Chun Hyonho, Keleş Sündüz
University of Wisconsin Madison, USA.
J R Stat Soc Series B Stat Methodol. 2010 Jan;72(1):3-25. doi: 10.1111/j.1467-9868.2009.00723.x.
Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data.
自20世纪60年代以来，偏最小二乘回归一直是普通最小二乘法的一种替代方法，用于处理多个科学研究领域中的多重共线性问题。最近，它在高维基因组数据分析中备受关注。我们表明，对于单变量响应，偏最小二乘估计量已知的渐近一致性在p非常大而n非常小的范式下并不成立。我们针对多变量响应回归与偏最小二乘法得出了类似结果。然后，我们提出了一种稀疏偏最小二乘公式，旨在通过生成原始预测变量的稀疏线性组合，同时实现良好的预测性能和变量选择。我们提供了稀疏偏最小二乘回归的有效实现，并通过模拟实验将其与著名的变量选择和降维方法进行比较。我们在基因表达与全基因组结合数据的联合分析中说明了稀疏偏最小二乘回归的实际效用。
