Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation (2302.02561v5)

Abstract: Previous studies have shown that leveraging domain index can significantly boost domain adaptation performance (arXiv:2007.01807, arXiv:2202.03628). However, such domain indices are not always available. To address this challenge, we first provide a formal definition of domain index from the probabilistic perspective, and then propose an adversarial variational Bayesian framework that infers domain indices from multi-domain data, thereby providing additional insight on domain relations and improving domain adaptation performance. Our theoretical analysis shows that our adversarial variational Bayesian framework finds the optimal domain index at equilibrium. Empirical results on both synthetic and real data verify that our model can produce interpretable domain indices which enable us to achieve superior performance compared to state-of-the-art domain adaptation methods. Code is available at https://github.com/Wang-ML-Lab/VDI.

• The paper introduces VDI, a variational Bayesian framework that infers continuous domain indices for enhanced domain adaptation.
• The paper rigorously defines domain indices by maximizing mutual information and reducing dependency on explicit domain representations.
• The paper's empirical validation shows superior performance over state-of-the-art methods on both synthetic and real-world datasets.

An Academic Summary of "Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation"

The paper explores a novel approach to enhancing domain adaptation (DA) performance by inferring domain indices using an adversarial variational Bayes framework. The authors present a formal definition of domain indices to address scenarios where these indices are not readily available, thereby limiting the applicability of existing DA methods that depend on them.

Introduction and Background

Domain adaptation methodologies are critical when addressing scenarios where the training and test datasets originate from differing domains. Traditional approaches strive to create domain-invariant features by decoupling a data point's latent representation from its domain identity. Recent advances in DA, however, demonstrate that using a more sophisticated representation of domain identity—as a continuous index rather than a discrete label—can significantly enhance performance metrics such as accuracy (CIDA, GRDA).

Despite the success, the challenge lies in the common unavailability of such indices, which significantly confines the broader application spectrum of domain-index-reliant DA techniques. The paper seeks to address this gap by defining domain indices probabilistically and developing a mechanism to infer them directly from data.

Methodology

The authors propose Variational Domain Indexing (VDI), an interpretable domain indexing framework using a variational Bayesian approach. The contributions include:

1. A rigorous probabilistic definition of domain indices focused on maximizing the mutual information between data, labels, and domain indices while minimizing dependency on domain representations.
2. Deployment of a variational Bayesian model to infer domain indices as latent variables from multidomain data without prior domain index knowledge.
3. Theoretical justifications illustrating that VDI's objective function accurately infers optimal domain indices by maximizing ELBO and minimizing adversarial losses.
4. Empirical results on synthetic and real-world datasets that demonstrate VDI's capability to produce meaningful and rich domain indices, resulting in superior DA performance over state-of-the-art methods.

Theoretical Analysis

The paper incorporates detailed theoretical analyses, ensuring that VDI's framework not only infers interpretable domain indices efficiently but also aligns with the probabilistic definition. The authors achieve this through:

• Formulating an ELBO optimization problem that encapsulates mutual information maximization.
• Incorporating adversarial training components that enforce independence between learned representations and inferred domain indices.
• Demonstrating that the global optimum of the VDI framework satisfies the custom-defined properties of domain indices.

Experimental Validation

The empirical evaluation spans several datasets, both synthetic (Circle, DG-15, DG-60) and real-world (TPT-48, CompCars). The experiments validate the robustness and effectiveness of VDI through:

• Consistently outperforming existing state-of-the-art DA methods in terms of task-specific metrics such as accuracy and mean square error.
• Inferring intuitive and meaningful domain indices that align with real-world semantical concepts, such as geographical divisions in climate datasets and differentiating automotive features in image datasets.

Implications and Future Work

The ability to automatically infer domain indices extends the reach and applicability of DA methodologies to a wider array of real-world problems, where explicitly known domain features are often lacking. Practically, this could improve model generalization across various domains without the need for bespoke data preprocessing or domain-specific modeling adjustments.

The paper proposes exploring the joint inference of domain identities alongside indices as a future avenue, potentially enhancing the adaptability of DA models further.

In summary, this research contributes foundational tools and insights crucial for advancing DA methodologies, offering a new lens through which domain disparities can be addressed more effectively.