Implicit Maximum Likelihood Estimation

TL;DR

This paper introduces a straightforward method for estimating parameters in implicit probabilistic models that avoids explicit likelihood calculations, demonstrating theoretical equivalence to maximum likelihood under certain conditions and showing promising experimental results.

Contribution

It proposes a novel estimation technique for implicit models that does not require explicit likelihood functions, applicable in finite-sample, finite-capacity settings.

Findings

Method is theoretically equivalent to maximum likelihood under certain conditions.

Experimental results show promising performance.

Applicable in non-asymptotic, finite-capacity scenarios.

Abstract

Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models that does not require knowledge of the form of the likelihood function or any derived quantities, but can be shown to be equivalent to maximizing likelihood under some conditions. Our result holds in the non-asymptotic parametric setting, where both the capacity of the model and the number of data examples are finite. We also demonstrate encouraging experimental results.