# Extracting individual variable information for their decoupling, direct mutual information and multi-feature Granger causality

arXiv: https://arxiv.org/abs/2311.13431 · HTML: https://mlsanity.com/paper/2311.13431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 11 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [Hierarchical correlation reconstruction with missing data, for example for biology-inspired neuron](https://mlsanity.com/paper/1804.06218/) (2018)
- [Modelling bid-ask spread conditional distributions using hierarchical correlation reconstruction](https://mlsanity.com/paper/1911.02361/) (2019)
- [Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction](https://mlsanity.com/paper/2206.06194/) (2022)
- [Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals](https://mlsanity.com/paper/2305.09478/) (2023)

## Abstract (arXiv)

Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. overlineX|Y as random variable containing information from X, but with removed information about Y, by using (x,y) leftrightarrow (barx=textrmCDFX|Y=y(x),y) reversible normalization. One application can be decoupling of individual information of variables: reversibly transform (X1,ldots,Xn)leftrightarrow(tildeX1,ldots tildeXn) together containing the same information, but being independent: forallineq j tildeXiperp tildeXj, tildeXiperp Xj. It requires detailed models of complex conditional probability distributions - it is generally a difficult task, but here can be done through multiple dependency reducing iterations, using imperfect methods (here HCR: Hierarchical Correlation Reconstruction). It could be also used for direct mutual information - evaluating direct information transfer: without use of intermediate variables. For causality direction there is discussed multi-feature Granger causality, e.g. to trace various types of individual information transfers between such decoupled variables, including propagation time (delay).