A minimum variance asynchronous Detection Error Trade-off performance analysis for multi-class detection problems

In a detection problem, the trade-off between the miss and false alarm probabilities are often shown as a Detection Error Trade-off (DET) curve. The DET curve is obtained by adjusting a decision threshold to vary the compromise between these probabilities. For a multi-class detection problem, each class has its own decision threshold, which leads to a multivariate detection error trade-off. In order to plot a DET curve, the decision thresholds are constrained to a single degree of freedom. Typically, they are synchronously constrained to use the same values. In this paper, a minimum variance DET analysis is proposed where the decision thresholds are asynchronously constrained such that the variances of the miss and false alarm probabilities are minimised. If the scores are normally distributed, the decision thresholds can be approximated as a linear univariate function and the resulting DET curve is also a straight line. In more general cases where the scores are not normally distributed, piecewise linear functions can be estimated iteratively, instead. The minimum variance asynchronous DET analysis is applied to a phone verification task on TIMIT database.