Domain Generalization via Conditional Invariant Representation (1807.08479v1)

Abstract: Domain generalization aims to apply knowledge gained from multiple labeled source domains to unseen target domains. The main difficulty comes from the dataset bias: training data and test data have different distributions, and the training set contains heterogeneous samples from different distributions. Let $X$ denote the features, and $Y$ be the class labels. Existing domain generalization methods address the dataset bias problem by learning a domain-invariant representation $h(X)$ that has the same marginal distribution $\mathbb{P}(h(X))$ across multiple source domains. The functional relationship encoded in $\mathbb{P}(Y|X)$ is usually assumed to be stable across domains such that $\mathbb{P}(Y|h(X))$ is also invariant. However, it is unclear whether this assumption holds in practical problems. In this paper, we consider the general situation where both $\mathbb{P}(X)$ and $\mathbb{P}(Y|X)$ can change across all domains. We propose to learn a feature representation which has domain-invariant class conditional distributions $\mathbb{P}(h(X)|Y)$. With the conditional invariant representation, the invariance of the joint distribution $\mathbb{P}(h(X),Y)$ can be guaranteed if the class prior $\mathbb{P}(Y)$ does not change across training and test domains. Extensive experiments on both synthetic and real data demonstrate the effectiveness of the proposed method.

• The paper introduces a novel framework that enforces conditional invariant representations to effectively address cross-domain distribution shifts.
• It leverages kernel mean embeddings and two regularization terms to minimize both local and global distribution gaps across domains.
• Empirical results on benchmark datasets show improved classification accuracy over traditional methods, underscoring its practical value.

Critical Analysis of "Domain Generalization via Conditional Invariant Representations"

The paper "Domain Generalization via Conditional Invariant Representations" by Ya Li et al. addresses a pivotal issue in machine learning: the challenge of transferring knowledge derived from multiple source domains to unseen target domains, particularly under conditions where both marginal and conditional distributions can vary. Domain generalization, as elucidated in this work, is integral to enhancing model adaptability in real-world applications, such as computer vision and medical diagnosis, where data shifts are prevalent.

Key Contributions

The primary contribution of this paper is the introduction of a novel method to tackle domain generalization by focusing on conditional invariant representations. Unlike traditional approaches that often presume invariant conditional distribution $\mathbb{P}(Y|X)$ or solely address the shifts in $\mathbb{P}(X)$, this work emphasizes the need for invariance in the class-conditional distribution $\mathbb{P}(h(X)|Y)$. This strategic shift is grounded in the recognition that real-world scenarios frequently exhibit changes in both feature and label distributions across domains.

The authors propose a framework for learning representations where the conditional distribution is invariant across domains, ensuring stability even when the prior distribution $\mathbb{P}(Y)$ remains constant. This approach is formalized through the introduction of two novel regularization terms that are essential to enforcing distributional invariance. The empirical results presented, encompassing synthetic and real datasets, underscore the efficacy of this methodology.

Methodological Innovations

The proposed method leverages kernel mean embeddings to achieve conditional invariance, drawing on insights from statistical learning theory. By minimizing distribution variances both locally (class-conditional) and globally (class prior-normalized), the approach intrinsically accounts for challenges posed by heterogeneous domain distributions. The paper contrasts its framework with prior domain generalization strategies that largely hinge on marginal distributional invariances.

Central to the method’s success is its ability to circumvent assumptions of stable conditional distributions across domains. Instead, it targets the variance through a constrained optimization problem, solvable via eigenvalue decomposition. This mathematically rigorous approach significantly advances the understanding of domain adaptation under dynamic feature-label relationships.

Experimental Evaluation

The experimental validation spans synthetic data and two real-world datasets—VLCS and Office+Caltech—common benchmarks in domain generalization research. The CIDG method leads to improvements in classification accuracy over baseline methods, including KPCA, SCA, and Undo-Bias. These results are noteworthy, particularly in scenarios where the traditional assumption of invariant $\mathbb{P}(Y|X)$ is violated, illustrating CIDG’s ability to retain discriminative power under distributional shifts.

Theoretical and Practical Implications

The theoretical implications of this research reside in refining the assumptions underlying domain generalization. By addressing conditional invariance, the paper proposes a more robust framework potentially applicable across varied domains beyond image classification. The work challenges researchers to reassess the typical assumptions of stability in conditional distributions, urging a closer look at how causal relationships can inform distributional changes.

Practically, this research has profound implications for industries reliant on robust model generalization, including autonomous vehicles, healthcare, and surveillance. By advancing reliable cross-domain learning capabilities, CIDG enhances the predictability and safety of models operating in complex, variable environments.

Future Directions

Future research could delve into deeper integrations with causal inference frameworks, potentially enhancing understanding of domain shifts. Furthermore, extending this methodology to unsupervised or semi-supervised settings could provide considerable scalability and applicability, especially in domains where labeled data is scarce or expensive. The exploration of dynamic distributional changes over time and space also presents a fertile ground for further investigation.

In conclusion, Li et al.’s work makes a substantial contribution to the field of domain generalization by challenging and expanding the current methodological boundaries. It offers a rigorous and effective approach to managing the inherent complexities of real-world data shifts, thereby setting a new trajectory for research and application in robust machine learning systems.