Abstract:
Recently, independent component analysis (ICA) - a popular method for blind signal separation - has found interest within the machine learning theory community due to nice algebraic properties of its cumulant-based solutions and due to recent observations that the mathematics underlying ICA also underly other problems of interest. This talk will explore a unifying algorithmic framework for a number of unsupervised machine learning problems including ICA, learning mixtures of spherical Gaussians, spectral clustering, and orthogonal tensor decompositions. The framework is based on maximizing certain functions on the unit sphere in order to recover a hidden basis of the space. The resulting algorithms for hidden basis recovery includes fast-converging fixed point methods such as the classic power iteration for matrix eigenvector recovery and its tensorial extension as special cases.

This talk will also highlight applications of hidden basis recovery within spectral clustering and blind signal separation.

Biography:
James Voss is a PhD student at the Ohio State University. He went to Michigan State University for his undergrad, receiving B.S. degrees in Mathematics and in Computer Science. His research interests are within theoretical aspects of machine learning. He has done work within independent component analysis, spectral clustering, and learning the parameters of mixture of Gaussian distributions with theoretical guarantees.

Host:
Dr. Jiayu Zhou and Dr. Anil K. Jain