Active Binary Classification of Random Fields

Abstract

Consider a sequence of n random variables \mathrm{X}\ {\buildrel \triangle\over=} (X_{1},\cdots, X_{n}) forming a random field (RF). X is assumed to be generated according to one of the two possible classes of probability measures \mathcal{P}\ {\buildrel \triangle\over=}\ \{\mathbb{P}_{i}: i\in\{1,\cdots, m\}\} and \mathcal{Q}\ {\buildrel \triangle\over=}\ \{\mathbb{Q}_{i}: i\in\{1, \cdots, m\}\}. Up to s realizations of each random variable X_{i} are available for sampling. This paper addresses the following two questions. 1) Given a target classification reliability, what is the minimum number of samples, on average, required to classify X? 2) What is an optimal sequence of sampling the random variables such that a classification decision can be formed with the fewest number of samples? This paper addresses these questions in the asymptote of large n.