Heuristic least-cost computation of discrete classification functions with uncertain argument values

Abstract

We consider the problem of minimizing the expected cost of computing the correct value of a discrete-valued function when it is costly to determine (“inspect”) the values of its arguments. This type of problem arises in distributed computing, in the design of interactive expert systems, in reliability analysis of coherent systems, in classification of pattern vectors, and in many other applications. In this paper, we first show that the general problem is NP-hard and then introduce several efficient heuristic sequential inspection procedures for solving it approximately. We obtain theoretical results showing that the heuristics are optimal in important special cases; moreover, their computational structures make them well suited for parallel implementation. Next, for the special case of linear threshold (or “discrete linear discriminant”) functions, which are widely used in statistical classification procedures, we use Monte Carlo simulation to analyze the performances of the heuristics and to compare the heuristic solutions with the exact (true minimum expected cost) solutions over a wide range of randomly generated test problems. All of the heuristics give average relative errors, compared to the exact optimal solutions, of less than 2%. The best heuristic for this class of functions gives an average relative error of less than 0.05% and runs two to four orders of magnitude faster than the exact solution procedure, for functions with ten arguments.