Joint estimation of thresholds in a bi-threshold verification problem

Verification problems are usually posted as a 2-class problem and the objective is to verify if an observation belongs to a class, say, A or its complement A’. However, we find that in a computer-assisted language learning application, because of the relatively low reliability of phoneme verification — with an equal-error-rate of more than 30% — a system built on conventional phoneme verification algorithm needs to be improved. In this paper, we propose to cast the problem as a 3-class verification problem with the addition of an “in-between” class besides A and A’. As a result, there are two thresholds to be designed in such a system. Although one may determine the two thresholds independently, better performance can be obtained by a joint estimation of these thresholds by allowing small deviation from the specified false acceptance and false rejection rates. This paper describes a cost-based approach to do that. Furthermore, issues such as per-phoneme thresholds vs. phoneme-class thresholds, and the use of bagging technique to improve the stability of thresholds are investigated. Experimental results on a kids’ corpus show that cost-based thresholds and bagging improve verification performance.