A simulation study on optimal scores for speaker recognition

In this article, we conduct a comprehensive simulation study for the optimal scores of speaker recognition systems that are based on speaker embedding. For that purpose, we first revisit the optimal scores for the speaker identification (SI) task and the speaker verification (SV) task in the sense of minimum Bayes risk (MBR) and show that the optimal scores for the two tasks can be formulated as a single form of normalized likelihood (NL). We show that when the underlying model is linear Gaussian, the NL score is mathematically equivalent to the PLDA likelihood ratio (LR), and the empirical scores based on cosine distance and Euclidean distance can be seen as approximations of this linear Gaussian NL score under some conditions.Based on the unified NL score, we conducted a comprehensive simulation study to investigate the behavior of the scoring component on both the SI task and SV task, in the case where the distribution of the speaker vectors perfectly matches the assumption of the NL model, as well as the case where some mismatch is involved. Importantly, our simulation is based on the statistics of speaker vectors derived from a practical speaker recognition system, hence reflecting the behavior of the NL scoring in real-life scenarios that are full of imperfection, including non-Gaussianality, non-homogeneity, and domain/condition mismatch.

Optimal interference range for minimum Bayes risk in binomial and Poisson wireless networks

Interference is the main performance-limiting factor in most wireless networks. Protocol interference model is extensively used in the design of wireless networks. However, the setting of interference range, a crucial part of the protocol interference model, is rather heuristic and remains an open problem. In this paper, we use the stochastic geometry and the direct approach to obtain the associated feasibility distributions. After that, we use the binary hypothesis testing to achieve the Bayes risk under binomial point process (BPP) and Poisson point process (PPP), respectively. According to the first derivative of the Bayes risk, we provide the equation to achieve the optimal interference range for minimum Bayes risk. We extend the method proposed by Wildman et al. to a more general situation. Furthermore, we show that for infinite PPP, those two methods converge to the same results. Several numerical results for wireless networks under BPP, finite PPP, and infinite PPP are given. Simulation results show that in the finite wireless network, the BPP method performs better than the PPP method.

Bayesian Analysis of a Shape Parameter of the Weibull-Frechet Distribution

In this paper, we estimate a shape parameter of the Weibull-Frechet distribution by considering the Bayesian approach under two non-informative priors using three different loss functions. We derive the corresponding posterior distributions for the shape parameter of the Weibull-Frechet distribution assuming that the other three parameters are known. The Bayes estimators and associated posterior risks have also been derived using the three different loss functions. The performance of the Bayes estimators are evaluated and compared using a comprehensive simulation study and a real life application to find out the combination of a loss function and a prior having the minimum Bayes risk and hence producing the best results. In conclusion, this study reveals that in order to estimate the parameter in question, we should use quadratic loss function under either of the two non-informative priors used in this study.