## Presented by the Computational NeuroEngineering Laboratory

“Quantification of Statistical Dependence in Random Processes”

Wednesday, Feb. 8 at 3:00pm

NEB 409

### Abstract

Unlike statistical independence, the notion of statistical dependence is not uniquely defined in statistics and probability theory. For many years, the accepted definition of statistical dependence was Pearson’s correlation, until Shannon proposed the concept of mutual information (MI). However, as a scalar-valued measure, mutual information can be very useful for random variables but far less specific for random processes. We propose a functional methodology to define multivariate statistical dependence as the eigenspectrum of a symmetrical and self-adjoint cross density kernel. Our definition leads to a cost function and a neural network architecture that allows the estimation of multivariate statistical dependence between random processes directly from realizations. One case of importance is the estimation of factorial codes for a random process, which demonstrates that the proposed framework is more general than the conventional neural network paradigms for classification and regression.

### Biography

Bo Hu is a PhD student in the Department of Electrical & Computer Engineering at the University of Florida. Bo Hu has a B.S. in biomedical engineering from Beijing University of Aeronautics and Astronautics, M.S. in electrical engineering from the University of Florida. His research interests include information theory, neural networks, and reproducing kernel Hilbert space.