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A Sampling-based Framework for Hypothesis Testing on Large Attributed Graphs

Yun Wang, Chrysanthi Kosyfaki, Sihem Amer-Yahia, Reynold Cheng

TL;DR

This work addresses hypothesis testing on large attributed graphs by formalizing node, edge, and path hypotheses and introducing a sampling-based framework. It introduces PHASE, a Path-Hypothesis-Aware SamplEr, which biases sampling toward elements specified by the hypothesis, and PHASE_{opt}, which uses non-backtracking walks and neighbor-limiting tricks to reduce runtime while preserving accuracy. The authors prove convergence properties for hypothesis estimators and demonstrate through experiments on MovieLens, DBLP, and Yelp that PHASE_{opt} can be at least 43x faster than PHASE with <=4% accuracy loss, while delivering tighter p-values and confidence intervals. The approach significantly improves practical hypothesis testing on large graphs and supports longer-path and more complex hypotheses, offering a path toward scalable, hypothesis-aware graph analytics.

Abstract

Hypothesis testing is a statistical method used to draw conclusions about populations from sample data, typically represented in tables. With the prevalence of graph representations in real-life applications, hypothesis testing in graphs is gaining importance. In this work, we formalize node, edge, and path hypotheses in attributed graphs. We develop a sampling-based hypothesis testing framework, which can accommodate existing hypothesis-agnostic graph sampling methods. To achieve accurate and efficient sampling, we then propose a Path-Hypothesis-Aware SamplEr, PHASE, an m- dimensional random walk that accounts for the paths specified in a hypothesis. We further optimize its time efficiency and propose PHASEopt. Experiments on real datasets demonstrate the ability of our framework to leverage common graph sampling methods for hypothesis testing, and the superiority of hypothesis-aware sampling in terms of accuracy and time efficiency.

A Sampling-based Framework for Hypothesis Testing on Large Attributed Graphs

TL;DR

This work addresses hypothesis testing on large attributed graphs by formalizing node, edge, and path hypotheses and introducing a sampling-based framework. It introduces PHASE, a Path-Hypothesis-Aware SamplEr, which biases sampling toward elements specified by the hypothesis, and PHASE_{opt}, which uses non-backtracking walks and neighbor-limiting tricks to reduce runtime while preserving accuracy. The authors prove convergence properties for hypothesis estimators and demonstrate through experiments on MovieLens, DBLP, and Yelp that PHASE_{opt} can be at least 43x faster than PHASE with <=4% accuracy loss, while delivering tighter p-values and confidence intervals. The approach significantly improves practical hypothesis testing on large graphs and supports longer-path and more complex hypotheses, offering a path toward scalable, hypothesis-aware graph analytics.

Abstract

Hypothesis testing is a statistical method used to draw conclusions about populations from sample data, typically represented in tables. With the prevalence of graph representations in real-life applications, hypothesis testing in graphs is gaining importance. In this work, we formalize node, edge, and path hypotheses in attributed graphs. We develop a sampling-based hypothesis testing framework, which can accommodate existing hypothesis-agnostic graph sampling methods. To achieve accurate and efficient sampling, we then propose a Path-Hypothesis-Aware SamplEr, PHASE, an m- dimensional random walk that accounts for the paths specified in a hypothesis. We further optimize its time efficiency and propose PHASEopt. Experiments on real datasets demonstrate the ability of our framework to leverage common graph sampling methods for hypothesis testing, and the superiority of hypothesis-aware sampling in terms of accuracy and time efficiency.
Paper Structure (20 sections, 1 theorem, 12 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 20 sections, 1 theorem, 12 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Definitions
  3. Attributed Graphs
  4. Hypotheses on Attributed Graphs
  5. Problem Statement and Challenges
  6. Sampling-based Hypothesis Testing
  7. Hypothesis-Agnostic Samplers
  8. Hypothesis-Aware Samplers
  9. PHASE Algorithm
  10. $\text{PHASE}_{\text{opt}}$ Algorithm
  11. Convergence of Hypothesis Estimators
  12. Experiments
  13. Experimental Setup
  14. Evaluation Measures
  15. PHASE vs $\text{PHASE}_{\text{opt}}$
  16. ...and 5 more sections

Key Result

Theorem 1

For any function $f$, where $\sum_{(u,v)\in \mathcal{E}}|f(u,v)|<\infty$, almost surely, i.e. the event occurs with probability one.

Figures (8)

  • Figure 1: DBLP network schema and paths
  • Figure 2: The Sampling-based Hypothesis Testing Framework on attributed graphs.
  • Figure 3: Transition probability matrices ${Q}$ for (a) node, (b) edge, and (c) path $(l=2)$ hypotheses (up to the first four rows). $x_i$ represents nodes in $\mathcal{G}$ satisfying the $i$-th node modifier on $\mathcal{P}$ and $y$ represents other nodes.
  • Figure 4: The convergence of hypothesis estimator for two path hypotheses: DB-P3 (left) and YP-P3 (right).
  • Figure 5: DBLP p-value and CI plot for the hypothesis DB-P1
  • ...and 3 more figures

Theorems & Definitions (4)

  • Definition 1: Attributed Graph
  • Definition 2: Path
  • Definition 3: Path Hypothesis
  • Theorem 1: SLLN