Optimal Sequential Multiclass Diagnosis

• 成果类型: Article
• 署名作者: Wang, Jue
• 署名单位: Queens University - Canada
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2114
• 发表日期: 2022
• 页码: 201-222
• 关键词: strategies; DESIGN; models; FAULT

摘要

Sequential multiclass diagnosis, also known as multihypothesis testing, is a classical sequential decision problem with broad applications. However, the optimal solution remains, in general, unknown as the dynamic program suffers from the curse of dimensionality in the posterior belief space. We consider a class of practical problems in which the observation distributions associated with different classes are related through exponential tilting and show that the reachable beliefs could be restricted on, or near, a set of low dimensional, time-dependent manifolds with closed-form expressions. This sparsity is driven by the low dimensionality of the observation distributions (which is intuitive) as well as by specific structural interrelations among them (which is less intuitive). We use a matrix factorization approach to uncover the potential low dimensionality hidden in high-dimensional beliefs and reconstruct the beliefs using a diagnostic statistic in lower dimension. For common univariate distributions, for example, normal, binomial, and Poisson, the belief reconstruction is exact and the optimal policies can be efficiently computed for a large number of classes. We also characterize the structure of the optimal policy in the reduced dimension. For multivariate distributions, we propose a low-rank matrix approximation scheme that works well when the beliefs are near the low-dimensional manifolds. The optimal policy significantly outperforms the state-of-the-art heuristic policy in quick diagnosis with noisy data.