pyPTE: Phase Transfer Entropy in Python

pyPTE is an open-source Python implementation of the Phase Transfer Entropy method, designed to analyze directed connectivity in networks influenced by oscillatory interactions. This tool is inspired by the following foundational works:

• Lobier et al., 2014: Phase transfer entropy: A novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions.
• Hillebrand et al., 2016: Direction of information flow in large-scale resting-state networks is frequency-dependent.

Installation

pip install pyPTE          # or: uv add pyPTE

The core requires only NumPy and SciPy. The adapters are optional:

pip install "pyPTE[mne]"      # MNE-Python adapter (also installs pandas)
pip install "pyPTE[pandas]"   # pandas adapter

Requires Python 3.11 or newer.

Quickstart

PTE takes an (n_channels, n_samples) array and returns two matrices, where entry [i, j] describes information flow from channel i to channel j.

import numpy as np
from pyPTE import PTE

rng = np.random.default_rng(0)
t = np.arange(8000) / 250.0

driver = np.sin(2 * np.pi * 10 * t) + 0.2 * rng.standard_normal(t.size)
target = 0.9 * np.roll(driver, 12) + 0.4 * rng.standard_normal(t.size)

dPTE, raw_PTE = PTE(np.vstack([driver, target]))

print(dPTE[0, 1])  # ~0.80 -> driver leads target
print(dPTE[1, 0])  # ~0.20 -> the reverse direction is suppressed

raw_PTE holds the transfer entropy in bits. dPTE is the direction-normalised form, where dPTE[i, j] + dPTE[j, i] == 1: values above 0.5 mean net flow from i to j, and 0.5 means no preferred direction.

Introduction

Phase Transfer Entropy (PTE) is a measure for directed connectivity in networks coupled by oscillatory interactions. The pyPTE library provides a Python implementation of this method, allowing researchers and developers to apply PTE analysis to their data.

Mathematical Background

The mathematical formulation of PTE can be described as follows:

Given two time series $X$ and $Y$, the PTE is defined as:

$$PTE_{X \to Y} = H(Y_{t+1} | Y_t) - H(Y_{t+1} | Y_t, X_t)$$

The PTE value quantifies the amount of uncertainty reduced in predicting the future phase of $Y$ when considering the current phase of $X$.

Contributing

Contributions to pyPTE are welcome! If you have suggestions, bug reports, or want to contribute code via Pull Requests

License

pyPTE is released under the GPL-3.0 license. For more details, see the LICENSE file.