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The Nature of Statistical Learning Theory

by Vladimir N. Vapnik , 1999
"... Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the deve ..."
Abstract - Cited by 13236 (32 self) - Add to MetaCart
Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based

A gentle tutorial on the EM algorithm and its application to parameter estimation for gaussian mixture and hidden markov models

by Jeff A. Bilmes , 1997
"... We describe the maximum-likelihood parameter estimation problem and how the Expectation-form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) fi ..."
Abstract - Cited by 693 (4 self) - Add to MetaCart
We describe the maximum-likelihood parameter estimation problem and how the Expectation-form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2

Estimating the Support of a High-Dimensional Distribution

by Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson , 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
Abstract - Cited by 783 (29 self) - Add to MetaCart
propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length

Pegasos: Primal Estimated sub-gradient solver for SVM

by Shai Shalev-Shwartz, Yoram Singer, Nathan Srebro, Andrew Cotter
"... We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a singl ..."
Abstract - Cited by 542 (20 self) - Add to MetaCart
We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a

Model-Based Clustering, Discriminant Analysis, and Density Estimation

by Chris Fraley, Adrian E. Raftery - JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION , 2000
"... Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little ..."
Abstract - Cited by 573 (29 self) - Add to MetaCart
for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster

Bayesian density estimation and inference using mixtures.

by Michael D Escobar , Mike West - J. Amer. Statist. Assoc. , 1995
"... JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about J ..."
Abstract - Cited by 653 (18 self) - Add to MetaCart
mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including problems of local versus global smoothing, uncertainty about density estimates

Learning low-level vision

by William T. Freeman, Egon C. Pasztor - International Journal of Computer Vision , 2000
"... We show a learning-based method for low-level vision problems. We set-up a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently prop ..."
Abstract - Cited by 579 (30 self) - Add to MetaCart
propagate image information. Monte Carlo simulations justify this approximation. We apply this to the \super-resolution " problem (estimating high frequency details from a low-resolution image), showing good results. For the motion estimation problem, we show resolution of the aperture problem

Convex Position Estimation in Wireless Sensor Networks

by Lance Doherty , Kristofer S. J. Pister , Laurent El Ghaoui
"... A method for estimating unknown node positions in a sensor network based exclusively on connectivity-induced constraints is described. Known peer-to-peer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem fo ..."
Abstract - Cited by 493 (0 self) - Add to MetaCart
A method for estimating unknown node positions in a sensor network based exclusively on connectivity-induced constraints is described. Known peer-to-peer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem

A new approach to the maximum flow problem

by Andrew V. Goldberg, Robert E. Tarjan - JOURNAL OF THE ACM , 1988
"... All previously known efficient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
Abstract - Cited by 672 (33 self) - Add to MetaCart
on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated

Estimating the number of clusters in a dataset via the Gap statistic

by Robert Tibshirani, Guenther Walther, Trevor Hastie , 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. k-means or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
Abstract - Cited by 502 (1 self) - Add to MetaCart
null distribution. Some theory is developed for the proposal and a simulation study that shows that the Gap statistic usually outperforms other methods that have been proposed in the literature. We also briey explore application of the same technique to the problem for estimating the number of linear
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