Theoretical Performance Guarantees for Partial Domain Adaptation via Partial Optimal Transport

TL;DR

This paper provides a theoretical foundation for partial domain adaptation using partial optimal transport, deriving generalization bounds and proposing a new algorithm that improves domain alignment and source data weighting.

Contribution

It introduces a theoretical analysis of partial domain adaptation via partial optimal transport and develops a practical algorithm with improved weighting schemes.

Findings

Theoretical generalization bounds support partial Wasserstein distance for domain alignment.

The proposed WARMPOT algorithm performs competitively with recent methods.

The new weighting scheme improves upon existing heuristic approaches.

Abstract

In many scenarios of practical interest, labeled data from a target distribution are scarce while labeled data from a related source distribution are abundant. One particular setting of interest arises when the target label space is a subset of the source label space, leading to the framework of partial domain adaptation (PDA). Typical approaches to PDA involve minimizing a domain alignment term and a weighted empirical loss on the source data, with the aim of transferring knowledge between domains. However, a theoretical basis for this procedure is lacking, and in particular, most existing weighting schemes are heuristic. In this work, we derive generalization bounds for the PDA problem based on partial optimal transport. These bounds corroborate the use of the partial Wasserstein distance as a domain alignment term, and lead to theoretically motivated explicit expressions for the empirical source loss weights. Inspired by these bounds, we devise a practical algorithm for PDA, termed WARMPOT. Through extensive numerical experiments, we show that WARMPOT is competitive with recent approaches, and that our proposed weights improve on existing schemes.