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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularization (machine Learning)
In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, following delineation is particularly helpful: * Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. * Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularization is essentially ubiquitous in modern machine learning appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called '' simple linear regression''; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Nikolayevich Tikhonov
Andrey Nikolayevich Tikhonov (russian: Андре́й Никола́евич Ти́хонов; October 17, 1906 – October 7, 1993) was a leading Soviet Russian mathematician and geophysicist known for important contributions to topology, functional analysis, mathematical physics, and ill-posed problems. He was also one of the inventors of the magnetotellurics method in geophysics. Other transliterations of his surname include "Tychonoff", "Tychonov", "Tihonov", "Tichonov." Biography Born in Gzhatsk, he studied at the Moscow State University where he received a Ph.D. in 1927 under the direction of Pavel Sergeevich Alexandrov. In 1933 he was appointed as a professor at Moscow State University. He became a corresponding member of the USSR Academy of Sciences on 29 January 1939 and a full member of the USSR Academy of Sciences on 1 July 1966. Research work Tikhonov worked in a number of different fields in mathematics. He made important contributions to topology, functiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity Analysis
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem. The process of recalculating outcomes under alternative assumptions to determine the impact of a variable under sensitivity analysis can be useful for a range of purposes, including: * Testing the robustness of the results of a model or system in the presence of uncertainty. * Increased understanding of the relationships between input and output variables in a system or model. * Uncertainty reduction, through the identification of model input that cause significant uncertainty in the output and should therefore be the focus of attention in order to increase robustness (perhap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leave One Out Error
For mathematical analysis and statistics, Leave-one-out error can refer to the following: * Leave-one-out cross-validation Stability (CVloo, for ''stability of Cross Validation with leave one out''): An algorithm f has CVloo stability β with respect to the loss function V if the following holds: \forall i\in\, \mathbb_S\\geq1-\delta_ * Expected-to-leave-one-out error Stability (Eloo_, for ''Expected error from leaving one out''): An algorithm f has Eloo_ stability if for each n there exists a\beta_^m and a \delta_^m such that: \forall i\in\, \mathbb_S\\geq1-\delta_^m, with \beta_^mand \delta_^m going to zero for n\rightarrow\inf Preliminary notations With X and Y being a subset of the real numbers R, or X and Y ⊂ R, being respectively an input space X and an output space Y, we consider a training set: S = \ of size m in Z = X \times Y drawn independently and identically distributed (i.i.d.) from an unknown distribution, here called "D". Then a learning algorithm is a functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
VC Theory
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Vapnik
Vladimir Naumovich Vapnik (russian: Владимир Наумович Вапник; born 6 December 1936) is one of the main developers of the Vapnik–Chervonenkis theory of statistical learning, and the co-inventor of the support-vector machine method, and support-vector clustering algorithm. Early life and education Vladimir Vapnik was born to a Jewish family in the Soviet Union. He received his master's degree in mathematics from the Uzbek State University, Samarkand, Uzbek SSR in 1958 and Ph.D in statistics at the Institute of Control Sciences, Moscow in 1964. He worked at this institute from 1961 to 1990 and became Head of the Computer Science Research Department. Academic career At the end of 1990, Vladimir Vapnik moved to the USA and joined the Adaptive Systems Research Department at AT&T Bell Labs in Holmdel, New Jersey. While at AT&T, Vapnik and his colleagues did work on the support-vector machine, which he also worked on much earlier before moving to the USA. They de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
