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Distributionally Robust Graph Out-of-Distribution Recommendation via Diffusion Model

Chu Zhao, Enneng Yang, Yuliang Liang, Jianzhe Zhao, Guibing Guo, Xingwei Wang

TL;DR

This work tackles the challenge of distribution shifts in graph-based recommendations by identifying that existing DRO methods overemphasize noisy training samples. It proposes DRGO, a Distributionally Robust Graph framework that combines a denoising diffusion module (via VGAE and latent-space diffusion), a Sinkhorn-DRO objective to handle non-overlapping distributions, and an entropy regularization term to prevent extreme sample weighting. Theoretical results include a generalization bound showing the risk under worst-case distributions is controlled by the distance between training and test distributions, plus gradient analyses explaining noise mitigation. Empirically, DRGO delivers state-of-the-art performance under popularity, temporal, and exposure shifts, while remaining robust to substantial noise, and ablation studies confirm the essential roles of diffusion and entropy regularization.

Abstract

The distributionally robust optimization (DRO)-based graph neural network methods improve recommendation systems' out-of-distribution (OOD) generalization by optimizing the model's worst-case performance. However, these studies fail to consider the impact of noisy samples in the training data, which results in diminished generalization capabilities and lower accuracy. Through experimental and theoretical analysis, this paper reveals that current DRO-based graph recommendation methods assign greater weight to noise distribution, leading to model parameter learning being dominated by it. When the model overly focuses on fitting noise samples in the training data, it may learn irrelevant or meaningless features that cannot be generalized to OOD data. To address this challenge, we design a Distributionally Robust Graph model for OOD recommendation (DRGO). Specifically, our method first employs a simple and effective diffusion paradigm to alleviate the noisy effect in the latent space. Additionally, an entropy regularization term is introduced in the DRO objective function to avoid extreme sample weights in the worst-case distribution. Finally, we provide a theoretical proof of the generalization error bound of DRGO as well as a theoretical analysis of how our approach mitigates noisy sample effects, which helps to better understand the proposed framework from a theoretical perspective. We conduct extensive experiments on four datasets to evaluate the effectiveness of our framework against three typical distribution shifts, and the results demonstrate its superiority in both independently and identically distributed distributions (IID) and OOD.

Distributionally Robust Graph Out-of-Distribution Recommendation via Diffusion Model

TL;DR

This work tackles the challenge of distribution shifts in graph-based recommendations by identifying that existing DRO methods overemphasize noisy training samples. It proposes DRGO, a Distributionally Robust Graph framework that combines a denoising diffusion module (via VGAE and latent-space diffusion), a Sinkhorn-DRO objective to handle non-overlapping distributions, and an entropy regularization term to prevent extreme sample weighting. Theoretical results include a generalization bound showing the risk under worst-case distributions is controlled by the distance between training and test distributions, plus gradient analyses explaining noise mitigation. Empirically, DRGO delivers state-of-the-art performance under popularity, temporal, and exposure shifts, while remaining robust to substantial noise, and ablation studies confirm the essential roles of diffusion and entropy regularization.

Abstract

The distributionally robust optimization (DRO)-based graph neural network methods improve recommendation systems' out-of-distribution (OOD) generalization by optimizing the model's worst-case performance. However, these studies fail to consider the impact of noisy samples in the training data, which results in diminished generalization capabilities and lower accuracy. Through experimental and theoretical analysis, this paper reveals that current DRO-based graph recommendation methods assign greater weight to noise distribution, leading to model parameter learning being dominated by it. When the model overly focuses on fitting noise samples in the training data, it may learn irrelevant or meaningless features that cannot be generalized to OOD data. To address this challenge, we design a Distributionally Robust Graph model for OOD recommendation (DRGO). Specifically, our method first employs a simple and effective diffusion paradigm to alleviate the noisy effect in the latent space. Additionally, an entropy regularization term is introduced in the DRO objective function to avoid extreme sample weights in the worst-case distribution. Finally, we provide a theoretical proof of the generalization error bound of DRGO as well as a theoretical analysis of how our approach mitigates noisy sample effects, which helps to better understand the proposed framework from a theoretical perspective. We conduct extensive experiments on four datasets to evaluate the effectiveness of our framework against three typical distribution shifts, and the results demonstrate its superiority in both independently and identically distributed distributions (IID) and OOD.
Paper Structure (31 sections, 1 theorem, 57 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 31 sections, 1 theorem, 57 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Problem Definition
  4. Distributionally Robust Optimization
  5. Methodology
  6. Limitations of DRO-based Recommendation Method
  7. Sinkhorn DRO
  8. Model Instantiations
  9. Denoising Diffusion Module
  10. Nominal Distribution
  11. Uncertainty Set
  12. Joint Optimization
  13. Theoretical Analysis
  14. Experiments
  15. Overall Performance (R1)
  16. ...and 16 more sections

Key Result

theorem 1

Assume the loss function $R(\theta,W_{q_i})$ is bounded by a constant $B$. For $\delta > 0$, with probability at least $1 - \delta$, the following inequality holds for all $f \in F$:

Figures (4)

  • Figure 1: (a) Divide the user-item interaction data in the Yelp2018 dataset into a major group (90%) and a minor group (10%) based on user activity levels. Inject an additional 10% of the data as a noise group. Compare the performance of DRO-LightGCN and our DRGO, observing the weight changes for each group across multiple iterations. (b) The model's performance under different noise levels on the Yelp2018 dataset.
  • Figure 2: The proposed DRGO model schematic. An bipartite graph is first processed using VGAE diffusion to obtain denoised embeddings. Then, betweenness centrality and $k$-means clustering are applied to construct the nominal distribution and uncertainty set. Finally, a joint optimization strategy is employed for optimization.
  • Figure 3: Relative performance decline with respect to noise ratio. We simulate different levels of noise by substituting 5%, 10%, 15%, and 25% of the interaction edges with artificial edges.
  • Figure 4: Analysis of the impact of various hyperparameters on model performance.

Theorems & Definitions (3)

  • theorem 1
  • proof
  • proof