Conditional Dependence via U-Statistics Pruning

• URL: http://arxiv.org/abs/2410.15888v2
• Date: Tue, 11 Mar 2025 16:52:01 GMT
• Title: Conditional Dependence via U-Statistics Pruning
• Authors: Ferran de Cabrera, Marc Vilà-Insa, Jaume Riba,
• Abstract summary: This paper presents a novel measure of conditional dependence based on the use of incomplete unbiased statistics of degree two.<n>The proposed approach is articulated as an extension of the Hilbert-Schmidt independence criterion, which becomes expressible through kernels that operate on 4-tuples of data.
• Score: 11.552000005640203
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the inversion of ill-conditioned autocorrelation matrices. This paper presents a novel measure of conditional dependence based on the use of incomplete unbiased statistics of degree two, which allows to re-interpret independence as uncorrelatedness on a finite-dimensional feature space. This formulation enables to prune data according to observations of the confounder itself, thus avoiding matrix inversions altogether. The proposed approach is articulated as an extension of the Hilbert-Schmidt independence criterion, which becomes expressible through kernels that operate on 4-tuples of data.

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