Fast learning by the α-ECME algorithm

The α-EM (expectation maximization) algorithm is a super-class of the traditional log-EM algorithm. The case of α=-1 corresponds to the. log-EM algorithm. For the stable region of α>-1, the α-EM algorithm outperforms the traditional method in terms of the learning speed measured by iterations and CPU time. Both the α-EM algorithm and the log-EM algorithm try to maximize the conditional expectation on the tentative complete data. On the other hand, there is an extension of the traditional EM algorithm which includes direct maximization on the incomplete-data likelihood-which is the true performance measure. This is the ECME (expectation and conditional maximization or either) algorithm. Thus, this paper describes the α-version of the ECME first. Then, a speed evaluation is made on this α-ECME algorithm using the extended Fisher information matrix. Examples of unsupervised and supervised learning are given. The α-ECME algorithm is more meritorious than the plain α-EM or α-ECM (expectation and conditional maximization) algorithms in terms of the iteration count. If the CPU time is of ultimate importance, the plain α-EM algorithm and the α-ECME algorithm are comparable