Variational Determinant Estimation with Spherical Normalizing Flows

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.

Accepted at 3rd Symposium on Advances in Approximate Bayesian Inference (AABI) 2021

References in corpus (2)

• Amortized Monte Carlo Integration
• Two equalities expressing the determinant of a matrix in terms of expectations over matrix-vector products

Cited by in corpus (1)

• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability