SPEED-UP OF CONVERGENCE OF THE EM ALGORITHM USING THE VECTOR <i>ε</i> ALGORITHM AND ITS IMPROVEMENT

DOI Web Site

Bibliographic Information

Other Title
  • Vector <i>ε</i> アルゴリズムによる EM アルゴリズムの収束の加速化とその改良
  • Vector εアルゴリズムによるEMアルゴリズムの収束の加速化とその改良
  • Vector eアルゴリズム ニ ヨル EM アルゴリズム ノ シュウソク ノ カソクカ ト ソノ カイリョウ

Search this article

Abstract

The EM algorithm is a popular iterative algorithm for finding maximum likelihood estimates from incomplete data. However, the drawback of the EM algorithm is to converge slowly when the proportion of missing data is large. In order to speed up the convergence of the EM algorithm, we propose the “ε-accelerated EM algorithm” that accelerates the convergence of the EM sequence using the vector ε algorithm. The ε-accelerated EM algorithm only uses the EM estimates to obtain an accelerated sequence for the EM sequence and then does not require the matrix computation such as matrix inversion or evaluation of Hessian and Jacobian matrices, and a line search for step length optimization. Thus the algorithm is successfully extended to the EM algorithm without affecting its stability, flexibility and simplicity. When the accelerated sequence has larger values of the likelihood than the current EM estimate, a re-starting of the EM iterations using the accelerated sequence is more effective to increases its speed of convergence. The re-starting algorithm called the “εR-accelerated EM algorithm” can further improve the EM algorithm and the ε-accelerated EM algorithm in the sense of that it can reduce the number of iterations and computation time. We examine the performance and properties of the ε-accelerated EM and εR-accelerated EM algorithms by using numerical experiments.

Journal

Keywords

Details 詳細情報について

Report a problem

Back to top