Kernel Embeddings of Conditional Distributions: A Unified Kernel Framework for Nonparametric Inference in Graphical Models

Abstract

Many modern applications of signal processing and machine learning, ranging from computer vision to computational biology, require the analysis of large volumes of high-dimensional continuous-valued measurements. Complex statistical features are commonplace, including multimodality, skewness, and rich dependency structures. Such problems call for a flexible and robust modeling framework that can take into account these diverse statistical features. Most existing approaches, including graphical models, rely heavily on parametric assumptions. Variables in the model are typically assumed to be discrete valued or multivariate Gaussians; and linear relations between variables are often used. These assumptions can result in a model far different from the data generating process.