Nonparametric Latent Variable Models via Kernel Embedding of Distributions

The key idea of kernel embedding of distributions is to map distributions into the RKHS associated with a kernel function, such that subsequent manipulations of distributions can be achieved via RKHS distances, linear transformations, and spectral decompositions. This framework has led to simple and effective nonparametric algorithms in many machine learning problems, such as two-sample test, covariate shift correction, time-series modeling and nonparametric belief propagation. In this talk, I will focus on my recent works on kernel embedding of latent variable models. The presence of latent variables in a distribution induces sophisticated low rank structures in its kernel embedding, which is exploited for designing nonparametric algorithms for recovering latent variable model structures, learning latent parameters and improving density estimation. These novel algorithms connect kernel embedding of distributions to tensors and higher order tensors, and exploit spectral decomposition of these objects for efficient learning. I will discuss both theoretical guarantees and empirical results for these new approaches.