Parameter Estimation in DAGs from Incomplete Data via Optimal Transport

TL;DR

This paper introduces a novel method for estimating parameters in directed graphical models with incomplete data using optimal transport, avoiding traditional likelihood-based assumptions and approximations.

Contribution

It presents a new optimal transport-based framework for parameter estimation in DAGs with incomplete data, bypassing the need for likelihood maximization or variational methods.

Findings

Effectively recovers ground-truth parameters.

Performs comparably or better than existing methods on downstream tasks.

Demonstrates versatility and robustness across experiments.

Abstract

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.