Related papers: Ultrahigh Dimensional Feature Selection via Kernel…

Variable selection is a widely studied problem in high dimensional statistics, primarily since estimating the precise relationship between the covariates and the response is of great importance in many scientific disciplines. However, most…

This study presents the m-arcsinh Kernel ('m-ar-K') Fast Independent Component Analysis ('FastICA') method ('m-ar-K-FastICA') for feature extraction. The kernel trick has enabled dimensionality reduction techniques to capture a higher…

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…

Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre screening of the variables may be necessary. A…

Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers…

Drug discovery is the process of identifying compounds which have potentially meaningful biological activity. A major challenge that arises is that the number of compounds to search over can be quite large, sometimes numbering in the…

A simple and intuitive method for feature selection consists of choosing the feature subset that maximizes a nonparametric measure of dependence between the response and the features. A popular proposal from the literature uses the…

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the…

Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…

Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the…

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Gini distance correlation (GDC) was recently proposed to measure the dependence between a categorical variable, Y, and a numerical random vector, X. It mutually characterizes independence between X and Y. In this article, we utilize the GDC…

We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such…

We introduce a two-step procedure, in the context of ultra-high dimensional additive models, which aims to reduce the size of covariates vector and distinguish linear and nonlinear effects among nonzero components. Our proposed screening…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

High-dimensional data are commonly seen in modern statistical applications, variable selection methods play indispensable roles in identifying the critical features for scientific discoveries. Traditional best subset selection methods are…