On the Theory of Conditional Feature Alignment for Unsupervised Domain-Adaptive Counting

TL;DR

This paper introduces a theoretical framework for conditional feature alignment in unsupervised domain adaptation for object counting, demonstrating improved cross-domain generalization and outperforming existing methods.

Contribution

It formalizes the concept of conditional divergence and provides a practical implementation that explicitly preserves density-related features across domains.

Findings

Outperforms existing unsupervised domain adaptation methods.

Tighter decision error bounds through conditional alignment.

Empirical validation on multiple datasets confirms effectiveness.

Abstract

Object counting models suffer when deployed across domains with differing density variety, since density shifts are inherently task-relevant and violate standard domain adaptation assumptions. To address this, we propose a theoretical framework of conditional feature alignment and provide a straightforward implementation. By theoretical analysis, our framework is feasible to achieve superior cross-domain generalization for counting. In the presented network, the features related to density are explicitly preserved across domains. Theoretically, we formalize the notion of conditional divergence by partitioning each domain into subsets and measuring divergences per condition. We then derive a joint error bound showing that, under discrete label spaces treated as condition sets, aligning distributions conditionally leads to tighter bounds on the combined source-target decision error than unconditional alignment. Empirically, we demonstrate the effectiveness of our approach through extensive experiments on multiple counting datasets with varying density distributions. The results show that our method outperforms existing unsupervised domain adaptation methods, empirically validating the theoretical insights on conditional feature alignment.