frites.conn.conn_covgc#

frites.conn.conn_covgc(data, dt, lag, t0, step=1, roi=None, times=None, method='gc', conditional=False, norm=False, gcrn=False, n_jobs=- 1, verbose=None, **kw_links)[source]#

Single-trial covariance-based Granger Causality for gaussian variables.

This function computes the (conditional) covariance-based Granger Causality (covgc) for each trial.

Note

Total Granger interdependence

TGI = gc.sum(axis=-1) = gc(x->y) + gc(y->x) + gc(x.y)

TGI = Hycy + Hxcx - Hxxcyy

Relations between Mutual Informarion and conditional entropies

This quantity can be defined as the Increment of Total Interdependence and it can be calculated from the different of two mutual informations as follows

\[\begin{split}Ixxyy &= I(X_{i+1}, X_{i}|Y_{i+1}, Y_{i}) \\ &= H(X_{i+1}) + H(Y_{i+1}) - H(X_{i+1},Y_{i+1}) \\ &= log(det_{xi1}) + log(det_{yi1}) - log(det_{xyi1}) \\ Ixy &= I(X_{i}|Y_{i}) \\ &= H(X_{i}) + H(Y_{i}) - H(X_{i}, Y_{i}) \\ &= log(det_{xi}) + log(det_{yi}) - log(det_{yxi}) \\ ITI &= Ixxyy - Ixy\end{split}\]

Parameters

datanumpy:array_like

Electrophysiological data. Several input types are supported :

Standard NumPy arrays of shape (n_epochs, n_roi, n_times)

mne.Epochs

xarray.DataArray of shape (n_epochs, n_roi, n_times)

dtpython:int

Duration of the time window for covariance correlation in samples

lagpython:int

Number of samples for the lag within each trial

t0numpy:array_like

Array of zero time in samples of length (n_window,)

steppython:int | 1

Number of samples stepping in the past for the lag within each trial

timesnumpy:array_like | python:None

Time vector array of shape (n_times,). If the input is an xarray, the name of the time dimension can be provided

roinumpy:array_like | python:None

ROI names of a single subject. If the input is an xarray, the name of the ROI dimension can be provided

method{‘gauss’, ‘gc’}

Method for the estimation of the covgc. Use either ‘gauss’ which assumes that the time-points are normally distributed or ‘gc’ in order to use the gaussian-copula.

conditionalbool | python:False

If True, the conditional Granger Causality is computed i.e the past is also conditioned by the past of other sources.

normbool | python:False

If True, the normalised Granger Causality is computed See [6].

n_jobspython:int | -1

Number of jobs to use for parallel computing (use -1 to use all jobs). The parallel loop is set at the pair level.

kw_linkspython:dict | {}

Additional arguments for selecting links to compute are passed to the function frites.conn.conn_links()

Returns

gcnumpy:array_like

Granger Causality arranged as (n_epochs, n_pairs, n_windows, 3) where the last dimension means :

0 : pairs[:, 0] -> pairs[:, 1] (x->y)

1 : pairs[:, 1] -> pairs[:, 0] (y->x)

2 : instantaneous (x.y)

Examples using `frites.conn.conn_covgc`#

Statistical analysis of a stimulus-specific network

Estimate the covariance-based Granger Causality

AR : simulate common driving input

AR : conditional covariance based Granger Causality

frites.conn.conn_covgc#

Examples using frites.conn.conn_covgc#

Examples using `frites.conn.conn_covgc`#