A novel formulation of independence detection based on the sample characteristic function

A novel independence test for continuous random sequences is proposed in this paper. The test is based on seeking for coherence in a particular fixed-dimension feature space based on a uniform sampling of the sample characteristic function of the data, providing significant computational advantages over kernel methods. This feature space relates uncorrelation and independence, allowing to analyze the second order statistics as it is encountered in traditional signal processing. As a result, the possibility of utilizing well known correlation tools arises, motivating the usage of Canonical Correlation Analysis as the main tool for detecting independence. Comparative simulation results are provided using a model based on fading AWGN channels.Peer ReviewedPostprint (published version

Squared-loss mutual information via high-dimension coherence matrix estimation

Squared-loss mutual information (SMI) is a surro- gate of Shannon mutual information that is more advantageous for estimation. On the other hand, the coherence matrix of a pair of random vectors, a power-normalized version of the sample cross-covariance matrix, is a well-known second-order statistic found in the core of fundamental signal processing problems, such as canonical correlation analysis (CCA). This paper shows that SMI can be estimated from a pair of independent and identically distributed (i.i.d.) samples as a squared Frobenius norm of a coherence matrix estimated after mapping the data onto some fixed feature space. Moreover, low computation complexity is achieved through the fast Fourier transform (FFT) by exploiting the Toeplitz structure of the involved autocorrelation matrices in that space. The performance of the method is analyzed via computer simulations using Gaussian mixture models.This work is supported by projects TEC2016-76409-C2-1-R (WINTER), Ministerio de Economia y Competividad, Spanish National Research Plan, and 2017 SGR 578 - AGAUR, Catalan Government.Peer ReviewedPostprint (published version

Non-parametric Methods for Correlation Analysis in Multivariate Data with Applications in Data Mining

In this thesis, we develop novel methods for correlation analysis in multivariate data, with a special focus on mining correlated subspaces. Our methods handle major open challenges arisen when combining correlation analysis with subspace mining. Besides traditional correlation analysis, we explore interaction-preserving discretization of multivariate data and causality analysis. We conduct experiments on a variety of real-world data sets. The results validate the benefits of our methods