Multi-track Turing machine - Revision history

83.114.238.227: /* Formal definition */

2014-12-22T21:40:33Z

Formal definition

← Older revision		Revision as of 23:40, 22 December 2014
Line 1:		Line 1:
	~~In [[data mining]], '''cluster-weighted modeling~~ (~~CWM~~)~~'''~~ is ~~an algorithm-based approach to non-linear prediction~~ of ~~outputs ([[Dependent~~ and ~~independent variables\|dependent variables]]) from inputs ([[Dependent~~ and ~~independent variables\|independent variables]]) based on [[density estimation]] using a set of models (clusters)~~ that ~~are each notionally appropriate in a sub-region of~~ the ~~input space~~. ~~The overall approach works in jointly input~~-~~output space and an initial version was proposed by [[Neil Gershenfeld]].<ref>Gershenfeld~~, ~~N. (1997) "Nonlinear Inference~~ and ~~Cluster-Weighted Modeling"~~, ~~''Annals~~ of the ~~New York Academy~~ of ~~Sciences''~~, ~~808~~, ~~18–24. {{DOI\|10~~.~~1111/j.1749-6632.1997.tb51651.x}}</ref>~~<~~ref name=nature~~>Gershenfeld, N., Schoner, B.* & Metois, E. (1999) [http://www.nature.com/nature/journal/v397/n6717/pdf/397329a0.pdf Cluster-weighted modelling for time-series analysis], Nature, 397 (28 Jan. 1999), 329–332 <~~/ref~~>		Bonus: WP Twin and WP Twin Auto Backup: (link to ) While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites. It is used by around 25% of all new websites, and there are more than 27 thousand plugins currently available. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. Hosted by Your Domain on Another Web Host - In this model, you first purchase multiple-domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage of the full power of Wordpress. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster. <br><br>

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	~~The procedure for cluster-weighted modeling of~~ an ~~input-output problem can be outlined as follows.<ref name=nature/> In order~~ to ~~construct predicted values for an output variable ''y'' from an input variable ''x'',~~ the ~~modeling and calibration procedure arrives at a [[joint probability distribution\|joint probability density function]], ''p''(''y'',''x''). Here~~ the ~~"variables" might be uni-variate, multivariate or time-series~~. ~~For convenience, any model parameters~~ are ~~not indicated in~~ the ~~notation here and several different treatments~~ of ~~these are possible, including~~ setting ~~them~~ to ~~fixed values as a step in~~ the ~~calibration or treating them using a [[Bayesian analysis]]~~. ~~The required predicted values are obtained by constructing~~ the ~~[[conditional probability distribution\|conditional probability density]] ''p''(''y''\|''x'') from which~~ the ~~prediction using the [[conditional expected value]] can be obtained, with the [[conditional variance]] providing an indication of uncertainty~~.

	~~The important step of the modeling is that ''p''(''y''\|''x'') is assumed~~ to ~~take the following form, as a [[mixture model]]:~~
	:<~~math~~>~~p(y,x)=\sum_1^n w_jp_j(y,x),~~ <~~/math~~>
	~~where ''n'' is~~ the ~~number~~ of ~~clusters and {''w<sub>j</sub>''} are weights that sum to one~~. ~~The functions ''p<sub>j</sub>''(''y''~~,~~''x'') are joint probability density functions that relate~~ to ~~each of~~ the ~~''n'' clusters~~. ~~These functions are modeled using a decomposition into a conditional~~ and ~~a [[marginal distribution\|marginal density]]:~~
	~~:<math>p_j(y,x)=p_j(y\|x)p_j(x), </math>~~
	~~where:~~
	:*'~~'p<sub>j</sub>''(''y''\|''x'') is~~ a ~~model for predicting ''y'' given ''x'', and given~~ that ~~the input-output pair should be associated~~ with ~~cluster ''j'' on~~ the ~~basis of~~ the ~~value of ''x''~~. ~~This model might be a [[regression analysis\|regression model]] in the simplest cases.~~

	~~:*''p~~<~~sub~~>j<~~/sub~~>~~''(''x'')~~ is ~~formally a density for values of ''x''~~, ~~given that the input-output pair should be associated with cluster ''j''. The relative sizes of these functions between the clusters determines whether a particular value of ''x''~~ is ~~associated~~ with ~~any given cluster~~-~~center~~. ~~This density might be a~~ [~~[Gaussian function~~]~~] centered~~ at ~~a parameter representing~~ the ~~cluster-center~~.

	~~In the same way~~ as ~~for [[regression analysis]]~~, ~~it will be important to consider preliminary [[data transformation]]s as part~~ of the ~~overall modeling strategy if~~ the ~~core components~~ of ~~the model are~~ to ~~be simple regression models for the cluster-wise condition densities, and [[normal distribution]]~~s ~~for the cluster~~-~~weighting densities ''p<sub>j</sub>''(''x'')~~.

	~~==General versions==~~
	~~The basic CWM algorithm gives~~ a ~~single output cluster for each input cluster.~~ ~~However~~, ~~CWM can be extended to multiple clusters which are still associated with the same input cluster~~.<~~ref name="feldkamp"~~>{{cite journal\|last=Feldkamp\|first=L.A.\|coauthors=Prokhorov, D.V.; Feldkamp, T.M.\|date=2001\|title=Cluster-weighted modeling with multiclusters\|journal=International Joint Conference on Neural Networks\|volume=3\|issue=1\|pages=1710&~~ndash~~;~~1714\|url=http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7474/20319/00938419.pdf?temp=x}}</ref~~> ~~Each cluster in CWM~~ is ~~localized to~~ a ~~Gaussian input region~~, ~~and this contains its own trainable local model~~.~~<ref name="mit">{{cite journal\|last=Boyden\|first=Edward S.\|title=Tree-based Cluster Weighted Modeling: Towards A Massively Parallel Real~~-~~Time Digital Stradivarius\|publisher=MIT Media Lab\|location=Cambridge, MA\|url=http://edboyden.org/violin.pdf}}</ref> It~~ is ~~recognized as~~ a ~~versatile inference algorithm which provides simplicity, generality,~~ and ~~flexibility; even when a feedforward layered network might be preferred, it is sometimes used as a "second opinion" on the nature of the training problem.<ref name="dearborn"/>~~

	~~The original form proposed by Gershenfeld describes two innovations:~~
	* Enabling CWM to ~~work with continuous streams of data~~
	* Addressing the ~~problem of local minima encountered by the CWM parameter adjustment process<ref name="dearborn">{{cite journal\|last=Prokhorov\|first=A New Approach~~ to ~~Cluster~~-~~Weighted Modeling Danil V.\|coauthors=Lee A. Feldkamp,~~ and ~~Timothy M~~. ~~Feldkamp\|title=A New Approach to Cluster-Weighted Modeling\|publisher=Ford Research Laboratory\|location=Dearborn~~, ~~MI\|url=http://home.comcast.net/~dvp/cwm.pdf}}</ref>~~

	~~CWM can be used to classify media in printer applications~~, ~~using at least two parameters to generate~~ an ~~output that has~~ a ~~joint dependency~~ on the ~~input parameters~~.~~<ref~~ name~~="media">{{cite journal\|last=Gao\|first=Jun\|coauthors=Ross R~~. Allen\|date=2003-07-24\|title=CLUSTER-WEIGHTED MODELING FOR MEDIA CLASSIFICATION\|publisher=World Intellectual Property Organization\|location=Palo Alto, CA \|url=http://www.wipo.int/pctdb/en/wo.jsp?wo=2003059630}}</ref>

	~~==References==~~
	~~{{Reflist}}~~

	~~[[Category:Multivariate statistics]]~~
	~~[[Category:Data clustering algorithms]]~~
	~~[[Category:Estimation of densities]]~~

46.244.238.12: /* Proof of equivalency to standard Turing machine */

2013-11-11T22:54:33Z

Proof of equivalency to standard Turing machine

← Older revision		Revision as of 00:54, 12 November 2013
Line 1:		Line 1:
	~~It involves expertise~~ and ~~knowledge of various tools~~ and ~~technologies used for creating websites. Also, you may want to opt for a more professioanl theme if you are planning~~ on ~~showing your site off to~~ a ~~high volume~~ of ~~potential customers~~ each ~~day. * A community forum for debate~~ of the ~~product together with some other customers~~ in ~~the comments spot~~. ~~2- Ask for the designs~~ and ~~graphics that will be provided along with the Word~~ - ~~Press theme. You can easily customize~~ the ~~titles~~ of ~~the posts in Word~~ - ~~Press blog in a way that only title comes in the new post link and not the date or category of posts~~. <br><br>~~Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates~~. ~~Best of all~~, ~~you can still have all the functionality that you desire when you use the Word - Press platform~~. ~~Well Managed Administration The Word~~ - ~~Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. E~~-~~commerce websites are meant to be buzzed with fresh contents~~, ~~graphical enhancements~~, ~~and functionalities~~. ~~Moreover~~, ~~many Word~~ - ~~Press themes need to be purchased and designing your own WP site~~ can be ~~boring~~. <br>~~<br>It is also popular because willing surrogates~~,~~as well as egg~~ and ~~sperm donors~~,~~are plentiful~~. ~~By using Word~~ - ~~Press MLM websites~~ or ~~blogs~~, ~~you~~ and ~~your companies presence on~~ the ~~internet~~ can be ~~created swiftly and simply~~. ~~all~~ the ~~necessary planning and steps of conversion~~ is ~~carried out in this phase~~, ~~such~~ as ~~splitting~~, ~~slicing~~, ~~CSS code~~, ~~adding images, header footer etc~~. The ~~animation can be quite subtle these as snow falling gently or some twinkling start in~~ the ~~track record which~~ are ~~essentially not distracting but as an alternative gives some viewing enjoyment~~ for the ~~visitor~~ of the ~~internet site~~. ~~Customization of web layout is easy due to~~ the ~~availability of huge selection of templates~~. <br><br>~~Whether your Word - Press themes~~ is ~~premium or not~~, ~~but nowadays every theme~~ is ~~designed~~ with ~~widget~~-~~ready~~. ~~Russell HR Consulting provides expert knowledge in~~ the ~~practical application of employment law~~ as ~~well~~ as ~~providing employment law training~~ and ~~HR support services~~. However, ~~you may not~~ be ~~able~~ to ~~find a theme that is in sync~~ with ~~your business~~. ~~It's now become a great place to sell it thanks to Woo~~ - ~~Commerce. If you have any sort of questions concerning where and ways to utilize [~~http://~~ammi~~.me/~~wordpress_backup_639634 wordpress dropbox backup], you can call us at our own web site~~. ~~The Pakistani culture~~ is ~~in demand of~~ a ~~main surgical treatment~~. <br><br>~~Someone with~~ a ~~basic knowledge of setting up~~ a ~~website should~~ be ~~able to complete~~ the ~~process in a couple~~ of ~~minutes however even basic users should find they are able~~ to ~~complete~~ the ~~installation in around 20 minutes~~ by ~~following~~ the ~~step by step guide online~~. ~~Here's a list of some exciting Word~~ - ~~Press features that have created waves in the web development industry~~:. ~~While deciding couple should consider the expertise of the doctor,clinics success rate~~,the ~~costs of fertility treatment~~,~~including fertility tests and IVF costs and overall ones own financial budget~~. ~~Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more~~. ~~However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account~~.		In [[data mining]], '''cluster-weighted modeling (CWM)''' is an algorithm-based approach to non-linear prediction of outputs ([[Dependent and independent variables\|dependent variables]]) from inputs ([[Dependent and independent variables\|independent variables]]) based on [[density estimation]] using a set of models (clusters) that are each notionally appropriate in a sub-region of the input space. The overall approach works in jointly input-output space and an initial version was proposed by [[Neil Gershenfeld]].<ref>Gershenfeld, N. (1997) "Nonlinear Inference and Cluster-Weighted Modeling", ''Annals of the New York Academy of Sciences'', 808, 18–24. {{DOI\|10.1111/j.1749-6632.1997.tb51651.x}}</ref><ref name=nature>Gershenfeld, N., Schoner, B.* & Metois, E. (1999) [http://www.nature.com/nature/journal/v397/n6717/pdf/397329a0.pdf Cluster-weighted modelling for time-series analysis], Nature, 397 (28 Jan. 1999), 329–332 </ref>

			==Basic form of model==
			The procedure for cluster-weighted modeling of an input-output problem can be outlined as follows.<ref name=nature/> In order to construct predicted values for an output variable ''y'' from an input variable ''x'', the modeling and calibration procedure arrives at a [[joint probability distribution\|joint probability density function]], ''p''(''y'',''x''). Here the "variables" might be uni-variate, multivariate or time-series. For convenience, any model parameters are not indicated in the notation here and several different treatments of these are possible, including setting them to fixed values as a step in the calibration or treating them using a [[Bayesian analysis]]. The required predicted values are obtained by constructing the [[conditional probability distribution\|conditional probability density]] ''p''(''y''\|''x'') from which the prediction using the [[conditional expected value]] can be obtained, with the [[conditional variance]] providing an indication of uncertainty.

			The important step of the modeling is that ''p''(''y''\|''x'') is assumed to take the following form, as a [[mixture model]]:
			:<math>p(y,x)=\sum_1^n w_jp_j(y,x), </math>
			where ''n'' is the number of clusters and {''w<sub>j</sub>''} are weights that sum to one. The functions ''p<sub>j</sub>''(''y'',''x'') are joint probability density functions that relate to each of the ''n'' clusters. These functions are modeled using a decomposition into a conditional and a [[marginal distribution\|marginal density]]:
			:<math>p_j(y,x)=p_j(y\|x)p_j(x), </math>
			where:
			:*''p<sub>j</sub>''(''y''\|''x'') is a model for predicting ''y'' given ''x'', and given that the input-output pair should be associated with cluster ''j'' on the basis of the value of ''x''. This model might be a [[regression analysis\|regression model]] in the simplest cases.

			:*''p<sub>j</sub>''(''x'') is formally a density for values of ''x'', given that the input-output pair should be associated with cluster ''j''. The relative sizes of these functions between the clusters determines whether a particular value of ''x'' is associated with any given cluster-center. This density might be a [[Gaussian function]] centered at a parameter representing the cluster-center.

			In the same way as for [[regression analysis]], it will be important to consider preliminary [[data transformation]]s as part of the overall modeling strategy if the core components of the model are to be simple regression models for the cluster-wise condition densities, and [[normal distribution]]s for the cluster-weighting densities ''p<sub>j</sub>''(''x'').

			==General versions==
			The basic CWM algorithm gives a single output cluster for each input cluster. However, CWM can be extended to multiple clusters which are still associated with the same input cluster.<ref name="feldkamp">{{cite journal\|last=Feldkamp\|first=L.A.\|coauthors=Prokhorov, D.V.; Feldkamp, T.M.\|date=2001\|title=Cluster-weighted modeling with multiclusters\|journal=International Joint Conference on Neural Networks\|volume=3\|issue=1\|pages=1710–1714\|url=http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7474/20319/00938419.pdf?temp=x}}</ref> Each cluster in CWM is localized to a Gaussian input region, and this contains its own trainable local model.<ref name="mit">{{cite journal\|last=Boyden\|first=Edward S.\|title=Tree-based Cluster Weighted Modeling: Towards A Massively Parallel Real-Time Digital Stradivarius\|publisher=MIT Media Lab\|location=Cambridge, MA\|url=http://edboyden.org/violin.pdf}}</ref> It is recognized as a versatile inference algorithm which provides simplicity, generality, and flexibility; even when a feedforward layered network might be preferred, it is sometimes used as a "second opinion" on the nature of the training problem.<ref name="dearborn"/>

			The original form proposed by Gershenfeld describes two innovations:
			* Enabling CWM to work with continuous streams of data
			* Addressing the problem of local minima encountered by the CWM parameter adjustment process<ref name="dearborn">{{cite journal\|last=Prokhorov\|first=A New Approach to Cluster-Weighted Modeling Danil V.\|coauthors=Lee A. Feldkamp, and Timothy M. Feldkamp\|title=A New Approach to Cluster-Weighted Modeling\|publisher=Ford Research Laboratory\|location=Dearborn, MI\|url=http://home.comcast.net/~dvp/cwm.pdf}}</ref>

			CWM can be used to classify media in printer applications, using at least two parameters to generate an output that has a joint dependency on the input parameters.<ref name="media">{{cite journal\|last=Gao\|first=Jun\|coauthors=Ross R. Allen\|date=2003-07-24\|title=CLUSTER-WEIGHTED MODELING FOR MEDIA CLASSIFICATION\|publisher=World Intellectual Property Organization\|location=Palo Alto, CA \|url=http://www.wipo.int/pctdb/en/wo.jsp?wo=2003059630}}</ref>

			==References==
			{{Reflist}}

			[[Category:Multivariate statistics]]
			[[Category:Data clustering algorithms]]
			[[Category:Estimation of densities]]

en>Jonataslr at 00:43, 7 July 2012

2012-07-07T00:43:17Z

New page

It involves expertise and knowledge of various tools and technologies used for creating websites. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. * A community forum for debate of the product together with some other customers in the comments spot. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. You can easily customize the titles of the posts in Word - Press blog in a way that only title comes in the new post link and not the date or category of posts. Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. By using Word - Press MLM websites or blogs, you and your companies presence on the internet can be created swiftly and simply. all the necessary planning and steps of conversion is carried out in this phase, such as splitting, slicing, CSS code, adding images, header footer etc. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for the visitor of the internet site. Customization of web layout is easy due to the availability of huge selection of templates. Whether your Word - Press themes is premium or not, but nowadays every theme is designed with widget-ready. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. However, you may not be able to find a theme that is in sync with your business. It's now become a great place to sell it thanks to Woo - Commerce. If you have any sort of questions concerning where and ways to utilize [http://ammi.me/wordpress_backup_639634 wordpress dropbox backup], you can call us at our own web site. The Pakistani culture is in demand of a main surgical treatment. Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.