Sequential controlled sensing for composite multihypothesis testing

Abstract

The problem of multihypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal is to design a policy to find the true hypothesis with minimum expected delay while ensuring that the probability of error is below a given constraint. The decision-maker can reduce the delay by intelligently choosing the control for observation collection in each time slot. A policy for this problem is derived that satisfies given constraints on the error probability, and it is shown that this policy is asymptotically optimal in the sense that it asymptotically achieves an information-theoretic lower bound on the expected delay. Numerical results are provided that illustrate an application of the policy to medical diagnostic inference.

Keywords:

• Active hypothesis testing
• composite hypothesis testing
• observation control
• sequential hypothesis testing

SUBJECT CLASSIFICATIONS:

• 62F05
• 62L05
• 62L10
• 62L15

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

The work of A. Deshmukh and V.V. Veeravalli was supported in part by the U.S. National Science Foundation under grant CIF 15-14245 and by the U.S. Air Force Office of Scientific Research (AFOSR) under grant FA9550-16-1-0077, through the University of Illinois at Urbana–Champaign. The work of S. Bhashyam was supported by the Indian Science and Engineering Board, Department of Science and Technology under project no. EMR/2016/002503.