Robust Kernel Bayes' Rule and Its Application

Abstract

Many problems in machine learning involve nding interesting non-linear relationships in high dimensional data. Kernel methods in statistical learning theory provide powerful techniques for analyzing such data. They can be used for both supervised and non-supervised learning problems like classi cation using support vector machines and kernel spectral clustering respectively. The basic idea behind kernel methods is to map/embed the data nonlinearly to a higher dimensional feature space, where linear algorithms are applied. Recent advances in kernel based methods allow embedding probability distribution, conditional and posterior distribution to the higher dimensional feature space. This thesis proposes a non-parametric method to robustly embed the conditional and posterior distribution in reproducing Kernel Hilbert Space (RKHS). Robust embedding is achieved by eigenvalue decomposition in RKHS and by retaining only the leading eigenvectors. The robust posterior distribution achieved using our approach can be applied to wide range of Bayesian inference problems. In this thesis, we apply it for recognizing food dishes from images, when no training images of target food dishes are given. Algorithms that aim to recognize objects for which we have no training examples (unseen object classes), are called zero-shot learning (ZSL) algorithms. Image features and attribute representations of food dishes are gathered using deep convolutional network and word vector space embedding of large web corpora respectively. Our approach try to learn the relation among image features and attributes which can further be used to classify food dishes given only attributes.