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MM algorithm : ウィキペディア英語版
MM algorithm
The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find their maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether you're doing maximization or minimization. MM itself is not an algorithm, but a description of how to construct an optimization algorithm.
The EM algorithm can be treated as a special case of the MM algorithm.〔(【引用サイトリンク】first=Kenneth )〕 However, in the EM algorithm complex conditional expectation and extensive analytical skills are usually involved, while in the MM algorithm convexity and inequalities are our major focus, and it is relatively easier to understand and apply in most of the cases.
==History==
The original idea of the MM algorithm can be dated back at least to 1970 when Ortega and Rheinboldt were doing their studies related to line search methods.〔
〕 The same idea kept reappearing under different guises in different areas until 2000 when Hunter and Lange put forth "MM" as general frame work.〔
〕 Recently studies have shown that it can be used in a wide range of context, like mathematics, statistics, machine learning, engineering, etc.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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