Using Eigencentrality to Estimate Joint, Conditional and Marginal Probabilities from Mixed-Variable Data: Method and Applications

TL;DR

This paper introduces a non-parametric graph-based method using eigencentrality to estimate joint, conditional, and marginal probabilities from mixed discrete and continuous data, applicable to various machine learning tasks.

Contribution

The paper proposes a novel eigencentrality-based approach for directly estimating probability distributions from mixed-variable data without parametric assumptions.

Findings

Effective in estimating probabilities in mixed-variable datasets

Applicable to classification, regression, and clustering tasks

Demonstrates versatility across multiple machine learning applications

Abstract

The ability to estimate joint, conditional and marginal probability distributions over some set of variables is of great utility for many common machine learning tasks. However, estimating these distributions can be challenging, particularly in the case of data containing a mix of discrete and continuous variables. This paper presents a non-parametric method for estimating these distributions directly from a dataset. The data are first represented as a graph consisting of object nodes and attribute value nodes. Depending on the distribution to be estimated, an appropriate eigenvector equation is then constructed. This equation is then solved to find the corresponding stationary distribution of the graph, from which the required distributions can then be estimated and sampled from. The paper demonstrates how the method can be applied to many common machine learning tasks including classification, regression, missing value imputation, outlier detection, random vector generation, and clustering.