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codependence

Concept Overview

Dependence measures that survive non-linearity, which Pearson correlation does not. Distance correlation is zero only under genuine independence. Mutual information and variation of information are information-theoretic and need a binning choice, which get_optimal_number_of_bins supplies. The angular distances turn a correlation into a proper metric — sqrt(2(1-rho)) and its absolute and squared variants — which is what hierarchical clustering needs in order to be well posed at all.

When to Use

Use it upstream of any clustering or feature-pruning step: hrp, hcaa and onc all consume a distance matrix, and feeding them raw correlation silently assumes the relationship is linear. Use distance correlation when you suspect a non-monotone relationship, and variation of information when you want a true metric on discrete variables. Bin selection materially changes mutual-information estimates, so fix it explicitly and record it alongside the result.

Mathematical Foundations

Mutual Information

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

Variation of Information

$VI(X,Y)=H(X)+H(Y)-2I(X;Y)$

Usage Examples

Rust

Distance correlation between series

use openquant::codependence::distance_correlation;

let x = vec![1.0, 2.0, 3.0, 4.0];
let y = vec![1.1, 1.9, 3.2, 3.8];
let dcor = distance_correlation(&x, &y)?;

API Reference

Python API

codependence.angular_distance
codependence.absolute_angular_distance
codependence.squared_angular_distance
codependence.distance_correlation
codependence.get_optimal_number_of_bins
codependence.get_mutual_info
codependence.variation_of_information_score

Rust API

distance_correlation
get_mutual_info
variation_of_information_score
angular_distance

Risk Notes and Caveats

Use with clustering and feature pruning workflows.
Bin selection materially impacts MI estimates.