Results 1  10
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131
Generalized Additive Models
, 1990
"... Liklihood based regression models, such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariate effects. We introduce the Local Scotinq procedure which replaces the liner form C Xjpj by a sum of smooth functions C Sj(Xj)a ..."
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Cited by 1314 (33 self)
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Liklihood based regression models, such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariate effects. We introduce the Local Scotinq procedure which replaces the liner form C Xjpj by a sum of smooth functions C Sj(Xj)a The Sj(.) ‘s are unspecified functions that are estimated using scatterplot smoothers. The technique is applicable to any likelihoodbased regression model: the class of Generalized Linear Models contains many of these. In this class, the Locul Scoring procedure replaces the linear predictor VI = C Xj@j by the additive predictor C ai ( hence, the name Generalized Additive Modeb. Local Scoring can also be applied to nonstandard models like Cox’s proportional hazards model for survival data. In a number of real data examples, the Local Scoring procedure proves to be useful in uncovering nonlinear covariate effects. It has the advantage of being completely automatic, i.e. no “detective work ” is needed on the part of the statistician. In a further generalization, the technique is modified to estimate the form of the link function for generalized linear models. The Local Scoring procedure is shown to be asymptotically equivalent to Local Likelihood estimation, another technique for estimating smooth covariate functions. They are seen to produce very similar results with real data, with Local Scoring being considerably faster. As a theoretical underpinning, we view Local Scoring and Local Likelihood as empirical maximizers of the ezpected loglikelihood, and this makes clear their connection to standard maximum likelihood estimation. A method for estimating the “degrees of freedom ” of the procedures is also given.
Fisher Discriminant Analysis With Kernels
, 1999
"... A nonlinear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) nonlinear decision functi ..."
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Cited by 312 (15 self)
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A nonlinear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) nonlinear decision function in input space. Large scale simulations demonstrate the competitiveness of our approach.
Unsupervised learning of finite mixture models
 IEEE Transactions on pattern analysis and machine intelligence
, 2002
"... AbstractÐThis paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectationmaximization ..."
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Cited by 267 (20 self)
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AbstractÐThis paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectationmaximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach. Index TermsÐFinite mixtures, unsupervised learning, model selection, minimum message length criterion, Bayesian methods, expectationmaximization algorithm, clustering. æ 1
ModelBased Clustering, Discriminant Analysis, and Density Estimation
 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 ..."
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Cited by 260 (24 self)
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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 systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as \How many clusters are there?", "Which clustering method should be used?" and \How should outliers be handled?". We outline a general methodology for modelbased 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 recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology, a...
A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirtythree Old and New Classification Algorithms
, 2000
"... . Twentytwo decision tree, nine statistical, and two neural network algorithms are compared on thirtytwo datasets in terms of classication accuracy, training time, and (in the case of trees) number of leaves. Classication accuracy is measured by mean error rate and mean rank of error rate. Both cr ..."
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Cited by 167 (7 self)
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. Twentytwo decision tree, nine statistical, and two neural network algorithms are compared on thirtytwo datasets in terms of classication accuracy, training time, and (in the case of trees) number of leaves. Classication accuracy is measured by mean error rate and mean rank of error rate. Both criteria place a statistical, splinebased, algorithm called Polyclass at the top, although it is not statistically signicantly dierent from twenty other algorithms. Another statistical algorithm, logistic regression, is second with respect to the two accuracy criteria. The most accurate decision tree algorithm is Quest with linear splits, which ranks fourth and fth, respectively. Although splinebased statistical algorithms tend to have good accuracy, they also require relatively long training times. Polyclass, for example, is third last in terms of median training time. It often requires hours of training compared to seconds for other algorithms. The Quest and logistic regression algor...
Mapreduce for machine learning on multicore
 In Proceedings of NIPS
, 2007
"... We are at the beginning of the multicore era. Computers will have increasingly many cores (processors), but there is still no good programming framework for these architectures, and thus no simple and unified way for machine learning to take advantage of the potential speed up. In this paper, we dev ..."
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Cited by 138 (7 self)
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We are at the beginning of the multicore era. Computers will have increasingly many cores (processors), but there is still no good programming framework for these architectures, and thus no simple and unified way for machine learning to take advantage of the potential speed up. In this paper, we develop a broadly applicable parallel programming method, one that is easily applied to many different learning algorithms. Our work is in distinct contrast to the tradition in machine learning of designing (often ingenious) ways to speed up a single algorithm at a time. Specifically, we show that algorithms that fit the Statistical Query model [15] can be written in a certain “summation form, ” which allows them to be easily parallelized on multicore computers. We adapt Google’s mapreduce [7] paradigm to demonstrate this parallel speed up technique on a variety of learning algorithms including locally weighted linear regression (LWLR), kmeans, logistic regression
Penalized Discriminant Analysis
 Annals of Statistics
, 1995
"... Fisher's linear discriminant analysis (LDA) is a popular dataanalytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predictors, ..."
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Cited by 131 (9 self)
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Fisher's linear discriminant analysis (LDA) is a popular dataanalytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predictors, such as those obtained by discretizing a function, or the greyscale values of the pixels in a series of images. In cases such as these it is natural, efficient, and sometimes essential to impose a spatial smoothness constraint on the coefficients, both for improved prediction performance and interpretability. We cast the classification problem into a regression framework via optimal scoring. Using this, our proposal facilitates the use of any penalized regression technique in the classification setting. The technique is illustrated with examples in speech recognition and handwritten character recognition. AMS 1991 Classifications: Primary 62H30, Secondary 62G07 1 Introduction Linear discrim...
Graphical models and automatic speech recognition
 Mathematical Foundations of Speech and Language Processing
, 2003
"... Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recog ..."
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Cited by 67 (13 self)
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Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recognition techniques commonly used as part of a speech recognition system can be described by a graph – this includes Gaussian distributions, mixture models, decision trees, factor analysis, principle component analysis, linear discriminant analysis, and hidden Markov models. Moreover, this paper shows that many advanced models for speech recognition and language processing can also be simply described by a graph, including many at the acoustic, pronunciation, and languagemodeling levels. A number of speech recognition techniques born directly out of the graphicalmodels paradigm are also surveyed. Additionally, this paper includes a novel graphical analysis regarding why derivative (or delta) features improve hidden Markov modelbased speech recognition by improving structural discriminability. It also includes an example where a graph can be used to represent language model smoothing constraints. As will be seen, the space of models describable by a graph is quite large. A thorough exploration of this space should yield techniques that ultimately will supersede the hidden Markov model.
Multiclass Linear Dimension Reduction by Weighted Pairwise Fisher Criteria
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the wellknown Kclass Fisher criterion associated with linear discriminant analysis (LDA). It can be seen that LDA weights contributions of individual class pairs according to ..."
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Cited by 64 (4 self)
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We derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the wellknown Kclass Fisher criterion associated with linear discriminant analysis (LDA). It can be seen that LDA weights contributions of individual class pairs according to the Euclidian distance of the respective class means. We generalize upon LDA by introducing a different weighting function.
Learning from incomplete data
, 1994
"... Realworld learning tasks often involve highdimensional data sets with complex patterns of missing features. In this paper we review the problem of learning from incomplete data from two statistical perspectivesthe likelihoodbased and the Bayesian. The goal is twofold: to place current neura ..."
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Cited by 58 (0 self)
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Realworld learning tasks often involve highdimensional data sets with complex patterns of missing features. In this paper we review the problem of learning from incomplete data from two statistical perspectivesthe likelihoodbased and the Bayesian. The goal is twofold: to place current neural network approaches to missing data within a statistical framework, and to describe a set of algorithms, derived from the likelihoodbased framework, that handle clustering, classification, and function approximation from incomplete data in a principled and efficient manner. These algorithms are based on mixture modeling and maketwo distinct appeals to the ExpectationMaximization (EM) principle (Dempster et al., 1977)both for the estimation of mixture components and for coping with the missing data.