Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification
arXiv:2603.09257v1 Announce Type: new Abstract: Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a distribution-free transductive setting, where learned representations are dependent, and test features are accessible during training. We derive global and class-wise bounds via optimal transport, expressed in terms of Wasserstein distances between encoded feature distributions. We demonstrate that our bounds are efficiently computable and strongly correlate with empirical generalization in graph node classification, improving upon classical complexity measures. Additionally, our analysis reveals how the GNN aggregation process transforms the representation distributions, inducing a trade-off between intra-class concentration and inter-class separation. This yields depth-dependent characterizations that capt
arXiv:2603.09257v1 Announce Type: new Abstract: Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a distribution-free transductive setting, where learned representations are dependent, and test features are accessible during training. We derive global and class-wise bounds via optimal transport, expressed in terms of Wasserstein distances between encoded feature distributions. We demonstrate that our bounds are efficiently computable and strongly correlate with empirical generalization in graph node classification, improving upon classical complexity measures. Additionally, our analysis reveals how the GNN aggregation process transforms the representation distributions, inducing a trade-off between intra-class concentration and inter-class separation. This yields depth-dependent characterizations that capture the non-monotonic relationship between depth and generalization error observed in practice. The code is available at https://github.com/ml-postech/Transductive-OT-Gen-Bound.
Executive Summary
This article presents a novel approach to transductive generalization via optimal transport, establishing new representation-based generalization bounds in a distribution-free transductive setting. The authors derive global and class-wise bounds via optimal transport, expressed in terms of Wasserstein distances between encoded feature distributions. The proposed method improves upon classical complexity measures and captures the non-monotonic relationship between depth and generalization error observed in practice. The authors demonstrate the efficiency and effectiveness of their approach in graph node classification tasks. This work contributes to the development of more accurate and robust machine learning models, particularly in graph-based applications.
Key Points
- ▸ Established new representation-based generalization bounds in a distribution-free transductive setting
- ▸ Derived global and class-wise bounds via optimal transport
- ▸ Improved upon classical complexity measures
- ▸ Captured the non-monotonic relationship between depth and generalization error
- ▸ Demonstrated efficiency and effectiveness in graph node classification tasks
Merits
Strength
The proposed approach is computationally efficient and strongly correlates with empirical generalization in graph node classification tasks.
Methodological Innovation
The use of optimal transport to derive representation-based generalization bounds is a novel and innovative approach that addresses the limitations of classical complexity measures.
Empirical Validation
The authors provide empirical evidence to support the effectiveness of their approach in graph node classification tasks, which is essential for establishing the credibility of their method.
Demerits
Limitation
The proposed approach is limited to graph node classification tasks and may not generalize to other domains or applications.
Scalability
The computational cost of the proposed method may be high for large-scale datasets, which could limit its practical applicability.
Interpretability
The use of optimal transport and Wasserstein distances may make it challenging to interpret the results and understand the underlying mechanisms of the proposed approach.
Expert Commentary
This article presents a significant contribution to the field of machine learning, particularly in the area of graph neural networks. The proposed approach is novel, efficient, and effective, and has the potential to improve the performance of graph neural networks in node classification tasks. The use of optimal transport and Wasserstein distances is a key innovation that addresses the limitations of classical complexity measures and provides a more accurate and robust measure of generalization error. However, the proposed approach is limited to graph node classification tasks and may not generalize to other domains or applications. Additionally, the computational cost of the proposed method may be high for large-scale datasets, which could limit its practical applicability. Overall, this article is a significant contribution to the field of machine learning and has the potential to impact a wide range of applications.
Recommendations
- ✓ Future research should focus on extending the proposed approach to other domains and applications, such as image and text classification.
- ✓ The authors should investigate the use of different optimal transport metrics and Wasserstein distances to improve the efficiency and effectiveness of the proposed approach.