Moment Varieties for Mixtures of Products

TL;DR

This paper investigates the algebraic structure of moment varieties associated with mixture distributions exhibiting conditional independence, focusing on their dimensions and defining equations within nonparametric algebraic statistics.

Contribution

It provides new insights into the dimensions and algebraic equations of moment varieties for mixture models with conditional independence.

Findings

Determined the dimensions of the moment varieties.

Derived defining polynomials for these varieties.

Connected secant varieties of toric varieties to independence structures.

Abstract

The setting of this article is nonparametric algebraic statistics. We study moment varieties of conditionally independent mixture distributions on $\mathbb{R}^n$. These are the secant varieties of toric varieties that express independence in terms of univariate moments. Our results revolve around the dimensions and defining polynomials of these varieties.