The Expectation-Maximization (EM) algorithm is one of the most popular algorithms for parameter estimation from incomplete data, but its convergence can be slowfor some large-scale or complex problems. Extrapolation methods can effectively accelerate EM, but to ensure stability, the learning rate of extrapolation must be compromised. This paper describes the TJ2aEM method, a targeted extrapolation method that can extrapolate much more aggressively than competing methods without causing instability problems. We analyze its convergence properties and report experimental results.

The expectation-maximization (EM) algorithm is one of the most popular algorithms for data mining from incomplete data. However, when applied to large data sets with a large proportion of missing data, the EM algorithm may converge slowly. The triple jump extrapolation method can effectively accelerate the EM algorithm by substantially reducing the number of iterations required for EM to converge. There are two options for the triple jump method, global extrapolation (TJEM) and componentwise extrapolation (CTJEM). We tried these two methods for a variety of probabilistic models and found that in general, global extraplolation yields a better performance, but there are cases where componentwise extrapolation yields very high speedup. In this paper, we investigate when componentwise extrapolation should be preferred. We conclude that, when the Jacobian of the EM mapping is diagonal or block diagonal, CTJEM should be preferred. We show how to determine whether a Jacobian is diagonal or block diagonal and experimentally confirm our claim. In particular, we show that CTJEM is especially effective for the semi-supervised Bayesian classifier model given a highly sparse data set.

Speaker verification concerns the problem of verifying whether a given utterance has been pronounced by a claimed authorized speaker. This problem is important because an accurate speaker verification system can be applied to many security applications. We present a new algorithm for speaker verification called OSCILLO. By applying tolerance interval analysis in statistics, OSCILLO can verify a speaker's ID without background speaker models. This greatly reduces the space requirement of the system and the time for both training and verification. Experimental results show that OSCILLO can achieve error rates comparable or better than the GMM-based system with background speaker models for three benchmark databases: TCC-300, TIMIT and NIST 2000.