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arXiv 2109.04671stat.MEstat.APstat.ML
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成分数据的交互作用模型和广义分数匹配

Interaction Models and Generalized Score Matching for Compositional Data

Shiqing Yu, Mathias Drton, Ali Shojaie

摘要:

诸如微生物组数据分析的应用已经引起了对组成数据的统计方法的新兴趣,即,以包含相对比例的概率向量形式的多变量数据。特别是,有相当大的兴趣,在这种相对比例之间的相互作用建模。为此,我们提出了一类指数族模型,适应一般模式的两两相互作用,同时支持的概率单纯形。特殊情况包括狄利克雷分布族以及艾奇逊的加性逻辑正态分布。通常,我们考虑的分布具有难以计算归一化常数的密度。为了规避这个问题,我们设计了有效的估计方法的基础上广义版本的分数匹配。我们的估计方法的高维分析表明,单纯形域的处理效率与以前研究的全维域。

英文摘要:

Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular, there is considerable interest in modeling interactions among such relative proportions. To this end we propose a class of exponential family models that accommodate general patterns of pairwise interaction while being supported on the probability simplex. Special cases include the family of Dirichlet distributions as well as Aitchison's additive logistic normal distributions. Generally, the distributions we consider have a density that features a difficult to compute normalizing constant. To circumvent this issue, we design effective estimation methods based on generalized versions of score matching. A high-dimensional analysis of our estimation methods shows that the simplex domain is handled as efficiently as previously studied full-dimensional domains.

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