Talk:Gibbs algorithm - Revision history

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	==Gibbs measure==		==Gibbs measure==
	This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:		This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:

Srich32977: Fixing style/layout errors

2014-08-15T20:48:14Z

Fixing style/layout errors

← Previous revision		Revision as of 20:48, 15 August 2014
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	This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6. (''Unsigned, [[User:146.50.1.141]], January 2007'')		This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6. (''Unsigned, [[User:146.50.1.141]], January 2007'')
	---------		---------

	On a similar note the article states <math>H</math> is the 'average log probability'. The expression given (entropy) is the negative of that quantity. This makes the language about 'minimising the average log probability' confusing - since we should actually be maximising it. - Summary, I think there is a sign error. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/62.25.109.195\|62.25.109.195]] ([[User talk:62.25.109.195\|talk]]) 11:54, 18 December 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->		On a similar note the article states <math>H</math> is the 'average log probability'. The expression given (entropy) is the negative of that quantity. This makes the language about 'minimising the average log probability' confusing - since we should actually be maximising it. - Summary, I think there is a sign error. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/62.25.109.195\|62.25.109.195]] ([[User talk:62.25.109.195\|talk]]) 11:54, 18 December 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

SineBot: Signing comment by 62.25.109.195 - "/* Gibbs Algorithm vs Gibbs Sampler */"

2013-12-18T11:56:05Z

Signing comment by 62.25.109.195 - "Gibbs Algorithm vs Gibbs Sampler: "

← Previous revision		Revision as of 11:56, 18 December 2013
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	On a similar note the article states <math>H</math> is the 'average log probability'. The expression given (entropy) is the negative of that quantity. This makes the language about 'minimising the average log probability' confusing - since we should actually be maximising it. - Summary, I think there is a sign error.		On a similar note the article states <math>H</math> is the 'average log probability'. The expression given (entropy) is the negative of that quantity. This makes the language about 'minimising the average log probability' confusing - since we should actually be maximising it. - Summary, I think there is a sign error. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/62.25.109.195\|62.25.109.195]] ([[User talk:62.25.109.195\|talk]]) 11:54, 18 December 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

62.25.109.195: /* Gibbs Algorithm vs Gibbs Sampler */

2013-12-18T11:54:53Z

Gibbs Algorithm vs Gibbs Sampler

← Previous revision		Revision as of 11:54, 18 December 2013
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	This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6. (''Unsigned, [[User:146.50.1.141]], January 2007'')		This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6. (''Unsigned, [[User:146.50.1.141]], January 2007'')
			---------

			On a similar note the article states <math>H</math> is the 'average log probability'. The expression given (entropy) is the negative of that quantity. This makes the language about 'minimising the average log probability' confusing - since we should actually be maximising it. - Summary, I think there is a sign error.

Linas: comments from User:146.50.1.141

2008-08-30T21:18:30Z

comments from User:146.50.1.141

← Previous revision		Revision as of 21:18, 30 August 2008
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	{{physics\|class=stub\|importance=low}}		{{physics\|class=stub\|importance=low}}

			==Gibbs measure==
	This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:		This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:

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	is a normalizing factor. '''T''' is a constant called the temperature, and U(f) is an energy function. For a specific choice of U(f), this leads to the (Gaussian) [[Normal_distribution]].		is a normalizing factor. '''T''' is a constant called the temperature, and U(f) is an energy function. For a specific choice of U(f), this leads to the (Gaussian) [[Normal_distribution]].

	Maybe the Gibbs distrubution should redirect to the [[Gibbs_measure]]		Maybe the Gibbs distrubution should redirect to the [[Gibbs_measure]] (''Unsigned, [[User:146.50.1.141]], January 2007'')
	:Now fixed. [[User:Linas\|linas]] ([[User talk:Linas\|talk]]) 21:16, 30 August 2008 (UTC)		:Now fixed. [[User:Linas\|linas]] ([[User talk:Linas\|talk]]) 21:16, 30 August 2008 (UTC)

	=== Gibbs Algorithm vs Gibbs Sampler ===		==Gibbs Algorithm vs Gibbs Sampler ==
	This article states that the Gibbs Algorithm is different from the Gibbs Sampler. But I encountered various interpretations of Markov Random Fields in terms of maximizing the Entropy, which is often defined as		This article states that the Gibbs Algorithm is different from the Gibbs Sampler. But I encountered various interpretations of Markov Random Fields in terms of maximizing the Entropy, which is often defined as

	<math> H = -\sum_i p_i \log p_i </math>		<math> H = -\sum_i p_i \log p_i </math>

	This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6.		This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6. (''Unsigned, [[User:146.50.1.141]], January 2007'')

Linas: fixed

2008-08-30T21:16:23Z

fixed

← Previous revision		Revision as of 21:16, 30 August 2008
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	{{physics\|class=\|importance=}}		{{physics\|class=stub\|importance=low}}

	This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:		This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:
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	Maybe the Gibbs distrubution should redirect to the [[Gibbs_measure]]		Maybe the Gibbs distrubution should redirect to the [[Gibbs_measure]]
			:Now fixed. [[User:Linas\|linas]] ([[User talk:Linas\|talk]]) 21:16, 30 August 2008 (UTC)

	=== Gibbs Algorithm vs Gibbs Sampler ===		=== Gibbs Algorithm vs Gibbs Sampler ===

146.50.1.141 at 16:54, 4 January 2007

2007-01-04T16:54:45Z

← Previous revision		Revision as of 16:54, 4 January 2007
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	is a normalizing factor. '''T''' is a constant called the temperature, and U(f) is an energy function. For a specific choice of U(f), this leads to the (Gaussian) [[Normal_distribution]].		is a normalizing factor. '''T''' is a constant called the temperature, and U(f) is an energy function. For a specific choice of U(f), this leads to the (Gaussian) [[Normal_distribution]].

			Maybe the Gibbs distrubution should redirect to the [[Gibbs_measure]]

	=== Gibbs Algorithm vs Gibbs Sampler ===		=== Gibbs Algorithm vs Gibbs Sampler ===

146.50.1.141 at 16:53, 4 January 2007

2007-01-04T16:53:02Z

← Previous revision		Revision as of 16:53, 4 January 2007
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	<math> H = -\sum_i p_i \log p_i </math>		<math> H = -\sum_i p_i \log p_i </math>

	This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/].		This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/] op page 5/6.

146.50.1.141 at 16:44, 4 January 2007

2007-01-04T16:44:11Z

← Previous revision		Revision as of 16:44, 4 January 2007
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	{{physics\|class=\|importance=}}		{{physics\|class=\|importance=}}

			This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:

			<math> P(f) = Z^{-1} \times e^{-\frac{1}{T} U(f)} </math>

			where

			<math> Z = \sum_{f \in F} e^{-\frac{1}{T} U(f)} </math>

			is a normalizing factor. '''T''' is a constant called the temperature, and U(f) is an energy function. For a specific choice of U(f), this leads to the (Gaussian) [[Normal_distribution]].

			=== Gibbs Algorithm vs Gibbs Sampler ===
			This article states that the Gibbs Algorithm is different from the Gibbs Sampler. But I encountered various interpretations of Markov Random Fields in terms of maximizing the Entropy, which is often defined as

			<math> H = -\sum_i p_i \log p_i </math>

			This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [http://www.ams.org/online_bks/conm1/].

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