Reproducibility and Robustness of Dimensionality Reduction

项目总结 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， 降低临界性的工具至关重要，而且经常使用。其中最常见的包括 聚类分析和因子分析。降维背后的基本原则是，我们可以用一个高的 维变量集由一些低维的总结而成。这当然是有必要理解的 它不仅可以处理复杂的数据，还可以克服高维、低样本量数据的问题。然而，关键是- 没有得到充分研究的苏是可重复性的。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)。这导致缺乏健壮性，当数据被 有点不安。这种缺乏稳健性的情况随着数据大小的增加而变得更加复杂--无论是在 在样本大小和收集的变量数量方面。此外，一个关键问题是缺乏概括性。在……里面 具体地说，特定个体组的降维可能从根本上缺乏概括性 传给其他群体的人。这在解释结果方面造成了重大问题。特别是有动力 通过环境流行病学研究收集暴露数据和营养流行病学，该项目 建议从根本上开发新的方法，以提高数字图像的稳健性和重复性。 通过以下具体目标减少阶段性。 (1)开发稳健的因素分析方法，旨在限制对任意假设的敏感性，并 数据的大小。 (2)开发稳健的基于模型的聚类方法，旨在限制对任意假设的敏感度- 数据的数量和大小。 (3)从多变量和分组数据中开发新的稳健聚类方法，旨在 避免增加p的混合模型的典型陷阱。 (4)开发稳健的共识方法，估计最能反映结构的低维摘要- 在各个亚群中都是如此。 (5)将建议的方法应用于来自关键流行病学队列的数据，这些队列已经测量了广泛的变量- 环境、行为和生物暴露的安全性，并提供通用软件 用于实施的包。该套装设计简单易用，可容纳广泛的 数据类型多样，进一步提高了再现性和透明度。

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.