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Methods for global measurement of transcript abundance such as microarrays and RNA-seq generate datasets in which the number of measured features far exceeds the number of observations. Extracting biologically meaningful and experimentally tractable insights from such data therefore requires high-dimensional prediction. Existing sparse linear approaches to this challenge have been stunningly successful, but some important issues remain. These methods can fail to select the correct features, predict poorly relative to non-sparse alternatives, or ignore any unknown grouping structures for the features. We propose a method called SuffPCR that yields improved predictions in high-dimensional tasks including regression and classification, especially in the typical context of omics with correlated features. SuffPCR first estimates sparse principal components and then estimates a linear model on the recovered subspace. Because the estimated subspace is sparse in the features, the resulting predictions will depend on only a small subset of genes. SuffPCR works well on a variety of simulated and experimental transcriptomic data, performing nearly optimally when the model assumptions are satisfied. We also demonstrate near-optimal theoretical guarantees.
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables are latent
We propose a supervised principal component regression method for relating functional responses with high dimensional covariates. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected integrated
Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenalls $tau$ function, which possesses identical e
Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis (SLFPCA) method t
Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to develop a robus