Valeur informationelle - Historique des versions

Pitpitt : Remplacement de texte : « ↵ » par «  ==Sources== »

2024-01-28T19:01:30Z

Remplacement de texte : « ↵<small> » par «  ==Sources== »

← Version précédente		Version du 28 janvier 2024 à 15:01
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	<!-- The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. -->		<!-- The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. -->

	~~<small>~~		==Sources==

	[https://arxiv.org/abs/1703.10534 Source : arxiv]		[https://arxiv.org/abs/1703.10534 Source : arxiv]

	[[Catégorie:GRAND LEXIQUE FRANÇAIS]]		[[Catégorie:GRAND LEXIQUE FRANÇAIS]]

Pitpitt le 17 mai 2023 à 01:54

2023-05-17T01:54:56Z

← Version précédente		Version du 16 mai 2023 à 21:54
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	== Définition ==		== Définition ==
	Caractère informatif~~. Valeur informationelle~~. Qui a pour but de donner des renseignements.		Caractère informatif. Qui a pour but de donner des renseignements.

	~~''' informativeness'''~~ = '''Valeur informationelle''' ~~????~~		== Français ==
			'''Valeur informationelle'''

	~~== Français ==~~
	''' contenu informatif '''		''' contenu informatif '''

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	[https://arxiv.org/abs/1703.10534 Source : arxiv]		[https://arxiv.org/abs/1703.10534 Source : arxiv]

	[[Catégorie:~~Publication~~]]		[[Catégorie:GRAND LEXIQUE FRANÇAIS]]

Pitpitt : Pitpitt a déplacé la page Contenu en information vers Valeur informationelle

2023-05-17T01:53:29Z

Pitpitt a déplacé la page Contenu en information vers Valeur informationelle

← Version précédente	Version du 16 mai 2023 à 21:53
(Aucune différence)

Pitpitt le 17 mai 2023 à 01:50

2023-05-17T01:50:39Z

← Version précédente		Version du 16 mai 2023 à 21:50
Ligne 1 :		Ligne 1 :
	== Définition ==		== Définition ==
	Caractère informatif. Valeur informationelle. Qui a pour but de donner des renseignements.		Caractère informatif. Valeur informationelle. Qui a pour but de donner des renseignements.

			''' informativeness''' = '''Valeur informationelle''' ????

	== Français ==		== Français ==

Pitpitt le 17 mai 2023 à 01:43

2023-05-17T01:43:18Z

← Version précédente		Version du 16 mai 2023 à 21:43
Ligne 1 :		Ligne 1 :
	== Définition ==		== Définition ==
	Caractère informatif. ~~Qui vise à informer~~. Qui a pour but de donner des renseignements.		Caractère informatif. Valeur informationelle. Qui a pour but de donner des renseignements.

	== Français ==		== Français ==

Pitpitt : Pitpitt a déplacé la page Informativeness vers Contenu en information

2023-05-17T01:41:32Z

Pitpitt a déplacé la page Informativeness vers Contenu en information

← Version précédente	Version du 16 mai 2023 à 21:41
(Aucune différence)

Pitpitt le 17 mai 2023 à 01:38

2023-05-17T01:38:44Z

← Version précédente		Version du 16 mai 2023 à 21:38
Ligne 1 :		Ligne 1 :
	== Définition ==		== Définition ==
	Caractère informatif. Qui vise à informer~~, qui~~ a pour but de donner des renseignements.		Caractère informatif. Qui vise à informer. Qui a pour but de donner des renseignements.

	== Français ==		== Français ==

Pitpitt le 17 mai 2023 à 01:38

2023-05-17T01:38:14Z

← Version précédente		Version du 16 mai 2023 à 21:38
Ligne 1 :		Ligne 1 :
	== Définition ==		== Définition ==
			Caractère informatif. Qui vise à informer, qui a pour but de donner des renseignements.

	== Français ==		== Français ==
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	<!-- The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. -->		<!-- The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. -->



	<small>		<small>

			[https://arxiv.org/abs/1703.10534 Source : arxiv]

	~~[https://arxiv.org/abs/1703.10534 Source : arxiv]~~
	[[Catégorie:Publication]]		[[Catégorie:Publication]]

Patrickdrouin le 16 mai 2023 à 20:47

2023-05-16T20:47:11Z

← Version précédente		Version du 16 mai 2023 à 16:47
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	~~==en construction==~~

	== Définition ==		== Définition ==
	~~XXXXXXXXX~~

	== Français ==		== Français ==
	''' ~~XXXXXXXXX~~ '''		''' contenu informatif '''

			''' contenu en information '''

	== Anglais ==		== Anglais ==
	''' ~~Informativeness~~'''		''' informativeness'''

	The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models.		<!-- Pas un terme, mais une difficulté de traduction -->

			<!-- The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. -->


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	[https://arxiv.org/abs/1703.10534 Source : arxiv]		[https://arxiv.org/abs/1703.10534 Source : arxiv]
			[[Catégorie:Publication]]

	[[Catégorie:~~vocabulary~~]]

Pitpitt : Page créée avec « ==en construction== == Définition == XXXXXXXXX == Français == ''' XXXXXXXXX ''' == Anglais == ''' Informativeness''' The learning of mixture models can be viewed as... »

2023-02-07T13:13:54Z

Page créée avec « ==en construction== == Définition == XXXXXXXXX == Français == ''' XXXXXXXXX ''' == Anglais == ''' Informativeness''' The learning of mixture models can be viewed as... »

Nouvelle page

==en construction==

== Définition ==
XXXXXXXXX

== Français ==
''' XXXXXXXXX '''

== Anglais ==
''' Informativeness'''

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an {\it optimal clustering} that minimizes the sum-of-squares distance between each point and its cluster center. In this paper, we consider fundamental (i.e., information-theoretic) limits of the solutions (clusterings) obtained by optimizing the sum-of-squares distance. In particular, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of spherical Gaussian distributions. We also generalize our results to log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models.

<small>

[https://arxiv.org/abs/1703.10534 Source : arxiv]

[[Catégorie:vocabulary]]

Valeur informationelle - Historique des versions

Pitpitt : Remplacement de texte : « ↵ » par « ==Sources== »

Pitpitt le 17 mai 2023 à 01:54

Pitpitt : Pitpitt a déplacé la page Contenu en information vers Valeur informationelle

Pitpitt le 17 mai 2023 à 01:50

Pitpitt le 17 mai 2023 à 01:43

Pitpitt : Pitpitt a déplacé la page Informativeness vers Contenu en information

Pitpitt le 17 mai 2023 à 01:38

Pitpitt le 17 mai 2023 à 01:38

Patrickdrouin le 16 mai 2023 à 20:47

Pitpitt : Page créée avec « ==en construction== == Définition == XXXXXXXXX == Français == ''' XXXXXXXXX ''' == Anglais == ''' Informativeness''' The learning of mixture models can be viewed as... »

Pitpitt : Remplacement de texte : « ↵ » par «  ==Sources== »

Pitpitt : Pitpitt a déplacé la page Contenu en information vers Valeur informationelle

Pitpitt : Pitpitt a déplacé la page Informativeness vers Contenu en information

Pitpitt : Page créée avec « ==en construction== == Définition == XXXXXXXXX == Français == ''' XXXXXXXXX ''' == Anglais == ''' Informativeness''' The learning of mixture models can be viewed as... »