Reproducibility and Robustness of Dimensionality Reduction

项目摘要 在现代生物医学研究中，收集高维数据已变得司空见惯，因此， 降低失真的工具是至关重要的，并且是常规使用的。其中最常见的反应包括 聚类分析和因子分析。降维背后的基本原则是，我们可以将高 通过一些低维的总结来描述变量的多维集合。这对于理解 复杂的数据，也克服了高维，低样本量数据的问题。然而，一个关键是- 尚未充分研究问题是可重复性。降维的标准方法可以 对调谐参数的选择和任意选择非常敏感（例如，选择内核或距离测量 ure）。这导致缺乏鲁棒性，当数据 有点不安随着数据大小的增加，这种鲁棒性的缺乏往往会变得更加严重-无论是在 样本量和收集的变量数量。此外，一个关键问题是缺乏普遍性。在 特别地，针对特定个体组的降维可能根本上缺乏普遍性 to other groups组of individuals个人.这在解释结果方面造成了重大问题。特别有动机 通过环境流行病学研究收集麻烦的数据和营养流行病学，该项目 建议从根本上开发新的方法，以提高DI的鲁棒性和再现性， 通过以下具体目标来减少抑郁症。 (1)开发强大的因素分析方法，旨在限制对任意假设的敏感性， 数据的大小。 (2)开发强大的基于模型的聚类方法，旨在限制对任意数据集的敏感性， 数据的大小和大小。 (3)开发新的方法，从多变量和分组数据中进行稳健的聚类， 避免混合模型的典型缺陷，随着p的增加。 (4)开发强大的共识方法，估计最能反映结构的低维摘要， 在亚群体中的真实性。 (5)将所提出的方法应用于来自关键流行病学队列的数据，这些队列测量了广泛的变量， 各种环境、行为和生物暴露，并提供通用软件 包实施。该软件包设计为易于使用， 数据类型的多样性，进一步帮助再现性和透明度。

PROJECT SUMMARY In modern biomedical studies it has become commonplace to collect high-dimensional data, and hence dimen- sionality reduction tools are of critical importance and are routinely used. Some of the most common include clustering and factor analysis. The basic tenet behind dimensionality reduction is that we can replace a high dimensional set of variables by some low-dimensional summary. This is certainly necessary to make sense of complex data and also overcome problems with high-dimensional, low sample size data. However, a critical is- sue that has not been adequately studied is reproducibility. Standard approaches for dimension reduction can be very sensitive to choice of tuning parameters and arbitrary choices (e.g., choice of kernel or distance meas- ure). This leads to a lack of robustness, with potentially very different results being produced when data are slightly perturbed. This lack of robustness tends to be compounded as the size of the data increases - both in terms of the sample size and number of variables collected. Also, a critical issue is lack of generalizability. In particular, dimensionality reduction for a particular group of individuals may fundamentally lack generalizability to other groups of individuals. This creates major problems in interpretation of results. Motivated in particular by environmental epidemiology studies collecting exposome data and by nutritional epidemiology, this project proposes to develop fundamentally new methods for improving robustness and reproducibility of di- mensionality reduction through the following specific aims. (1) Develop robust methods of factor analysis designed to limit sensitivity to arbitrary assumptions and size of the data. (2) Develop robust methods of model-based clustering designed to limit sensitivity to arbitrary assump- tions and size of the data. (3) Develop novel methods for robust clustering from multivariate and grouped data designed to avoid typical pitfalls of mixture models with increasing p. (4) Develop robust consensus methods that estimate low dimensional summaries that best reflect struc- ture across subpopulations. (5) Apply the proposed methods to data from key epidemiologic cohorts that have measured a wide va- riety of environmental, behavioral, and biological exposures and provide a general use software package for implementation. This package is designed to be easily used and accommodate a broad variety of data types, further aiding reproducibility and transparency.