
	Where results make sense

Topic: Vapnik Chervonenkis theory

Related Topics

VC theory

Computational learning theory

Vladimir Vapnik

Support vector machine

VC dimension

Reinforcement learning

Pattern recognition

Codimension

Data clustering

Quadratic programming

Reproducing kernel Hilbert space

Data compression

Vector space

Affine transformation

Optimization

In the News (Tue 1 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Vapnik Chervonenkis theory at AllExperts
		Vapnik Chervonenkis theory (also known as VC theory) was developed during 1960-1990 by Vladimir Vapnik and Alexey Chervonenkis.
		The theory is a form of computational learning theory, which attempts to explain the learning process from a statistical point of view.
		VC theory is also referred to as statistical learning theory by Vapnik and his close colleagues.
	en.allexperts.com /e/v/va/vapnik_chervonenkis_theory.htm (281 words)

	Vapnik Chervonenkis theory - Wikipedia, the free encyclopedia
		Vapnik Chervonenkis theory (also known as VC theory) was developed during 1960-1990 by Vladimir Vapnik and Alexey Chervonenkis.
		The theory is a form of computational learning theory, which attempts to explain the learning process from a statistical point of view.
		VC theory is also referred to as statistical learning theory by Vapnik and his close colleagues.
	en.wikipedia.org /wiki/Vapnik_Chervonenkis_theory (244 words)

	Vapnik, The Nature of Statistical Learning Theory
		Vapnik is one of the Big Names in machine learning and statistical inference; this is his statement of ``what is important,'' how to do it, and who figured out how to do it.
		Vapnik assumes that we have access to a sequence of independent random variables, all drawn from the (stationary) true distribution.
		Vapnik's view of the history of the field is considerably more idiosyncratic than most of his opinions: in epitome, it is that everything important was done by himself and Chervonenkis in the late 1960s and early 1970s, and that everyone else, American computer scientists especially, are a bunch of wankers.
	cscs.umich.edu /~crshalizi/reviews/vapnik-nature (857 words)

	Support Vector Machines - The Book
		Support Vector Machines are a very specific class of algorithms, characterised by the use of kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by acting on the margin, or on other `dimension independent' quantities such as the number of support vectors.
		Cortes and Vapnik, and in 1995 the algorithm was extended to the regression case.
		Since most recent advances in kernels, learning theory, and implementation are discussed at the ends of the relevant chapters, we only give a brief overview of some of the improvements recently obtained from the point of view of the overall algorithm.
	www.support-vector.net /chapter_6.html (912 words)

	Support Vector Machines - The Book
		VC theory has since been used to analyse the performance of learning systems as diverse as decision trees, neural networks, and others; many learning heuristics and principles used in practical applications of machine learning have been explained in terms of VC theory.
		VC theory has recently also come to be known as Statistical Learning Theory, and is extensively described in the recent book of Vapnik, and in other books that preceded it, as well as earlier papers by Vapnik and Chervonenkis.
		Vapnik and Chervonenkis obtained bounds for the case when the margin is measured on the combined training and test sets using a quantity analogous to the fat-shattering dimension.
	www.support-vector.net /chapter_4.html (1020 words)

	Vladimir Vapnik - Wikipedia, the free encyclopedia
		Vladimir Naumovich Vapnik is one of the main developers of Vapnik Chervonenkis theory.
		He was born in the Soviet Union; received a master's degree in mathematics from the Uzbek State University in Samarkand (now Uzbekistan), in 1958; and received a Ph.D in statistics from the Institute of Control Science in Moscow in 1964.
		In 2006, Vapnik was inducted into the U.S. National Academy of Engineering.
	en.wikipedia.org /wiki/Vladimir_Vapnik (249 words)

	VC dimension
		The VC dimension (for Vapnik Chervonenkis dimension) is a measure of the capacity of a classification algorithm.
		It is one of the core concepts in Vapnik Chervonenkis theory.
		The VC dimension has utility in statistical learning theory, because it can predict a probabilistic upper bound on the test error of a classification model.
	www.xasa.com /wiki/en/wikipedia/v/vc/vc_dimension.html (364 words)

	Shattered Sets: Origin of Term "Shattered" in Vapnik Chervonenkis Theory, (VC Dimension)
		One notion that has become widely used in the theory of Vapnik-Chervonenkis dimension is that of a shattered set.
		The relevance of this concept to uniform laws of large numbers is due to Vapnik and Chervonenkis.
		This theory has been rolling along for almost thirty years now, and it may be useful to do a survey that attends to the mathematics --- not just etymological curiosities.
	www-stat.wharton.upenn.edu /~steele/Rants/ShatteredSets.html (637 words)

	Vapnik Chervonenkis theory
		Vapnik Chervonenkis theory is one of the topics in focus at Global Oneness.
		VC theory covers four parts (as explained in The Nature of Statistical Learning Theory): Theory of consistency of learning process...
		The use of the maximum-margin hyperplane is motivated by Vapnik Chervonenkis theory, which provides a probabilistic test error bound that is minimized when...
	www.experiencefestival.com /vapnik_chervonenkis_theory (653 words)

	Computational learning theory - Definition, explanation
		In statistics, computational learning theory is a mathematical field related to the analysis of machine learning algorithms.
		Because the training set is finite and the future is uncertain, learning theory usually does not yield absolute guarantees of performance of the algorithms.
		For example, PAC theory inspired boosting, VC theory led to support vector machines, and Bayesian inference led to belief networks (by Judea Pearl).
	www.calsky.com /lexikon/en/txt/c/co/computational_learning_theory.php (502 words)

	Vladimir Vapnik
		Vladimir Naumovich Vapnik is one of the main developers of Vapnik Chervonenkis theory.
		He was born in Soviet Union; received a master's degree in mathematics from the Uzbek State University in Samarkand (now Uzbekistan), in 1958; and received a Ph.D in statistics from the Institute of Control Science in Moscow in 1964.
		At AT&T; Bell Labs (later Shannon Labs) from 1991 through 2001?, Vapnik and his colleagues developed the theory of the support vector machine.
	www.wikimoz.org /wiki/en/wikipedia/v/vl/vladimir_vapnik.html (149 words)

	Citations: Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension - Blumer, Ehrenfeucht, ... (Site not responding. Last check: 2007-10-17)
		Occam s Razor is a principle in the philosophy of science which stipulates that a shorter theory is to be preferred as long as it remains adequate.
		The Vapnik Chervonenkis dimension of C, in short VC Dim(C) is the cardinality of the greatest set s X shattered by C. That means, the Vapnik Chervonenkis dimension is given by VC Gamma Dim(C) max s2fsjs Xfs cjc2Cg=2 s....
		The Vapnik Chervonenkis dimension VC (is the supremum (possibly infinite) of the set of integers k for which there is some set S of cardinality k that can be shattered by.
	citeseer.ist.psu.edu /context/34170/0 (3039 words)

	Histogram regression estimation using data-dependent partitions, Andrew Nobel
		In addition, it is shown that empirically optimal regression trees are consistent when the size of the trees grows with the number of samples at an appropriate rate.
		VAPNIK, V. and CHERVONENKIS, A. On the uniform convergence of relative frequencies of events to their probabilities.
		VAPNIK, V. and CHERVONENKIS, A. Necessary and sufficient conditions for the uniform convergence of means to their expectations.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1032526958 (516 words)

	CITIDEL: Viewing 'Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension' (Site not responding. Last check: 2007-10-17)
		Valiant, L.G., "A theory of the learnable," Comm.
		Vapnik, V.N. and A.Ya.Chervonenkis, "On the uniform convergence of relative frequencies of events to their probabilities," Th.
		Vapnik, V.N. and A.Ya.Chervonenkis, Theory of Pattern Recognition (in Russian), Nauka, Moscow, 1974.
	www.citidel.org /?op=getobj&identifier=oai:ACMDL:articles.12158 (406 words)

	Tutorials at NIPS 1997
		Vladimir Vapnik, currently Member of Technical Staff, AT&T Labs-Research, is one of the creators of the theory of learning and generalization, the so-called VC theory (abbreviation for the Vapnik-Chervonenkis theory).
		This theory is a cornerstone for developing principles of inference from small sample sizes which can control the generalization ability of learning machines.
		Vladimir Vapnik is the author of 7 monographs and more than 100 articles devoted to various problems of statistics and problems of learning and generalization.
	www.cs.cmu.edu /Groups/NIPS/1997/Tutorials.html (1631 words)

	Glossary: TCM Glossary \| Toomre Capital Markets LLC
		Much of the work in COLT can be traced to Leslie Valiant's seminal paper on "A theory of the learnable" (1984) as well as E.M. Gold's "Language identification in the limit" (1967).
		Statistical Learning Theory (also known as VC theory after Vapnik Chervonenkis) is a subset of the research field Computational Learning Theory which attempts to explain the learning process from a statistical point of view.
		The main goal of statistical learning theory is to provide a framework for studying the problem of inference, that is of gaining knowledge, making predictions, making decisions or constructing models from a set of data.
	www.toomre.com /glossary/1 (2870 words)

	MIT OpenCourseWare \| Mathematics \| 18.465 Topics in Statistics: Statistical Learning Theory, Spring 2004 \| Home (Site not responding. Last check: 2007-10-17)
		The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks.
		Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.
		Your use of the MIT OpenCourseWare site and course materials is subject to the conditions and terms of use in our Legal Notices section.
	ocw.mit.edu /OcwWeb/Mathematics/18-465Spring-2004/CourseHome/index.htm (110 words)

	A model approach to society (May 2003) - Physics World - PhysicsWeb
		My views on the "absolute truth" of theories and our ability to make accurate predictions are best illustrated by some work in probability theory that was carried out by Vladimir Vapnik and Alexey Chervonenkis in 1968.
		Our existing knowledge is "measured" by the volume of the inner regions, while their surface area is a measure of "what we know we don't know".
		Maxwell's theory of electromagnetism, for example, united the previously disjointed phenomena of electricity and magnetism.
	www.physicsweb.org /articles/world/16/5/2/1 (1493 words)

	Imaging On-Line Store
		The theory of pattern recognition is concerned with estimating the errors of optimal classifiers and with designing classifiers from sample data whose errors are close to minimal.
		Of special importance is the Vapnik- Chervonenkis theory, which relates the design cost to the VC dimension of a classification rule.
		As to the question posed in the title, the paper argues that nonlinear filtering possesses its own integrity because classification rules and constraints depend on signal and image properties, both in theory and the manner in which expert knowledge is applied in design.
	www.imaging.org /store/epub.cfm?abstrid=27277 (164 words)

	Machine Learning at UCSC: Current Research
		Here $d$ is a dimension that is defined from the scaling of small volumes with respect to a suitable distance in the space of rules.
		The advantage of our theory over the well-established Vapnik-Chervonenkis theory is that our bounds can be considerably tighter in many cases, and are more reflectve of the true behavior (functional form) of learning curves.
		The disadvantages of our theory are that its application requires knowledge of the input distribution, and it is limited so far to finite cardinality function classes.
	www.cse.ucsc.edu /research/ml/research.html (2172 words)

	625.775 Data Mining \| Course Description \| Johns Hopkins University \| Engineering and Applied Science Programs For ...
		With the advent of large data warehouses, organizations have access to huge quantities of potentially valuable data that they would like to mine in order to produce business intelligence.
		This course provides an advanced introduction to the theory and practice of data mining.
		Prerequisites: Multivariate calculus, familiarity with linear algebra and matrix theory (e.g., 625.409) and a course in statistics (such as 625.403).
	www.epp.jhu.edu /courses/625/775 (205 words)

	A Probabilistic Theory of Pattern Recognition (Stochastic Modelling and Applied Probability) by Luc Devroye , Laszlo ...
		Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed.
		The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches.
		The book includes a discussion of distance measures, nonparametric methods based on kernels or nearest neighbors, Vapnik-Chervonenkis theory, epsilon entropy, parametric classification, error estimation, free classifiers, and neural networks.
	www.notpricyatall.com /A-Probabilistic-Theory-of-Pattern-Recognition-Stochastic-Modelling-and-Applied-Probability-0_0387946187_1 (122 words)

	CENTRE FOR MATHEMATICAL PHYSICS & STOCHASTICS
		It is intended to bring together specialists from different areas such as probability theory, stochastic processes, statistics, physics, finance and analysis, and to discuss pathwise, stochastic and product integration techniques.
		Our presentation will be also guided by showing up some aspects of the development of empirical process theory from its classical origin up to the present which offers now a wide variety of applications in statistics as demonstrated e.g.
		This concept has served very well in the theory of law convergence of empirical processes when the underlying topological space is metrizable or at least has sufficiently many continuous functions.
	www.imstat.org /BULLETIN/IMSBulletinNov_Dec_1998/node24.html (1246 words)

	Shattering
		The concept of 'shattering' of a set of points plays an important role in Vapnik Chervonenkis theory, also known as VC-theory.
		The set $A$ is often assumed to be finite, because, in empirical processes, we are interested in the shattering of finite sets of data points.
		In probability theory, the 'cumulative distribution function (cdf)', often called simply the 'distribution function', is of great importance, and is defined as
	wiki-shorts.freestat.pl /51-4381-Shattering.html (510 words)

	Data Mining (Fitton, Close) Course Homepage \| Johns Hopkins University \| Engineering and Applied Science Programs For ...
		Multivariate calculus, familiarity with linear algebra and matrix theory (e.g., 625.409) and a course in statistics (such as 625.403).
		This course is an advanced introduction to the theory and practice of data mining.
		Students will learn a process model for data mining from problem definition through data preparation, model development, deployment and results measurement, and be able to put this process model into practice on real datasets using freely available software.
	www.epp.jhu.edu /course-homepages/viewpage.php?homepage_id=2791 (966 words)

	Alexey Chervonenkis . Russia . Vapnik Chervonenkis theory
		mathematician, and one of the main developers of the Vapnik Chervonenkis theory, an important part of computational learning theory.
		Russia The vast lands of present-day Russia were home to ununited tribes who were variously overwhelmed by invading Goths, Huns, and Turkic Avars between the third and sixth centuries A.D. The Iranian Scythians populated the southern steppes, and a Turkic people, the Khazars, ruled the western portion of these lands through the eighth...
		VC theory covers four parts as explained in The Nature of Statistical Learning Theory : Theory of consistency of learning processes What...
	www.uk.kunsimuna.net /Alexey_Chervonenkis_UK_317133_tb (252 words)

	COLT: 2000 Program
		Our bounds give formal verification to the well-known intuition that TD methods are subject to a bias-variance trade-off, and they lead to schedules for k and lambda that are predicted to be better than any fixed values for these parameters.
		We show that under the same weak learning assumption used for decision tree learning there exists a greedy BP-growth algorithm whose training error is guaranteed to decline as $2^{-\beta\sqrt{T}}$, where $T$ is the size of the branching program and $\beta$ is a constant determined by the weak learning hypothesis.
		Then we prove that the particularization of our notion to specific known protocols such as equivalence, membership, and membership and equivalence queries results in exactly the same combinatorial notions currently known to characterize learning in these models, such as strong consistency dimension, extended teaching dimension, and certificate size.
	www.learningtheory.org /colt2000/schedule-abs.html (5801 words)

	The Book Pl@ce: Title Detail (Site not responding. Last check: 2007-10-17)
		Emphasizing issues of computational efficiency, this text introduces a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics.
		Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning.
		Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting.
	www.bookends.co.uk /bookplace/display.asp?K=180624200990200&aub=Umesh&m=8&dc=12 (178 words)

Try your search on: Qwika (all wikis)