High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso

Makoto Yamada,Leonid Sigal,Eric P Xing,Masashi Sugiyama,Wittawat Jitkrittum

doi:10.1162/neco_a_00537

Abstract

The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this letter, we consider a feature-wise kernelized Lasso for capturing nonlinear input-output dependency. We first show that with particular choices of kernel functions, nonredundant features with strong statistical dependence on output values can be found in terms of kernel-based independence measures such as the Hilbert-Schmidt independence criterion. We then show that the globally optimal solution can be efficiently computed; this makes the approach scalable to high-dimensional problems. The effectiveness of the proposed method is demonstrated through feature selection experiments for classification and regression with thousands of features.

Highlights

Finding a subset of features in high-dimensional supervised learning is an important problem with many realworld applications such as gene selection from microarray data (Xing et al, 2001; Ding and Peng, 2005; Suzuki et al, 2009; Huang et al, 2010), document categorization (Forman, 2008), and prosthesis control (Shenoy et al, 2008).1.1 Problem DescriptionLet X (⊂ Rd) be the domain of input vector x and Y(⊂ R) be the domain of output data1 y
The least absolute shrinkage and selection operator (Lasso) (Tibshirani, 1996) allows computationally efficient feature selection based on the assumption of linear dependency between input features and output values
We use kernel regression (KR) (Scholkopf and Smola, 2002) with the Gaussian kernel for evaluating the mean squared error and the mean correlation when the top m = 10, 20, . . . , 50 features selected by each method are used

Summary

Introduction

Let X (⊂ Rd) be the domain of input vector x and Y(⊂ R) be the domain of output data y. Suppose we are given n independent and identically distributed (i.i.d.) paired samples,. We denote the original data by X = [x1, . The goal of supervised feature selection is to find m features (m < d) of input vector x that are responsible for predicting output y. The least absolute shrinkage and selection operator (Lasso) (Tibshirani, 1996) allows computationally efficient feature selection based on the assumption of linear dependency between input features and output values. The Lasso optimization problem is given as min α∈Rd

Methods

Results

Conclusion