Hilbert space embeddings of independence tests of several variables with radial basis functions

2024/07/09 by Jean Carlo Guella, Guella, Jean Carlo
Mathematics · #42A82 #43A35 #44A10 #46E22 #62H15 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.06854

openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the Lancaster/Streitberg interactions, and are multivariate extensions of Bernstein functions. Addressing a gap in these two probability contexts of interactions, we introduce an indexed measure of independence that generalizes the Lancaster interaction. We present several examples of these functions derived from high-order completely monotone functions.

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