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arXiv · 2407.06854

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

Jean Carlo Guella
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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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Jean Carlo Guella. 2024-07-09. Hilbert space embeddings of independence tests of several variables with radial basis functions. https://arxiv.org/abs/2407.06854

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