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Distributionally Robust Graph-based Recommendation System

Bohao Wang, Jiawei Chen, Changdong Li, Sheng Zhou, Qihao Shi, Yang Gao, Yan Feng, Chun Chen, Can Wang

TL;DR

Distributionally Robust GNN (DR-GNN) is proposed that incorporates Distributional Robust Optimization (DRO) into the GNN-based recommendation and addresses two core challenges: to enable DRO to cater to graph data intertwined with GNN, GNN is reinterpreted as a graph smoothing regularizer, thereby facilitating the nuanced application of DRO.

Abstract

With the capacity to capture high-order collaborative signals, Graph Neural Networks (GNNs) have emerged as powerful methods in Recommender Systems (RS). However, their efficacy often hinges on the assumption that training and testing data share the same distribution (a.k.a. IID assumption), and exhibits significant declines under distribution shifts. Distribution shifts commonly arises in RS, often attributed to the dynamic nature of user preferences or ubiquitous biases during data collection in RS. Despite its significance, researches on GNN-based recommendation against distribution shift are still sparse. To bridge this gap, we propose Distributionally Robust GNN (DR-GNN) that incorporates Distributional Robust Optimization (DRO) into the GNN-based recommendation. DR-GNN addresses two core challenges: 1) To enable DRO to cater to graph data intertwined with GNN, we reinterpret GNN as a graph smoothing regularizer, thereby facilitating the nuanced application of DRO; 2) Given the typically sparse nature of recommendation data, which might impede robust optimization, we introduce slight perturbations in the training distribution to expand its support. Notably, while DR-GNN involves complex optimization, it can be implemented easily and efficiently. Our extensive experiments validate the effectiveness of DR-GNN against three typical distribution shifts. The code is available at https://github.com/WANGBohaO-jpg/DR-GNN.

Distributionally Robust Graph-based Recommendation System

TL;DR

Distributionally Robust GNN (DR-GNN) is proposed that incorporates Distributional Robust Optimization (DRO) into the GNN-based recommendation and addresses two core challenges: to enable DRO to cater to graph data intertwined with GNN, GNN is reinterpreted as a graph smoothing regularizer, thereby facilitating the nuanced application of DRO.

Abstract

With the capacity to capture high-order collaborative signals, Graph Neural Networks (GNNs) have emerged as powerful methods in Recommender Systems (RS). However, their efficacy often hinges on the assumption that training and testing data share the same distribution (a.k.a. IID assumption), and exhibits significant declines under distribution shifts. Distribution shifts commonly arises in RS, often attributed to the dynamic nature of user preferences or ubiquitous biases during data collection in RS. Despite its significance, researches on GNN-based recommendation against distribution shift are still sparse. To bridge this gap, we propose Distributionally Robust GNN (DR-GNN) that incorporates Distributional Robust Optimization (DRO) into the GNN-based recommendation. DR-GNN addresses two core challenges: 1) To enable DRO to cater to graph data intertwined with GNN, we reinterpret GNN as a graph smoothing regularizer, thereby facilitating the nuanced application of DRO; 2) Given the typically sparse nature of recommendation data, which might impede robust optimization, we introduce slight perturbations in the training distribution to expand its support. Notably, while DR-GNN involves complex optimization, it can be implemented easily and efficiently. Our extensive experiments validate the effectiveness of DR-GNN against three typical distribution shifts. The code is available at https://github.com/WANGBohaO-jpg/DR-GNN.
Paper Structure (27 sections, 3 theorems, 9 equations, 4 figures, 5 tables)

This paper contains 27 sections, 3 theorems, 9 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. PRELIMINARY
  3. GNN-based Recommender Systems
  4. Distributionally Robust Optimization
  5. METHODS
  6. Distributionally Robust GNN
  7. Graph Edge-Addition Strategy
  8. Theoretical Analyses
  9. Discussions
  10. EXPERIMENTS
  11. Performance Comparison (RQ1 and RQ2)
  12. Evaluations on Popularity Shift Setting.
  13. Evaluations on Temporal Shift Setting.
  14. Evaluations on Exposure Shift Setting.
  15. Ablation Study (RQ3)
  16. ...and 12 more sections

Key Result

Lemma 1

Performing graph aggregation in LightGCN is equivalent to optimizing the following graph smoothness regularizer using gradient descent with appropriate learning rate: Here, $P_{u}$ denotes the distribution of the neighbor nodes of $u$ and $\theta$ represents the model parameters. The embeddings of nodes $u$ and $v$ are denoted by $\mathrm{E}_u$ and $\mathrm{E}_v$, respectively.

Figures (4)

  • Figure 1: The performance comparison of MF koren2009matrix and LightGCN he_lightgcn_2020 under both in-distribution (IID) and out-of-distribution (OOD) testing scenarios. For the OOD testing, here we introduce popularity shift in Yelp2018 and temporal shift in Movielens-1M. More details about experimental setting refer to section \ref{['sec:4']}.
  • Figure 2: Illustration of how DR-GNN augments LightGCN: it gives edge weights during graph aggregation and introduces new nodes as neighbors.
  • Figure 3: t-SNE Visualization on Douban. DR-GNN ensures that the representations of hot items and cold items are almost distributed in the same space.
  • Figure 4: Analysis of the role of $\alpha$. (a) Left: The performance of DR-GNN in terms of NDCG across different $\alpha$ on three datasets with varying degrees of distribution shift. (b) Right: The relationship between the degree of distribution shift and the optimal $\alpha$.

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • theorem 1