Implicit Bayes Adaptation: A Collaborative Transport Approach

TL;DR

This paper introduces an implicit Bayesian approach to domain adaptation using optimal transport, incorporating geometric and cluster priors to enhance robustness and performance in machine learning tasks.

Contribution

It proposes a novel implicit Bayesian framework for domain adaptation that refines the metric and leverages cluster priors within an optimal transport setting.

Findings

Improved domain adaptation robustness and accuracy.

Effective integration of geometric and cluster priors.

Validated through experimental results.

Abstract

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the $l^2$ Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.