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Computational Learning Theory
In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms. Overview Theoretical results in machine learning mainly deal with a type of inductive learning called supervised learning. In supervised learning, an algorithm is given samples that are labeled in some useful way. For example, the samples might be descriptions of mushrooms, and the labels could be whether or not the mushrooms are edible. The algorithm takes these previously labeled samples and uses them to induce a classifier. This classifier is a function that assigns labels to samples, including samples that have not been seen previously by the algorithm. The goal of the supervised learning algorithm is to optimize some measure of performance such as minimizing the number of mistakes made on new samples. In addition to performance bounds, computational learning theory studies the t ...
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ...
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Alexey Chervonenkis
Alexey Yakovlevich Chervonenkis (russian: link=no, Алексей Яковлевич Червоненкис; 7 September 1938 – 22 September 2014) was a Soviet and Russian mathematician. Along with Vladimir Vapnik, he was one of the main developers of the Vapnik–Chervonenkis theory, also known as the "fundamental theory of learning" - an important part of computational learning theory. Chervonenkis held joint appointments with the Russian Academy of Sciences and Royal Holloway, University of London. Alexey Chervonenkis got lost in Losiny Ostrov National Park on 22 September 2014, and later during a search operation was found dead near Mytishchi, a suburb of Moscow. He had died of hypothermia Hypothermia is defined as a body core temperature below in humans. Symptoms depend on the temperature. In mild hypothermia, there is shivering and mental confusion. In moderate hypothermia, shivering stops and confusion increases. In severe h .... References External linksChervone ...
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Dana Ron
Dana Ron Goldreich ( he, דנה רון גולדרייך; b. 1964) is a computer scientist, a professor of electrical engineering at the Tel Aviv University, Israel. Prof. Ron is one of the pioneers of research in property testing, and a leading researcher in that area. Professional career Dana Ron obtained her B.A. (1987) and M.A. (1989) in computer science from the Hebrew University in Jerusalem. Her Ph.D. (1995), also from the Hebrew University, was in the area of machine learning. Between the years 1995-97 she was an NSF post-doctoral fellow at the Massachusetts Institute of Technology (MIT). She was a Bunting fellow in 1997/8, and the Radcliffe fellow at Harvard University in 2003/4. Her research interests include sublinear-time algorithms (in particular property testing), randomized algorithms, and computational learning theory. She is married to Oded Goldreich, who is also a computer scientist at the Weizmann Institute, and has collaborated with Goldreich on approximation ...
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Oded Goldreich
Oded Goldreich ( he, עודד גולדרייך; b. 1957) is a professor of Computer Science at the Faculty of Mathematics and Computer Science of Weizmann Institute of Science, Israel. His research interests lie within the theory of computation and are, specifically, the interplay of randomness and computation, the foundations of cryptography, and computational complexity theory. He won the Knuth Prize in 2017 and was selected in 2021 to receive the Israel Prize in mathematics. Biography Goldreich received a DSc in Computer Science at Technion in 1983 under Shimon Even. Goldreich has contributed to the development of pseudorandomness, zero knowledge proofs, secure function evaluation, property testing,Oded Goldreich, Shafi Goldwasser, and Dana Ron. 1998 Property Testing and its connection to Learning and Approximation. ''Journal of the ACM'', pages 653-750. and other areas in cryptography and computational complexity. Goldreich has also authored several books including: ''Fou ...
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VC Dimension
VC may refer to: Military decorations * Victoria Cross, a military decoration awarded by the United Kingdom and also by certain Commonwealth nations ** Victoria Cross for Australia ** Victoria Cross (Canada) ** Victoria Cross for New Zealand * Victorious Cross, Idi Amin's self-bestowed military decoration Organisations * Ocean Airlines (IATA airline designator 2003-2008), Italian cargo airline * Voyageur Airways (IATA airline designator since 1968), Canadian charter airline * Visual Communications, an Asian-Pacific-American media arts organization in Los Angeles, US * Viet Cong (also Victor Charlie or Vietnamese Communists), a political and military organization from the Vietnam War (1959–1975) Education * Vanier College, Canada * Vassar College, US * Velez College, Philippines * Virginia College, US Places * Saint Vincent and the Grenadines (ISO country code), a state in the Caribbean * Sri Lanka (ICAO airport prefix code) * Watsonian vice-counties, subdivisions of Great Brita ...
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Error Tolerance (PAC Learning)
Error tolerance (PAC learning) In PAC learning, error tolerance refers to the ability of an algorithm to learn when the examples received have been corrupted in some way. In fact, this is a very common and important issue since in many applications it is not possible to access noise-free data. Noise can interfere with the learning process at different levels: the algorithm may receive data that have been occasionally mislabeled, or the inputs may have some false information, or the classification of the examples may have been maliciously adulterated. Notation and the Valiant learning model In the following, let X be our n-dimensional input space. Let \mathcal be a class of functions that we wish to use in order to learn a \-valued target function f defined over X. Let \mathcal be the distribution of the inputs over X. The goal of a learning algorithm \mathcal is to choose the best function h \in \mathcal such that it minimizes error(h) = P_( h(x) \neq f(x)). Let us suppose we hav ...
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Stability (learning Theory)
Stability, also known as algorithmic stability, is a notion in computational learning theory of how a machine learning, machine learning algorithm is perturbed by small changes to its inputs. A stable learning algorithm is one for which the prediction does not change much when the training data is modified slightly. For instance, consider a machine learning algorithm that is being trained to Handwriting recognition, recognize handwritten letters of the alphabet, using 1000 examples of handwritten letters and their labels ("A" to "Z") as a training set. One way to modify this training set is to leave out an example, so that only 999 examples of handwritten letters and their labels are available. A stable learning algorithm would produce a similar statistical classification, classifier with both the 1000-element and 999-element training sets. Stability can be studied for many types of learning problems, from Natural language processing, language learning to inverse problems in physic ...
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Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ...
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Grammar Induction
Grammar induction (or grammatical inference) is the process in machine learning of learning a formal grammar (usually as a collection of ''re-write rules'' or '' productions'' or alternatively as a finite state machine or automaton of some kind) from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs. Grammar classes Grammatical inference has often been very focused on the problem of learning finite state machines of various types (see the article Induction of regular languages for details on these approaches), since there have been efficient algorithms for this problem since the 1980s. Since the beginning of the century, these approaches have been extended to the problem of inference of context-free grammars and richer formalisms, such as multipl ...
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Belief Networks
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Bayesian networks that model sequences of variables (''e.g.'' speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. Graphical model ...
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Support Vector Machine
In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laboratories by Vladimir Vapnik with colleagues (Boser et al., 1992, Guyon et al., 1993, Cortes and Vapnik, 1995, Vapnik et al., 1997) SVMs are one of the most robust prediction methods, being based on statistical learning frameworks or VC theory proposed by Vapnik (1982, 1995) and Chervonenkis (1974). Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non- probabilistic binary linear classifier (although methods such as Platt scaling exist to use SVM in a probabilistic classification setting). SVM maps training examples to points in space so as to maximise the width of the gap between the two categories. New ...
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Boosting (meta-algorithm)
In machine learning, boosting is an ensemble meta-algorithm for primarily reducing bias, and also variance in supervised learning, and a family of machine learning algorithms that convert weak learners to strong ones. Boosting is based on the question posed by Kearns and Valiant (1988, 1989):Michael Kearns(1988)''Thoughts on Hypothesis Boosting'' Unpublished manuscript (Machine Learning class project, December 1988) "Can a set of weak learners create a single strong learner?" A weak learner is defined to be a classifier that is only slightly correlated with the true classification (it can label examples better than random guessing). In contrast, a strong learner is a classifier that is arbitrarily well-correlated with the true classification. Robert Schapire's affirmative answer in a 1990 paper to the question of Kearns and Valiant has had significant ramifications in machine learning and statistics, most notably leading to the development of boosting. When first introduced, ...
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