Variational Determinant Estimation with Spherical Normalizing Flows
This work addresses the problem of high variance in determinant estimation for researchers and practitioners working with large matrices, offering a more efficient and accurate method.
This paper introduces the Variational Determinant Estimator (VDE), which significantly reduces the variance of determinant estimation, even with low sample sizes. In an ideal scenario with a tight variational bound, VDE achieves zero variance, allowing for an exact log determinant estimate from a single sample.
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.