max_ordar=None, warn_gain_estimation_failure=False)

A driven auto-regressive (DAR) model, as described in [1].

This model uses the simple parametrization:

\[y(t) + \sum_{i=1}^p a_i(t) y(t-i)= \sigma(t)\varepsilon(t)\]

with:

\[a_i(t) = \sum_{k=0}^m a_{ik} x(t)^k\]

and:

\[\log{\sigma(t)} = \sum_{k=0}^m b_{k} x(t)^k\]

Parameters

ordarint >= 0

Order of the autoregressive model (p)

ordrivint >= 0

Order of the taylor expansion for sigdriv (m)

criterionNone or string in (‘bic’, ‘aic’, ‘logl’)

If not None, select the criterion used for model selection.

normalizeboolean

If True, the basis vectors are normalized to unit energy.

orthoboolean

If True, the basis vectors are orthogonalized.

centerboolean

If True, we subtract the mean in sigin

iter_gainint >=0

Maximum number of iteration in gain estimation

eps_gainfloat >= 0

Threshold to stop iterations in gain estimation

use_driver_phaseboolean

If True, we divide the driver by its instantaneous amplitude.

References

[1] Dupre la Tour, T. , Tallot, L., Grabot, L., Doyere, V., van Wassenhove, V., Grenier, Y., & Gramfort, A. (2017). Non-linear Auto-Regressive Models for Cross-Frequency Coupling in Neural Time Series. bioRxiv, 159731.

__init__(self, ordar=1, ordriv=0, criterion=None, normalize=True, ortho=True, center=True, iter_gain=10, eps_gain=0.0001, progress_bar=False, use_driver_phase=False, max_ordar=None, warn_gain_estimation_failure=False)

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(self[, ordar, ordriv, criterion, …])	Initialize self.
copy(self)	Creates a (deep) copy of a model
degrees_of_freedom(self)	Number of parameters of the fitted model
fit(self, sigin, sigdriv, fs[, …])	Estimate the model from input signals
fit_transform(self, sigin, sigdriv, fs[, …])	Same as fit, but returns the residual instead of the model object
get_criterion(self, criterion[, train])	Get the criterion (logL, AIC, BIC) of the fitted model
get_title(self[, name, criterion])	Get the name and orders of the model
likelihood_ratio(self, ar0)	Computation of the likelihood ratio test
plot(self[, title, frange, mode, vmin, …])	Plot the PSD as a function of the driver
plot_lines(self[, title, frange, mode, ax, …])	Plot the PSD as a function of the driver
transform(self, sigin, sigdriv, fs[, …])	Whiten a signal with the already fitted model

Attributes

aic	Akaike information criterion (AIC) of the model
bic	Bayesian information criterion (BIC) of the model
logl	Log likelihood of the model
ordar_	AR order of the model, different from self.ordar if a model selection has been performed
tmax	Scaling of self.logl, self.aic, and self.bic

Examples using pactools.dar_model.DAR

Fitting a DAR model

Grid-search and cross-validation

Phase shift and temporal delay in PAC