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Quantifying User Coherence: A Unified Framework for Cross-Domain Recommendation Analysis

Michaël Soumm, Alexandre Fournier-Montgieux, Adrian Popescu, Bertrand Delezoide

TL;DR

Novel information-theoretic measures for understanding recommender systems are introduced: a "surprise" measure quantifying users' deviations from popular choices, and a "conditional surprise" measure capturing user interaction coherence, providing insights into algorithm behavior.

Abstract

The effectiveness of Recommender Systems (RS) is closely tied to the quality and distinctiveness of user profiles, yet despite many advancements in raw performance, the sensitivity of RS to user profile quality remains under-researched. This paper introduces novel information-theoretic measures for understanding recommender systems: a "surprise" measure quantifying users' deviations from popular choices, and a "conditional surprise" measure capturing user interaction coherence. We evaluate 7 recommendation algorithms across 9 datasets, revealing the relationships between our measures and standard performance metrics. Using a rigorous statistical framework, our analysis quantifies how much user profile density and information measures impact algorithm performance across domains. By segmenting users based on these measures, we achieve improved performance with reduced data and show that simpler algorithms can match complex ones for low-coherence users. Additionally, we employ our measures to analyze how well different recommendation algorithms maintain the coherence and diversity of user preferences in their predictions, providing insights into algorithm behavior. This work advances the theoretical understanding of user behavior and practical heuristics for personalized recommendation systems, promoting more efficient and adaptive architectures.

Quantifying User Coherence: A Unified Framework for Cross-Domain Recommendation Analysis

TL;DR

Novel information-theoretic measures for understanding recommender systems are introduced: a "surprise" measure quantifying users' deviations from popular choices, and a "conditional surprise" measure capturing user interaction coherence, providing insights into algorithm behavior.

Abstract

The effectiveness of Recommender Systems (RS) is closely tied to the quality and distinctiveness of user profiles, yet despite many advancements in raw performance, the sensitivity of RS to user profile quality remains under-researched. This paper introduces novel information-theoretic measures for understanding recommender systems: a "surprise" measure quantifying users' deviations from popular choices, and a "conditional surprise" measure capturing user interaction coherence. We evaluate 7 recommendation algorithms across 9 datasets, revealing the relationships between our measures and standard performance metrics. Using a rigorous statistical framework, our analysis quantifies how much user profile density and information measures impact algorithm performance across domains. By segmenting users based on these measures, we achieve improved performance with reduced data and show that simpler algorithms can match complex ones for low-coherence users. Additionally, we employ our measures to analyze how well different recommendation algorithms maintain the coherence and diversity of user preferences in their predictions, providing insights into algorithm behavior. This work advances the theoretical understanding of user behavior and practical heuristics for personalized recommendation systems, promoting more efficient and adaptive architectures.
Paper Structure (37 sections, 2 theorems, 19 equations, 13 figures, 5 tables, 1 algorithm)

This paper contains 37 sections, 2 theorems, 19 equations, 13 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Approach
  4. Notations and Problem Formulation
  5. Coherence measures
  6. Interpretation and Properties
  7. User Coherence Segmentation
  8. Regression Model as an Analytical tool
  9. Experimental Setup
  10. Datasets
  11. Data Processing
  12. Recommender Algorithms
  13. Training
  14. Results and Analysis
  15. Experimental Properties of the Measures
  16. ...and 22 more sections

Key Result

Proposition 1

Let $\pi_u$ be the distribution from which $u$ is drawn, and $\pi_u^{\geq 1}$ be the distribution of $u$ conditioned on $|u| \geq1$. Let $S^*(u)=\mathbb{E}_{\pi_u^{\geq 1}}[\widetilde{S}(u)]$ and $CS^*(u)= \mathbb{E}_{\pi_u^{\geq 1}}[\widetilde{CS}(u)]$. Then:

Figures (13)

  • Figure 1: Performance in Recall@20 of different RS, averaged over datasets, w.r. to our proposed Conditional Surprise ($CS(u)$) measure, standardized between 0 and 1, with a moving average smoothing. All RS performance collapse for high values of $CS(u)$.
  • Figure 2: Distribution of the measures across datasets. S denotes the Surprise measure, and CS the Conditional Surprise measure. CS shows remarkable stability across all datasets.
  • Figure 3: Overall algorithms performance across datasets, measured in Recall@20 with confidence intervals at 95%.
  • Figure 4: Comparison of $S(u)$ and $\widetilde{S}(u)$ against $|u|$ on the Netflix dataset, with a regression fo $S(u)$ on $|u|$. Similar graphs are produced for other datasets and for $CS(u)$ (see appendix).
  • Figure 5: Average marginal effect of the variables on the performance. Each value corresponds to the causal variation in Recall@20 when the variable goes up by 1 standard deviation.
  • ...and 8 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof