Sergio Chavez Research Project

Sergio Chavez (UNC Math Grad)

Title: Using wavelet analysis to test for dependence in high-dimensional problems

Summary of work:
Looking at the independence problem in statistics from a Fourier and wavelet analysis point view. The orthonormal properties of many bases such as the Fourier, Legendre, Haar and Walsh have produced interesting results in the independence problem, one of which has the ability to efficiently work on high-dimensional data sets. This refers to the Haar wavelets who have local support that can be used in a hierarchical approach, meaning that computations can be done faster. The hope is that we can determine if a scalar random variable Y is dependent on a random variable vector X regardless of the dimension of X or the dependency between constituent components.

Keywords: Multivariate independence, Haar wavelets, fast wavelet transforms, fast algorithms, hierarchical trees