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'''Minimum message length''' (MML) is a formal [[information theory]] restatement of [[Occam's Razor]]: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of the model, followed by a statement of data encoded concisely using that model). MML was invented by [[Chris Wallace (computer scientist)|Chris Wallace]], first appearing in the seminal (Wallace and Boulton, 1968).
The procedure of house coffee roasting is decades aged. It has gone on for centuries when it was started by roasting green coffee beans over an open fire in pans. It eventually went to roasting over coals in cast iron skillets, or rotating iron drums over a fire. Up until about World War I, it was usual to roast coffee at house. In the 20th century, commercial roasting and grinding moved inside to the scene and it became less popular for individuals to roast their own coffee.<br><br>The green coffee weight loss extract method of losing weight is one perfect way to reduce those extra fats. You are able to ask why these beans are green. It's considering these beans have not been roasted. Why the usual coffee beans a great deal of folks are familiar with are dark in color is basically considering these beans have been roasted about 475 levels Fahrenheit. That process can in actual fact make the beans drop its fat-burning and anti-oxidant element which it usually possess. Evidently, the [http://greencoffeeweightlossplan.com green coffee bean extract] come in its most all-natural state and therefore could create folks lose fat naturally.<br><br>So what are these magic beans? Green coffee beans are merely regular beans which haven't been roasted. It's not the caffeine inside green coffee which assists we lose fat. No, the key to fat loss is an active compound called chloregnic acid found inside green coffee beans, which may inhibit the intake of glucose (sugar) into the bloodstream, whilst simultaneously boosting the launch of stored fat to be burned for power ( thereby marketing fat reduction because sugar consumption is regarded as the key factors you get fat). Don't expect to get rid of weight from a morning Starbucks latte though.<br><br>Chlorogenic acid has additional blessings. Not only usually it assist to remove inches from a waistline, it usually also boost cholesterol, blood lipids, and insulin sensitivity. On top of these good health advantages are also immune program advantages. Chlorogenic acid is an antioxidant. It fights free radical damage, helping to boost immune function and supporting advantageous wellness.<br><br>To create this powerful extract, the green seeds are soaked in water plus then concentrated. Green coffee beans have a healthy chemical which roasted beans never have: Chlorogenic Acid. Chlorogenic Acid works by lowering blood glucose degrees. Sugar turns to fat in the body, plus the bean extract could attack glucose before it gets that far.<br><br>When the desired roasting point is reached, be sure to dump the beans inside to a cool bowl for cooling down. This is significant thus which the heat will be removed plus the roasting stopped to have a more consistent roast. Stir the house coffee roasted beans usually throughout the initial cool down period. Let them cool for at least 24 hours. Many people think which the complete flavor change takes which lengthy. Grind the coffee plus brew in the favorite brewer and enjoy the freshest cup of coffee that can be made.<br><br>Omega-3 has become increasingly popular for helping with conditions ranging from anxiety to aging. Studies show which this healthy essential fatty acid (EFA) can even enable with arthritis, acne plus depression. Many of you don't eat enough fish to get our daily dosage, thus try a supplement like Nordic Naturals Omega-3 Formula. Look for a supplement with a minimal of 600 mg of DHA.<br><br>But, a lifestyle that includes regular exercise, right nutrition, and possibly even a good fat reduction product, will probably result in healthy, permanent weight reduction, whether or not YOUR results are not typical.
 
MML is intended not just as a theoretical construct, but as a technique that may be deployed in practice. It differs from the related concept of [[Kolmogorov complexity]] in that it does not require use of a [[Turing completeness|Turing-complete]] language to model data. The relation between Strict MML (SMML) and [[Kolmogorov complexity]] is outlined in [http://comjnl.oxfordjournals.org/cgi/reprint/42/4/270 Wallace and Dowe (1999a)]. Further, a variety of mathematical approximations to "Strict" MML can be used — see, e.g., [http://www.csse.monash.edu.au/mml/toc.pdf Chapters 4 and 5] of [http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-10129-22-35893962-0,00.html Wallace (posthumous) 2005].
 
==Definition==
 
[[Claude E. Shannon|Shannon]]'s ''[[A Mathematical Theory of Communication]]'' (1949) states that in an optimal code, the message length (in binary) of an event <math>E</math>, <math>\operatorname{length}(E)</math>, where <math>E</math> has probability <math>P(E)</math>, is given by <math>\operatorname{length}(E) = -\log_2(P(E))</math>.
 
[[Bayes's theorem]] states that the probability of a (variable) hypothesis <math>H</math> given fixed evidence <math>E</math> is proportional to <math>P(E|H) P(H)</math>, which, by the definition of conditional probability, is equal to <math>P(H \and E)</math>. We want the model (hypothesis) with the highest such ''posterior probability''. Suppose we encode a message which represents (describes) both model and data jointly. Since <math>\operatorname{length}(H \and E) = -\log_2(P(H \and E))</math>, the most probable model will have the shortest such message. The message breaks into two parts: <math>-\log_2(P(H \and E)) = -\log_2(P(H)) + -\log_2(P(E|H))</math>. The first part encodes the model itself. The second part contains information (e.g., values of parameters, or initial conditions, etc.) that, when processed by the model, outputs the observed data.
 
MML naturally and precisely trades model complexity for goodness of fit. A more complicated model takes longer to state (longer first part) but probably fits the data better (shorter second part).  So, an MML metric won't choose a complicated model unless that model pays for itself.
 
==Continuous-valued parameters==
 
One reason why a model might be longer would be simply because its various parameters are stated to greater precision, thus requiring transmission of more digits. Much of the power of MML derives from its handling of how accurately to state parameters in a model, and a variety of approximations that make this feasible in practice. This allows it to usefully compare, say, a model with many parameters imprecisely stated against a model with fewer parameters more accurately stated.
 
==Key features of MML==
 
* MML can be used to compare models of different structure. For example, its earliest application was in finding [[mixture model]]s with the optimal number of classes. Adding extra classes to a mixture model will always allow the data to be fitted to greater accuracy, but according to MML this must be weighed against the extra bits required to encode the parameters defining those classes.
* MML is a method of [[Bayesian model comparison]]. It gives every model a score.
* MML is scale-invariant and statistically invariant. Unlike many Bayesian selection methods, MML doesn't care if you change from measuring length to volume or from Cartesian co-ordinates to polar co-ordinates.
* MML is statistically consistent. For problems like the [http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#DoweWallace1997 Neyman-Scott] (1948) problem or factor analysis where the amount of data per parameter is bounded above, MML can estimate all parameters with statistical consistency.
* MML accounts for the precision of measurement. It uses the [[Fisher information]] (in the Wallace-Freeman 1987 approximation, or other hyper-volumes in [http://www.csse.monash.edu.au/~dld/CSWallacePublications/CSWallace2005book_toc.pdf other approximations]) to optimally discretize continuous parameters. Therefore the posterior is always a probability, not a probability density.
* MML has been in use since 1968. MML coding schemes have been developed for several distributions, and many kinds of machine learners including unsupervised classification, decision trees and graphs, DNA sequences, [[Bayesian network]]s, neural networks (one-layer only so far), image compression, image and function segmentation, etc.
 
==See also==
* [[Minimum description length]] — a supposedly non-Bayesian alternative with a possibly different motivation, which was introduced 10 years later — for comparisons, see, e.g., (sec. 10.2 of [http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-10129-22-35893962-0,00.html Wallace (posthumous) 2005]) and (sec. 11.4.3, pp [http://www.csse.monash.edu.au/~dld/Publications/2005/ComleyDowe2005MMLGeneralizedBayesianNetsAsymmetricLanguages_p272.jpg 272]-[http://www.csse.monash.edu.au/~dld/Publications/2005/ComleyDowe2005MMLGeneralizedBayesianNetsAsymmetricLanguages_p273.jpg 273] of [http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005 Comley and Dowe, 2005]) and [http://comjnl.oxfordjournals.org/cgi/reprint/42/4 the special issue on Kolmogorov Complexity in the Computer Journal: Vol. 42, No. 4, 1999].
* [[Kolmogorov complexity]] — absolute complexity (within a constant, depending on the particular choice of Universal [[Turing machine|Turing Machine]]); MML is typically a computable approximation (see [http://comjnl.oxfordjournals.org/cgi/reprint/42/4/270 Wallace and Dowe (1999a)] below for elaboration)
* [[Algorithmic information theory]]
* [[Grammar induction]]
 
==External links==
* Links to all [http://www.csse.monash.edu.au/~dld/CSWallacePublications/ Chris Wallace]'s known publications.
* [[Chris Wallace (computer scientist)|C.S. Wallace]], [http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-10129-22-35893962-0,00.html Statistical and Inductive Inference by Minimum Message Length], Springer-Verlag (Information Science and Statistics), ISBN 0-387-23795-X, May 2005 - [http://www.springer.com/west/home/statistics/theory?SGWID=4-10129-22-35893962-detailsPage=ppmmedia|toc chapter headings], [http://www.csse.monash.edu.au/mml/toc.pdf table of contents] and [http://books.google.com/books?ie=ISO-8859-1&id=3NmFwNHaNbUC&q=wallace+%22statistical+and+inductive+inference+by+minimum+message+length%22&dq=wallace+%22statistical+and+inductive+inference+by+minimum+message+length%22 sample pages].
* A [http://www.allisons.org/ll/Images/People/Wallace/ searchable database of Chris Wallace's publications].
* [http://comjnl.oxfordjournals.org/cgi/reprint/42/4/270 Minimum Message Length and Kolmogorov Complexity] (by [http://www.csse.monash.edu.au/~dld/CSWallacePublications/ C.S. Wallace] and [http://www.csse.monash.edu.au/~dld D.L. Dowe], Computer Journal, Vol. 42, No. 4, 1999, [http://comjnl.oxfordjournals.org/cgi/reprint/42/4/270 pp270-283]).
*[http://www.allisons.org/ll/MML/20031120e/ History of MML, CSW's last talk].
* [http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#NeedhamDowe2001 Message Length as an Effective Ockham's Razor in Decision Tree Induction], by S. Needham and [http://www.csse.monash.edu.au/~dld D. Dowe], Proc. [http://www.ai.mit.edu/conferences/aistats2001 8th International Workshop on AI and Statistics] (2001), [http://www.csse.monash.edu.au/~dld/Publications/2001/Needham+Dowe2001_Ockham.pdf pp253-260].  (Shows how [[Occam's razor]] works fine when interpreted as [http://www.csse.monash.edu.au/~dld/MML.html MML].)
* L.Allison,
* [http://dx.doi.org/10.1017/S0956796804005301 Models for machine learning and data mining in functional programming], J. Functional Programming, 15(1), pp15–32, Jan. 2005 (MML, FP, and Haskell [http://www.allisons.org/ll/Publications/200309/READ-ME.shtml code]).
* J.W.Comley and [http://www.csse.monash.edu.au/~dld D.L. Dowe] (2005), "[http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005 Minimum Message Length, MDL and Generalised Bayesian Networks with Asymmetric Languages]", [http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10478&mode=toc Chapter 11] (pp [http://www.csse.monash.edu.au/~dld/Publications/2005/ComleyDowe2005MMLGeneralizedBayesianNetsAsymmetricLanguages_p265.jpg 265]-[http://www.csse.monash.edu.au/~dld/Publications/2005/ComleyDowe2005MMLGeneralizedBayesianNetsAsymmetricLanguages_p294.jpg 294]) in P. Grunwald, M. A. Pitt and I. J. Myung (ed.), [http://mitpress.mit.edu/catalog/item/default.asp?sid=4C100C6F-2255-40FF-A2ED-02FC49FEBE7C&ttype=2&tid=10478 Advances in Minimum Description Length: Theory and Applications], M.I.T. Press (MIT Press), April 2005, [http://mitpress.mit.edu/catalog/item/default.asp?sid=4C100C6F-2255-40FF-A2ED-02FC49FEBE7C&ttype=2&tid=10478 ISBN] [http://mitpress.mit.edu/catalog/item/default.asp?sid=4C100C6F-2255-40FF-A2ED-02FC49FEBE7C&ttype=2&tid=10478 0-262-07262-9].
[See also [http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2003 Comley and Dowe (2003)], [http://www.csse.monash.edu.au/~dld/Publications/2003/Comley+Dowe03_HICS2003_GeneralBayesianNetworksAsymmetricLanguages.pdf .pdf]. Comley & Dowe ([http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2003 2003], [http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005 2005]) are the first two papers on MML Bayesian nets using both discrete and continuous valued parameters.]
* Dowe, David L. (2010). [http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf MML, hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness], in Handbook of Philosophy of Science (Volume 7: Handbook of Philosophy of Statistics), Elsevier, [http://japan.elsevier.com/products/books/HPS.pdf ISBN 978-0-444-51862-0], pp [http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf 901-982].
* [http://www.csse.monash.edu.au/~lloyd/tildeMML/ Minimum Message Length (MML)], LA's MML introduction, [http://www.allisons.org/ll/MML/ (MML alt.)].
* [http://www.csse.monash.edu.au/~dld/MML.html Minimum Message Length (MML), researchers and links].
* [http://www.csse.monash.edu.au/mml/ Another MML research website.]
* [http://www.csse.monash.edu.au/~dld/Snob.html Snob page] for MML [[mixture model]]ling.
* [http://ai.ato.ms/MITECS/Entry/wallace MITECS]: [http://www.csse.monash.edu.au/~dld/CSWallacePublications/ Chris Wallace] wrote an entry on MML for MITECS. (Requires account)
* [http://www.cs.helsinki.fi/u/floreen/sem/mikko.ps mikko.ps]: Short introductory slides by Mikko Koivisto in Helsinki]
* [[Akaike information criterion]] ([[Akaike information criterion|AIC]]) method of [[model selection]], and a [http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#DoweGardnerOppy2007 comparison] with MML: [http://www.csse.monash.edu.au/~dld D.L. Dowe], S. Gardner & G. Oppy (2007), "[http://bjps.oxfordjournals.org/cgi/content/abstract/axm033v1 Bayes not Bust! Why Simplicity is no Problem for Bayesians]", [http://bjps.oxfordjournals.org Brit. J. Philos. Sci.], Vol. 58, Dec. 2007, pp709–754.
 
{{Statistics}}
{{Least Squares and Regression Analysis}}
 
[[Category:Algorithmic information theory]]

Latest revision as of 08:03, 19 December 2014

The procedure of house coffee roasting is decades aged. It has gone on for centuries when it was started by roasting green coffee beans over an open fire in pans. It eventually went to roasting over coals in cast iron skillets, or rotating iron drums over a fire. Up until about World War I, it was usual to roast coffee at house. In the 20th century, commercial roasting and grinding moved inside to the scene and it became less popular for individuals to roast their own coffee.

The green coffee weight loss extract method of losing weight is one perfect way to reduce those extra fats. You are able to ask why these beans are green. It's considering these beans have not been roasted. Why the usual coffee beans a great deal of folks are familiar with are dark in color is basically considering these beans have been roasted about 475 levels Fahrenheit. That process can in actual fact make the beans drop its fat-burning and anti-oxidant element which it usually possess. Evidently, the green coffee bean extract come in its most all-natural state and therefore could create folks lose fat naturally.

So what are these magic beans? Green coffee beans are merely regular beans which haven't been roasted. It's not the caffeine inside green coffee which assists we lose fat. No, the key to fat loss is an active compound called chloregnic acid found inside green coffee beans, which may inhibit the intake of glucose (sugar) into the bloodstream, whilst simultaneously boosting the launch of stored fat to be burned for power ( thereby marketing fat reduction because sugar consumption is regarded as the key factors you get fat). Don't expect to get rid of weight from a morning Starbucks latte though.

Chlorogenic acid has additional blessings. Not only usually it assist to remove inches from a waistline, it usually also boost cholesterol, blood lipids, and insulin sensitivity. On top of these good health advantages are also immune program advantages. Chlorogenic acid is an antioxidant. It fights free radical damage, helping to boost immune function and supporting advantageous wellness.

To create this powerful extract, the green seeds are soaked in water plus then concentrated. Green coffee beans have a healthy chemical which roasted beans never have: Chlorogenic Acid. Chlorogenic Acid works by lowering blood glucose degrees. Sugar turns to fat in the body, plus the bean extract could attack glucose before it gets that far.

When the desired roasting point is reached, be sure to dump the beans inside to a cool bowl for cooling down. This is significant thus which the heat will be removed plus the roasting stopped to have a more consistent roast. Stir the house coffee roasted beans usually throughout the initial cool down period. Let them cool for at least 24 hours. Many people think which the complete flavor change takes which lengthy. Grind the coffee plus brew in the favorite brewer and enjoy the freshest cup of coffee that can be made.

Omega-3 has become increasingly popular for helping with conditions ranging from anxiety to aging. Studies show which this healthy essential fatty acid (EFA) can even enable with arthritis, acne plus depression. Many of you don't eat enough fish to get our daily dosage, thus try a supplement like Nordic Naturals Omega-3 Formula. Look for a supplement with a minimal of 600 mg of DHA.

But, a lifestyle that includes regular exercise, right nutrition, and possibly even a good fat reduction product, will probably result in healthy, permanent weight reduction, whether or not YOUR results are not typical.