On Kernel Parameter Selection in Hilbert-Schmidt Independence Criterion

Measuring Statistical Dependence with Hilbert-Schmidt Norms

We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. Fir...

Kernel Measures of Independence for non-iid Data

Many machine learning algorithms can be formulated in the framework of statistical independence such as the Hilbert Schmidt Independence Criterion. In this paper, we extend this criterion to deal with structured and interdependent observations. This is achieved by modeling the structures using undirected graphical models and comparing the Hilbert space embeddings of distributions. We apply this...

Canonical Correlation Analysis based on Hilbert-Schmidt Independence Criterion and Centered Kernel Target Alignment

Canonical correlation analysis (CCA) is a well established technique for identifying linear relationships among two variable sets. Kernel CCA (KCCA) is the most notable nonlinear extension but it lacks interpretability and robustness against irrelevant features. The aim of this article is to introduce two nonlinear CCA extensions that rely on the recently proposed Hilbert-Schmidt independence c...

Canonical Correlation Analysis based on Hilbert-Schmidt Independence Criterion and Centered Kernel Target Alignment: Supplementary Materials

High-Dimensional Feature Selection by Feature-Wise Non-Linear Lasso

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 paper, we consider a feature-wise kernelized Lasso for capturing non-linear inp...