MM algorithm - Revision history

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2024-12-13T07:42:23Z

Add: pmid, issue. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Optimization algorithms and methods | #UCB_Category 40/168

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	\|journal=[[International Statistical Review]]		\|journal=[[International Statistical Review]]
	\|year=2022 \|volume=90		\|year=2022 \|volume=90
			\|issue=Suppl 1
	\|pages=S52–S66		\|pages=S52–S66
	\|doi=10.1111/insr.12526		\|doi=10.1111/insr.12526
			\|pmid=37204987
	\|pmc=10191373		\|pmc=10191373
	}}</ref>		}}</ref>

OAbot: Open access bot: pmc updated in citation with #oabot.

2023-08-14T13:22:24Z

Open access bot: pmc updated in citation with #oabot.

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	\|pages=S52–S66		\|pages=S52–S66
	\|doi=10.1111/insr.12526		\|doi=10.1111/insr.12526
			\|pmc=10191373
	}}</ref>		}}</ref>

WikiCleanerBot: v2.05b - Bot T20 CW#61 - Fix errors for CW project (Reference before punctuation)

2023-05-19T07:53:20Z

v2.05b - Bot T20 CW#61 - Fix errors for CW project (Reference before punctuation)

← Previous revision		Revision as of 07:53, 19 May 2023
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	\|isbn=978-1-61197-439-3		\|isbn=978-1-61197-439-3
	}}</ref>		}}</ref>
	However, in the EM algorithm [[conditional expectation]]s are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases<ref>{{cite journal		However, in the EM algorithm [[conditional expectation]]s are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases.<ref>{{cite journal
	\|last1=Lange\|first1=K.		\|last1=Lange\|first1=K.
	\|last2=Zhou\|first2=H.		\|last2=Zhou\|first2=H.
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	\|pages=S52–S66		\|pages=S52–S66
	\|doi=10.1111/insr.12526		\|doi=10.1111/insr.12526
	}}</ref>.		}}</ref>

	==History==		==History==

24.205.59.179 at 13:08, 13 May 2023

2023-05-13T13:08:25Z

← Previous revision		Revision as of 13:08, 13 May 2023
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	The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization. Despite the name, MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].		The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization. Despite the name, MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].

	The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>~~Kenneth~~ Lange: "MM Optimization Algorithms~~", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>~~		The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>{{cite book
			\|last1=Lange \|first1=Kenneth
			\|title=MM Optimization Algorithms
			\|publisher=SIAM
			\|year=2016
			\|doi=10.1137/1.9781611974409
			\|isbn=978-1-61197-439-3
			}}</ref>
	However, in the EM algorithm [[conditional expectation]]s are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases<ref>{{cite journal		However, in the EM algorithm [[conditional expectation]]s are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases<ref>{{cite journal
	\|last1=Lange\|first1=K.		\|last1=Lange\|first1=K.

24.205.59.179 at 12:57, 13 May 2023

2023-05-13T12:57:15Z

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	\|last2=Zhou\|first2=H.		\|last2=Zhou\|first2=H.
	\|title=A legacy of EM algorithms		\|title=A legacy of EM algorithms
	\|journal=[[~~nternational~~ Statistical Review]]		\|journal=[[International Statistical Review]]
	\|year=2022 \|volume=90		\|year=2022 \|volume=90
	\|pages=S52–S66		\|pages=S52–S66

24.205.59.179 at 12:56, 13 May 2023

2023-05-13T12:56:33Z

← Previous revision		Revision as of 12:56, 13 May 2023
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	The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>		The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>
	However, in the EM algorithm [[conditional expectation]]s are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases.{{~~clarify\|date=July~~ ~~2020}}~~		However, in the EM algorithm [[conditional expectation]]s are usually involved, while in the MM algorithm convexity and inequalities are the main focus, and it is easier to understand and apply in most cases<ref>{{cite journal
			\|last1=Lange\|first1=K.
			\|last2=Zhou\|first2=H.
			\|title=A legacy of EM algorithms
			\|journal=[[nternational Statistical Review]]
			\|year=2022 \|volume=90
			\|pages=S52–S66
			\|doi=10.1111/insr.12526
			}}</ref>.

	==History==		==History==

2A02:8108:50BF:C694:1CE0:EDD5:D67C:A239: tackle a little inconsistency

2022-01-07T08:59:19Z

tackle a little inconsistency

← Previous revision		Revision as of 08:59, 7 January 2022
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	The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization. MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].		The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization. Despite the name, MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].

	The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>		The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>

2A02:8108:50BF:C694:1CE0:EDD5:D67C:A239: /* Algorithm */ no need for the figure to dangle around at the bottom

2022-01-07T08:57:05Z

Algorithm: no need for the figure to dangle around at the bottom

← Previous revision		Revision as of 08:57, 7 January 2022
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	==Algorithm==		==Algorithm==
			[[File:Mmalgorithm.jpg\|right\|thumb\|MM algorithm]]
	The MM algorithm works by finding a surrogate function that minorizes or majorizes the objective function. Optimizing the surrogate function will either improve the value of the objective function or leave it unchanged.		The MM algorithm works by finding a surrogate function that minorizes or majorizes the objective function. Optimizing the surrogate function will either improve the value of the objective function or leave it unchanged.

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	: <math> f(\theta_{m+1}) \ge g(\theta_{m+1}\|\theta_m) \ge g(\theta_m\|\theta_m)= f(\theta_m)</math>		: <math> f(\theta_{m+1}) \ge g(\theta_{m+1}\|\theta_m) \ge g(\theta_m\|\theta_m)= f(\theta_m)</math>

	The marching of <math>\theta_m </math> and the surrogate functions relative to the objective function is shown in the figure. ~~[[File:Mmalgorithm.jpg\|right\|thumb\|MM algorithm]]~~		The marching of <math>\theta_m </math> and the surrogate functions relative to the objective function is shown in the figure.

	Majorize-Minimization is the same procedure but with a convex objective to be minimised.		Majorize-Minimization is the same procedure but with a convex objective to be minimised.

Samratiisc at 10:49, 13 August 2021

2021-08-13T10:49:34Z

← Previous revision		Revision as of 10:49, 13 August 2021
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	The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a ~~maximization~~ or a ~~minimization~~. MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].		The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization. MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].

	The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>		The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>

PeterLeopold: grammar correction: parallel construction their -> its

2020-11-25T22:04:19Z

grammar correction: parallel construction their -> its

← Previous revision		Revision as of 22:04, 25 November 2020
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	The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find ~~their~~ maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a maximization or a minimization. MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].		The '''MM algorithm''' is an iterative [[optimization]] method which exploits the [[convex function\|convexity]] of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a maximization or a minimization. MM itself is not an algorithm, but a description of how to construct an [[optimization algorithm]].

	The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>		The [[expectation–maximization algorithm]] can be treated as a special case of the MM algorithm.<ref>{{cite web\|last=Lange\|first=Kenneth\|title=The MM Algorithm\|url=http://www.stat.berkeley.edu/~aldous/Colloq/lange-talk.pdf}}</ref><ref>Kenneth Lange: "MM Optimization Algorithms", SIAM, {{ISBN\|978-1-611974-39-3}} (2016).</ref>