Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning (1702.08811v3)

Abstract: The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distribution matching approaches exist that can be interpreted as the matching of weighted sums of moments, e.g. Maximum Mean Discrepancy (MMD), an explicit order-wise matching of higher order moments has not been considered before. We propose to match the higher order central moments of probability distributions by means of order-wise moment differences. Our model does not require computationally expensive distance and kernel matrix computations. We utilize the equivalent representation of probability distributions by moment sequences to define a new distance function, called Central Moment Discrepancy (CMD). We prove that CMD is a metric on the set of probability distributions on a compact interval. We further prove that convergence of probability distributions on compact intervals w.r.t. the new metric implies convergence in distribution of the respective random variables. We test our approach on two different benchmark data sets for object recognition (Office) and sentiment analysis of product reviews (Amazon reviews). CMD achieves a new state-of-the-art performance on most domain adaptation tasks of Office and outperforms networks trained with MMD, Variational Fair Autoencoders and Domain Adversarial Neural Networks on Amazon reviews. In addition, a post-hoc parameter sensitivity analysis shows that the new approach is stable w.r.t. parameter changes in a certain interval. The source code of the experiments is publicly available.

• The paper introduces CMD as a metric that minimizes differences in central moments to improve domain-invariant representation learning in neural networks.
• It provides theoretical proofs confirming CMD as a valid metric that guarantees convergence in distribution.
• Empirical evaluations on object recognition and sentiment analysis tasks demonstrate state-of-the-art performance with reduced computational complexity.

Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning

The paper discusses Central Moment Discrepancy (CMD), a novel metric for domain-invariant representation learning within the context of unsupervised domain adaptation using neural networks. This research addresses the challenge of leveraging labeled data from source domains to facilitate learning in target domains lacking labeled data, a common scenario in many real-world applications where label acquisition is costly.

Key Contributions

1. Introduction of CMD: The authors propose CMD as a new regularization method that explicitly minimizes the differences in central moments of probability distributions. While existing approaches like Maximum Mean Discrepancy (MMD) and KL-divergence focus on matching weighted sums of moments or first moments, respectively, CMD aims to match higher-order moments directly in the activation space.
2. Theoretical Foundations: CMD is rigorously defined as a metric on probability distributions over compact intervals. The paper provides proofs establishing CMD's status as a valid metric and demonstrating that convergence in CMD implies convergence in distribution.
3. Empirical Evaluation: The CMD method was empirically tested on two benchmark datasets: the Office dataset for object recognition and the Amazon reviews dataset for sentiment analysis. CMD was shown to achieve state-of-the-art performance in many domain adaptation tasks, outperforming methods based on MMD, Variational Fair Autoencoders, and Domain Adversarial Neural Networks.
4. Computational Efficiency: Unlike MMD, CMD does not require computationally intensive kernel matrix computations, making it more scalable for large datasets. The complexity of CMD is linearly proportional to the number of samples, which is a significant improvement over the quadratic complexity associated with MMD.
5. Parameter Stability: The paper includes a post-hoc parameter sensitivity analysis, suggesting that CMD is robust to changes in its parameters within specific intervals. This robustness implies a reduced need for exhaustive parameter tuning, further facilitating its practical application.

Implications and Future Directions

The introduction of CMD has several implications for the field of domain adaptation:

• Enhanced Distribution Matching: By explicitly addressing higher-order moments, CMD provides a more comprehensive approach to distribution matching, potentially leading to more robust feature representations across domains.
• Scalability: The reduction in computational complexity compared to kernel-based methods like MMD increases CMD's applicability in scenarios with large-scale datasets, which are becoming increasingly common in real-world applications.
• Theoretical Impact: Theoretical guarantees regarding CMD's properties as a metric and its implications for distributional convergence offer a solid foundation for its integration into deep learning frameworks.

Future research could explore extending CMD to other application areas, such as generative models, where distribution matching plays a crucial role. Additionally, investigating variants of CMD that could handle more complex dependencies between features or integrating CMD into architectures like transformers may prove beneficial.

In summary, the CMD method represents an important development in domain adaptation, providing a novel and efficient approach to learning domain-invariant representations by focusing on the explicit matching of higher-order moments in the hidden layers of neural networks.