Herding as a Learning System with Edge-of-Chaos Dynamics

TL;DR

Herding is a deterministic dynamical system operating at the edge of chaos that generates model states and parameters for probabilistic modeling, offering a novel approach distinct from traditional MCMC and maximum likelihood methods.

Contribution

This paper introduces herding as a new deterministic learning system at the edge of chaos, extending its application to models with latent variables and discriminative learning.

Findings

Herding exhibits fast convergence of moments due to edge of chaos dynamics.

Herding generates deterministic sequences that mimic sampling from probabilistic models.

The approach generalizes to latent variable models and discriminative settings.

Abstract

Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" from an associated MRF model. Herding differs from maximum likelihood estimation in that the sequence of parameters does not converge to a fixed point and differs from an MCMC posterior sampling approach in that the sequence of states is generated deterministically. Herding may be interpreted as a"perturb and map" method where the parameter perturbations are generated using a deterministic nonlinear dynamical system rather than randomly from a Gumbel distribution. This chapter studies the distinct statistical characteristics of the herding algorithm and shows that the fast convergence rate of the controlled moments may be attributed to edge of chaos dynamics. The herding algorithm can also be generalized to models with latent variables and to a discriminative learning setting. The perceptron cycling theorem ensures that the fast moment matching property is preserved in the more general framework.