首次给出分数匹配学习多项式指数族的有限样本复杂度边界。
Finite Sample Bounds for Learning with Score Matching
- 基于分数匹配方法分析多项式指数族结构学习的样本需求
- 样本量与模型维度呈多项式依赖，优于以往渐近结果
- 适合关注高维统计理论和学习算法可靠性研究者
连续指数族分布（支持集无界）在高维统计中的学习仍是重要研究方向。近年来，由于相比最大似然估计计算更简便，分数匹配已成为连续变量指数族学习的常用方法。然而，其统计性质的理论理解仍不充分。本文针对多项式指数族，首次提供了分数匹配结构学习的非渐近样本复杂度分析。推导出的样本边界显示，样本量与模型维度呈多项式关系。这是首个此类结果，此前所有工作仅给出样本复杂度的渐近界限。
原文摘要 · Abstract (English)
Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high-dimensional statistics. In recent years, score matching has become a widely used method for learning exponential families with continuous variables due to its computational ease when compared against maximum likelihood estimation. However, theoretical understanding of the statistical properties of score matching is still lacking. In this work, we provide a non-asymptotic sample complexity analysis for learning the structure of exponential families of polynomials with score matching. The derived sample bounds show a polynomial dependence on the model dimension. These bounds are the first of its kind, as all prior work has shown only asymptotic bounds on the sample complexity.
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