infoflow

Multiplex information-flow network inference from time series, built on dit.

infoflow infers a directed network from multivariate time series and splits each edge's transfer entropy into three layers (James, Barnett & Crutchfield 2016):

• intrinsic flow, I[Y_t : X_past ↓ W], which remains after any processing of the target's context W;
• synergistic flow, the part of transfer entropy that needs the context (TE − intrinsic);
• shared flow, the part of time-delayed mutual information carried by common history or drivers (TDMI − intrinsic).

Each node also carries its active information storage. The pipeline is mostly hands-off and nonparametric:

1. Preprocess. Rank-based discretization (equal-frequency bins or ordinal patterns) and embedding are chosen per node by cross-validated predictive information, and each node gets a history budget.
2. Skeleton. Parents are selected by greedy multivariate transfer entropy with non-uniform embedding and hierarchical maximum, minimum, omnibus, and sequential statistics with FDR, plus a synergy-aware pair search and a TDMI screen.
3. Layers. Each edge's flows are estimated from one joint distribution, with context merging, cross-fitting, bootstrap intervals, and per-layer tests.
4. Interpretation. Edges are labelled confounded, mediated, or direct, and possible latent confounding is flagged.

import infoflow
from infoflow.datasets import common_driver

data = common_driver(n=3000, seed=0)       # (samples, processes) array
net = infoflow.infer_multiplex(data, prng=0)
net.dataset                                # xarray Dataset (layer, source, target)
net.to_networkx()                          # networkx MultiDiGraph with a layer attribute

Installation

infoflow currently needs the development version of dit (dit.inference Markov-order, ordinal, and surrogate tools):

pip install "infoflow @ git+https://github.com/dit/infoflow"