用扩散模型提升假设检验与变化点检测的性能
Diffusion-Based Hypothesis Testing and Change-Point Detection
- 将评分函数方法扩展为基于扩散的版本，增强检测能力
- 理论证明扩散算法在特定条件下可达到最优性能
- 通过数值优化权重矩阵，实测显示性能显著优于传统方法
评分基方法在建模与生成任务中日益流行。尽管已有研究利用评分函数进行假设检验与变化点检测，但其性能通常不及基于似然的方法。近期工作通过矩阵函数或权重矩阵对评分函数进行变换，将评分基Fisher散度推广为扩散散度。本文进一步将评分基的假设检验与变化点检测停止规则拓展至扩散基形式，并理论上量化了这些扩散基算法的性能，研究了最优性能可实现的场景。我们提出一种数值优化权重矩阵的方法，并通过数值模拟验证了扩散基算法的优势。
原文摘要 · Abstract (English)
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we extend the score-based hypothesis test and change-point detection stopping rule into their diffusion-based analogs. Additionally, we theoretically quantify the performance of these diffusion-based algorithms and study scenarios where optimal performance is achievable. We propose a method of numerically optimizing the weight matrix and present numerical simulations to illustrate the advantages of diffusion-based algorithms.
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