Density Deconvolution with Normalizing Flows

TL;DR

This paper explores using normalizing flows for density deconvolution with arbitrary noise, employing variational inference, and shows flows outperform Gaussian mixtures in real data experiments.

Contribution

It introduces a novel approach combining normalizing flows with variational inference for density deconvolution with arbitrary noise distributions.

Findings

Normalizing flows can outperform Gaussian mixtures in density deconvolution.

Variational inference is used to handle intractable likelihoods.

Experiments demonstrate the effectiveness of the proposed method on real data.

Abstract

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but would like to exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Since both adjustments lead to an intractable likelihood, we resort to amortized variational inference. We demonstrate some problems involved in this approach, however, experiments on real data demonstrate that flows can already out-perform Gaussian mixtures for density deconvolution.