Information-Based Network Inference

Dany Mukesha

2026-05-13

One promising area that is currently underutilized in mainstream biology/bioinformatics, despite being computationally efficient and solvable on a standard PC, is Information-Based Network Inference using “Part Mutual Information” (PMI).

While biologists often use correlation or standard Mutual Information (MI) to build gene regulatory networks, these methods struggle with “indirect dependencies” (e.g., if Gene A regulates Gene B, and Gene B regulates Gene C, a standard tool might wrongly show a direct link between A and C).

A common limitation mentioned in most recent bioinformatics publications (such as those dealing with single-cell RNA sequencing or “multi-omics” integration) is the “curse of dimensionality” and the false-positive rate in network reconstruction.

Most current tools use “Partial Correlation,” which only works if the relationship is linear (a straight line). However, biological systems are non-linear. Researchers often admit their networks contain many “false edges” because they cannot efficiently calculate non-linear conditional independence on a standard computer.

Part Mutual Information (PMI) is a relatively new statistical metric designed to identify the “direct” strength between two variables (like two genes) while stripping away the influence of all other variables.

Why it’s better:

1. Non-linear: Unlike standard correlation, it catches complex biological “curves.”
2. No “False Links”: It specifically quantifies only the direct connection.
3. Low Power Requirements: It does not require a supercomputer or a GPU. It uses basic math (logarithms and probability distributions) that a standard laptop CPU can calculate in seconds.

It is possible to use publicly available data from the TCGA (The Cancer Genome Atlas) or GEO (Gene Expression Omnibus), using a Step-by-Step Approach:

1. Download Data: Grab a simple CSV file of gene expression levels for a specific disease (e.g., Lung Cancer).

2. Define the Variables: Let $X$ be Gene 1, $Y$ be Gene 2, and $Z$ be the “background” genes.

3. Calculate PMI: Instead of the standard Mutual Information formula:

   $$I(X; Y) = \sum \sum P(x, y) \log \frac{P(x, y)}{P(x)P(y)}$$

   The PartMI package already implements the PMI formula, which uses a “partial” joint probability. This allows you to see if $X$ and $Y$ are actually talking to each other, or if they just look like they are because $Z$ is talking to both of them.

Why this hasn’t been widely implemented yet (I think!)

Most biologists rely on “off-the-shelf” software like WGCNA (Weighted Gene Co-expression Network Analysis). WGCNA is old and uses simple correlation. So, creating a user-friendly, lightweight software tool that replaces WGCNA with PMI would be a major contribution to the field.

It solves the “limitation of indirect edges” frequently cited in papers, it uses open data, and it runs perfectly on a normal home/office PC.