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Speaker verification based on the log-likelihood ratio (LLR) is essentially a task of modeling and testing two hypotheses: the null hypothesis and the alternative hypothesis. Since the alternative hypothesis involves unknown imposters, it is usually hard to characterize a priori. In this paper, we propose a framework to better characterize the alternative hypothesis with the goal of optimally separating client speakers from imposters. The proposed framework is built on either a weighted arithmetic combination or a weighted geometric combination of useful information extracted from a set of pre-trained anti-speaker models. The parameters associated with the combinations are then optimized using minimum verification error training such that both the false acceptance probability and the false rejection probability are minimized. Our experiment results show that the proposed framework outperforms conventional LLR-based approaches.