可扩展到大数据的正则化群PLS的统一并行算法
A Unified Parallel Algorithm for Regularized Group PLS Scalable to Big Data
摘要：
偏最小二乘（PLS）方法已被大量利用来分析两组数据之间的关联。这些强大的方法可以应用于数据集的变量的数量大于观察的数量，并在变量之间存在高度共线性。不同的稀疏版本的PLS已被开发来整合多个数据集，同时选择的贡献变量。稀疏建模是获得更好的估计值和识别多个数据集之间关联的关键因素。PLS方法的稀疏版本的基石是矩阵的SVD（从原始数据矩阵的收缩版本构建）和线性回归中的最小二乘最小化之间的联系。我们在这里提出了最流行的PLS方法的准确描述，以及它们的数学证明。提出了一种统一的算法来执行所有四种类型的PLS，包括其正则化版本。提供了减少计算时间的各种方法，我们展示了整个过程如何可扩展到大数据集。
英文摘要：
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in presence of high collinearity between variables. Different sparse versions of PLS have been developed to integrate multiple data sets while simultaneously selecting the contributing variables. Sparse modelling is a key factor in obtaining better estimators and identifying associations between multiple data sets. The cornerstone of the sparsity version of PLS methods is the link between the SVD of a matrix (constructed from deflated versions of the original matrices of data) and least squares minimisation in linear regression. We present here an accurate description of the most popular PLS methods, alongside their mathematical proofs. A unified algorithm is proposed to perform all four types of PLS including their regularised versions. Various approaches to decrease the computation time are offered, and we show how the whole procedure can be scalable to big data sets.
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