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Register a new userUltrahigh Dimensional Feature Selection via Kernel Canonical Correlation Analysis
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Added by
Tianqi Liu
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
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High-dimensional variable selection is an important issue in many scientific fields, such as genomics. In this paper, we develop a sure independence feature screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS, for short). KCCA- SIS is easy to be implemented and applied. Compared to the sure independence screen- ing procedure based on the Pearson correlation (SIS, for short) developed by Fan and Lv [2008], KCCA-SIS can handle nonlinear dependencies among variables. Compared to the sure independence screening procedure based on the distance correlation (DC- SIS, for short) proposed by Li et al. [2012], KCCA-SIS is scale free, distribution free and has better approximation results based on the universal characteristic of Gaussian Kernel (Micchelli et al. [2006]). KCCA-SIS is more general than SIS and DC-SIS in the sense that SIS and DC-SIS correspond to certain choice of kernels. Compared to supremum of Hilbert Schmidt independence criterion-Sure independence screening (sup-HSIC-SIS, for short) developed by Balasubramanian et al. [2013], KCCA-SIS is scale free removing the marginal variation of features and response variables. No model assumption is needed between response and predictors to apply KCCA-SIS and it can be used in ultrahigh dimensional data analysis. Similar to DC-SIS and sup- HSIC-SIS, KCCA-SIS can also be used directly to screen grouped predictors and for multivariate response variables. We show that KCCA-SIS has the sure screening prop- erty, and has better performance through simulation studies. We applied KCCA-SIS to study Autism genes in a spatiotemporal gene expression dataset for human brain development, and obtained better results based on gene ontology enrichment analysis comparing to the other existing methods.
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This paper proposes a canonical-correlation-based filter method for feature selection. The sum of squared canonical correlation coefficients is adopted as the feature ranking criterion. The proposed method boosts the computational speed of the ranking criterion in greedy search. The supporting theorems developed for the feature selection method are fundamental to the understanding of the canonical correlation analysis. In empirical studies, a synthetic dataset is used to demonstrate the speed advantage of the proposed method, and eight real datasets are applied to show the effectiveness of the proposed feature ranking criterion in both classification and regression. The results show that the proposed method is considerably faster than the definition-based method, and the proposed ranking criterion is competitive compared with the seven mutual-information-based criteria.
Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimensional classification (Tibshirani et al., 2003). Within the context of the linear model, Fan and Lv (2008)showed that this simple correlation ranking possesses a sure independence screening property under certain conditions and that its revision, called iteratively sure independent screening (ISIS), is needed when the features are marginally unrelated but jointly related to the response variable. In this paper, we extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Even in the least-squares setting, the new method improves ISIS by allowing variable deletion in the iterative process. Our technique allows us to select important features in high-dimensional classification where the popularly used two-sample t-method fails. A new technique is introduced to reduce the false discovery rate in the feature screening stage. Several simulated and two real data examples are presented to illustrate the methodology.
Canonical correlation analysis (CCA) is a classical and important multivariate technique for exploring the relationship between two sets of continuous variables. CCA has applications in many fields, such as genomics and neuroimaging. It can extract meaningful features as well as use these features for subsequent analysis. Although some sparse CCA methods have been developed to deal with high-dimensional problems, they are designed specifically for continuous data and do not consider the integer-valued data from next-generation sequencing platforms that exhibit very low counts for some important features. We propose a model-based probabilistic approach for correlation and canonical correlation estimation for two sparse count data sets (PSCCA). PSCCA demonstrates that correlations and canonical correlations estimated at the natural parameter level are more appropriate than traditional estimation methods applied to the raw data. We demonstrate through simulation studies that PSCCA outperforms other standard correlation approaches and sparse CCA approaches in estimating the true correlations and canonical correlations at the natural parameter level. We further apply the PSCCA method to study the association of miRNA and mRNA expression data sets from a squamous cell lung cancer study, finding that PSCCA can uncover a large number of strongly correlated pairs than standard correlation and other sparse CCA approaches.
Classical canonical correlation analysis (CCA) requires matrices to be low dimensional, i.e. the number of features cannot exceed the sample size. Recent developments in CCA have mainly focused on the high-dimensional setting, where the number of features in both matrices under analysis greatly exceeds the sample size. These approaches impose penalties in the optimization problems that are needed to be solve iteratively, and estimate multiple canonical vectors sequentially. In this work, we provide an explicit link between sparse multiple regression with sparse canonical correlation analysis, and an efficient algorithm that can estimate multiple canonical pairs simultaneously rather than sequentially. Furthermore, the algorithm naturally allows parallel computing. These properties make the algorithm much efficient. We provide theoretical results on the consistency of canonical pairs. The algorithm and theoretical development are based on solving an eigenvectors problem, which significantly differentiate our method with existing methods. Simulation results support the improved performance of the proposed approach. We apply eigenvector-based CCA to analysis of the GTEx thyroid histology images, analysis of SNPs and RNA-seq gene expression data, and a microbiome study. The real data analysis also shows improved performance compared to traditional sparse CCA.
Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To overcome these challenges, we propose a semiparametric approach for sparse canonical correlation analysis based on Gaussian copula. Our main contribution is a truncated latent Gaussian copula model for data with excess zeros, which allows us to derive a rank-based estimator of the latent correlation matrix for mixed variable types without the estimation of marginal transformation functions. The resulting canonical correlation analysis method works well in high-dimensional settings as demonstrated via numerical studies, as well as in application to the analysis of association between gene expression and micro RNA data of breast cancer patients.
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