A BLOCK COORDINATE DESCENT METHOD FOR A MAXIMUM LIKELIHOOD ESTIMATION PROBLEMS OF MIXTURE DISTRIBUTIONS

作者：Yamakawa Yuya^*; Yamashita Nobuo

来源：Pacific Journal of Optimization, 2015, 11(4): 669-686.

• maximum likelihood estimation
• mixture distributions
• mixture coefficient
• block coordinate descent method
• regularization
• EM algorithm

In this paper, we propose a block coordinate descent method for a maximum likelihood estimation problem of mixture distributions. The maximum likelihood estimation problem considered in the paper consists of not only a log-likelihood function but also some proper convex functions such as the L-1 regularization and/or indicator functions. Then, we may estimate parameters in distributions with some regularizations and constraints on parameters. Especially, a parameter estimation with lower constraints on mixture coefficients is the main contribution of this paper. Since the problem has the additional convex function, it cannot be solved by the usual EM algorithm. Thus, we consider a block coordinate descent method as a solver of the problem, and show its global convergence by using the results in Tseng (J. Optim. Theory Appl. 109-3, 2001). Moreover, we discuss concrete implementations when a distribution is Gaussian. In particular, we propose efficient methods for a maximum likelihood estimation for special cases.

• 出版日期2015-10