Variational Determinant Estimation with Spherical Normalizing Flows

TL;DR

This paper presents the Variational Determinant Estimator (VDE), a novel method combining variational inference and spherical normalizing flows to accurately estimate determinants with low variance and minimal samples.

Contribution

The paper introduces VDE, a variational extension that reduces variance in determinant estimation using importance-weighted inference and hyperspherical normalizing flows.

Findings

VDE significantly reduces variance at low sample sizes.

A single sample can yield an exact determinant estimate in ideal conditions.

VDE approaches zero variance with a tight variational bound.

Abstract

This paper introduces the Variational Determinant Estimator (VDE), a variational extension of the recently proposed determinant estimator discovered by arXiv:2005.06553v2. Our estimator significantly reduces the variance even for low sample sizes by combining (importance-weighted) variational inference and a family of normalizing flows which allow density estimation on hyperspheres. In the ideal case of a tight variational bound, the VDE becomes a zero variance estimator, and a single sample is sufficient for an exact (log) determinant estimate.