On Learning Invariant Representation for Domain Adaptation (1901.09453v2)

Abstract: Due to the ability of deep neural nets to learn rich representations, recent advances in unsupervised domain adaptation have focused on learning domain-invariant features that achieve a small error on the source domain. The hope is that the learnt representation, together with the hypothesis learnt from the source domain, can generalize to the target domain. In this paper, we first construct a simple counterexample showing that, contrary to common belief, the above conditions are not sufficient to guarantee successful domain adaptation. In particular, the counterexample exhibits \emph{conditional shift}: the class-conditional distributions of input features change between source and target domains. To give a sufficient condition for domain adaptation, we propose a natural and interpretable generalization upper bound that explicitly takes into account the aforementioned shift. Moreover, we shed new light on the problem by proving an information-theoretic lower bound on the joint error of \emph{any} domain adaptation method that attempts to learn invariant representations. Our result characterizes a fundamental tradeoff between learning invariant representations and achieving small joint error on both domains when the marginal label distributions differ from source to target. Finally, we conduct experiments on real-world datasets that corroborate our theoretical findings. We believe these insights are helpful in guiding the future design of domain adaptation and representation learning algorithms.

• The paper demonstrates that invariant representation learning can increase target error when conditional shifts exist between domains.
• It establishes an information-theoretic lower bound on joint errors, revealing a critical trade-off in domain adaptation.
• Empirical results on digit classification tasks underscore that over-training invariant features may misalign representations with target distributions.

Analyzing the Boundaries of Learning Invariant Representations for Domain Adaptation

The paper "On Learning Invariant Representation for Domain Adaptation" addresses the complexities involved in utilizing deep neural networks for unsupervised domain adaptation (UDA), particularly focusing on the learning of domain-invariant representations. Domain adaptation seeks to apply knowledge from a labeled source domain to a different, often unlabeled target domain. The hypothesis is that by learning invariant features that align the source and target domains while maintaining low classification error in the source domain, satisfactory generalization to the target domain can be achieved.

The authors scrutinize this hypothesis by constructing a counterexample, highlighting that alignment of domain-invariant representations together with minimal source error does not necessarily assure generalization to the target domain. This scenario arises primarily due to conditional shift—where class-conditional feature distributions differ across domains—demonstrating that invariant representation can, paradoxically, exacerbate target domain error.

To establish a theoretical foundation, the authors extend on existing frameworks of domain adaptation by proving an information-theoretic lower bound on joint errors for any invariant representation-based adaptation methods. Their findings uncover a fundamental trade-off: achieving invariant representations might necessitate an increase in joint errors when marginal label distributions significantly diverge from source to target.

Significantly, the paper proposes a novel generalization upper bound which incorporates the conditional shift, offering insights into a sufficient condition necessary for successful domain adaptation. Unlike prior bounds which hinge on the notion of optimal joint error across domains, this new bound replaces that term with a quantifiable measure of conditional distribution shift. This provides a clearer interpretation of the factors influencing domain adaptation efficacy.

Empirical validation on domain adaptation tasks in digit classification—spanning datasets such as MNIST, USPS, and SVHN—reinforces the theoretical insights. Experimental results showcase how over-training invariant representations can misalign them with the target, particularly when disparities exist in label distributions. A meticulous analysis of these results emphasizes the paper's theoretical contribution and spotlights the non-trivial complexity underlying real-world adaptation scenarios.

The implications of this research are manifold. Practically, it challenges existing methodologies in UDA that predominantly focus on naive alignment of feature representations, advocating instead for nuanced approaches that consider conditional discrepancies. Theoretically, it refines understanding of UDA intricacies, setting a path for developing robust algorithms that judiciously balance source accuracy with conditional consistency.

In conclusion, while traversing deep learning's potential for UDA, the paper serves as a pivotal reference for researchers and practitioners to re-evaluate the design of future algorithms in this challenging landscape. The discussion on balancing representation invariance with conditional accuracy might shape advancements in AI capable of more adeptly bridging the domain gap.