| The herding algorithm was recently proposed as a deterministic algorithm to learn Markov random fields (MRFs). Instead of obtaining a fixed set of model parameters, herding drives a set of dynamical parameters and generates an infinite sequence of model states describing the learned distribution. It integrates the learning and inference phases effectively, and entertains a fast rate of convergence in the inference phase compared to the widely used Markov chain Monte Carlo methods. Herding is therefore a promising alternative to the conventional training-prediction two step paradigm in applying MRFs. In this thesis we study the properties of the herding algorithm from the perspective of both a statistical learning method and a nonlinear dynamical system. We further provide a mild condition for its moment matching property to hold and thereby derive a general framework for the herding algorithm. Under that framework three extensions of herding dynamics are proposed with a wide range of applications. We also discuss the application of herding as a sampling algorithm from the input distribution. Two more variants of herding are introduced to sample discrete and continuous distributions respectively, accompanied with discussion on the conditions when the sampler is unbiased. |
