Lebanon, Guy
Overview
Works:  7 works in 9 publications in 1 language and 12 library holdings 

Genres:  Textbooks 
Roles:  Author 
Publication Timeline
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Most widely held works by
Guy Lebanon
Riemannian geometry and statistical machine learning by Guy Lebanon(
Book
)
2 editions published between 2005 and 2015 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Statistical machine learning algorithms deal with the problem of selecting an appropriate statistical model from a model space [theta] based on a training set [x[subscript i]]n/i=1 [subset] X or [(x[subscript i], y[subscript i])]n/i=1 [subset] X x Y. In doing so they either implicitly or explicitly make assumptions on the geometries of the model space [theta] and the data space X. Such assumptions are crucial to the success of the algorithms as different geometries are appropriate for different models and data spaces. By studying these assumptions we are able to develop new theoretical results that enhance our understanding of several popular learning algorithms. Furthermore, using geometrical reasoning we are able to adapt existing algorithms such as radial basis kernels and linear margin classifiers to nonEuclidean geometries. Such adaptation is shown to be useful when the data space does not exhibit Euclidean geometry. In particular, we focus in our experiments on the space of text documents that is naturally associated with the Fisher information metric on corresponding multinomial models."
2 editions published between 2005 and 2015 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Statistical machine learning algorithms deal with the problem of selecting an appropriate statistical model from a model space [theta] based on a training set [x[subscript i]]n/i=1 [subset] X or [(x[subscript i], y[subscript i])]n/i=1 [subset] X x Y. In doing so they either implicitly or explicitly make assumptions on the geometries of the model space [theta] and the data space X. Such assumptions are crucial to the success of the algorithms as different geometries are appropriate for different models and data spaces. By studying these assumptions we are able to develop new theoretical results that enhance our understanding of several popular learning algorithms. Furthermore, using geometrical reasoning we are able to adapt existing algorithms such as radial basis kernels and linear margin classifiers to nonEuclidean geometries. Such adaptation is shown to be useful when the data space does not exhibit Euclidean geometry. In particular, we focus in our experiments on the space of text documents that is naturally associated with the Fisher information metric on corresponding multinomial models."
Boosting and maximum likelihood for exponential models by Guy Lebanon(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Abstract: "Recent research has considered the relationship between boosting and more standard statistical methods, such as logistic regression, concluding that AdaBoost is similar but somehow still very different from statistical methods in that it minimizes a different loss function. In this paper we derive an equivalence between AdaBoost and the dual of a convex optimization problem. In this setting, it is seen that the only difference between minimizing the exponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normalized to form a conditional probability distribution over labels; the two methods minimize the same KullbackLeibler divergence objective function subject to identical feature constraints. In addition to establishing a simple and easily understood connection between the two methods, this framework enables us to derive new regularization procedures for boosting that directly correspond to penalized maximum likelihood. Experiments on UCI datasets, comparing exponential loss and maximum likelihood for parallel and sequential update algorithms, confirm our theoretical analysis, indicating that AdaBoost and maximum likelihood typically yield identical results as the number of features increases to allow the models to fit the training data."
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Abstract: "Recent research has considered the relationship between boosting and more standard statistical methods, such as logistic regression, concluding that AdaBoost is similar but somehow still very different from statistical methods in that it minimizes a different loss function. In this paper we derive an equivalence between AdaBoost and the dual of a convex optimization problem. In this setting, it is seen that the only difference between minimizing the exponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normalized to form a conditional probability distribution over labels; the two methods minimize the same KullbackLeibler divergence objective function subject to identical feature constraints. In addition to establishing a simple and easily understood connection between the two methods, this framework enables us to derive new regularization procedures for boosting that directly correspond to penalized maximum likelihood. Experiments on UCI datasets, comparing exponential loss and maximum likelihood for parallel and sequential update algorithms, confirm our theoretical analysis, indicating that AdaBoost and maximum likelihood typically yield identical results as the number of features increases to allow the models to fit the training data."
Moire pattern synthesis by Guy Lebanon(
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Probability : the analysis of data, volume 1 by Guy Lebanon(
Book
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
"This volume focuses on probability theory. There are many excellent textbooks on probability, and yet this book differs from others in several ways. Probability theory is a wide field. This book focuses on the parts of probability that are most relevant for statistics and machine learning. The book contains almost all of the mathematical prerequisites, including set theory, metric spaces, linear algebra, differentiation, integration, and measure theory. Almost all results in the book appear with a proof. Probability textbooks are typically either elementary or advanced. This book strikes a balance by attempting to avoid measure theory where possible, but resorting to measure theory and other advanced material in a few places where they are essential. The book uses R to illustrate concepts. Full code is available in the book, facilitating reproducibility of experiments and letting readers experiment with variations of the code. I am not aware of a single textbook that covers the material from probability theory that is necessary and sufficient for an indepth understanding of statistics and machine learning. This book represents my best effort in that direction. Since this book is part of a series of books on data analysis, it does not include any statistics or machine learning. Such content is postponed to future volumes."
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
"This volume focuses on probability theory. There are many excellent textbooks on probability, and yet this book differs from others in several ways. Probability theory is a wide field. This book focuses on the parts of probability that are most relevant for statistics and machine learning. The book contains almost all of the mathematical prerequisites, including set theory, metric spaces, linear algebra, differentiation, integration, and measure theory. Almost all results in the book appear with a proof. Probability textbooks are typically either elementary or advanced. This book strikes a balance by attempting to avoid measure theory where possible, but resorting to measure theory and other advanced material in a few places where they are essential. The book uses R to illustrate concepts. Full code is available in the book, facilitating reproducibility of experiments and letting readers experiment with variations of the code. I am not aware of a single textbook that covers the material from probability theory that is necessary and sufficient for an indepth understanding of statistics and machine learning. This book represents my best effort in that direction. Since this book is part of a series of books on data analysis, it does not include any statistics or machine learning. Such content is postponed to future volumes."
Computing the volume element of a family of metrics on the multinomial simplex by Guy Lebanon(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Abstract: "We compute the differential volume element of a family of metrics on the multinomial simplex. The metric family is composed of pullbacks of the Fisher information metric through a continuous group of transformations. This note complements the paper by Lebanon [3] that describes a metric learning framework and applies the results below to text classification."
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Abstract: "We compute the differential volume element of a family of metrics on the multinomial simplex. The metric family is composed of pullbacks of the Fisher information metric through a continuous group of transformations. This note complements the paper by Lebanon [3] that describes a metric learning framework and applies the results below to text classification."
Diffusion kernels on statistical manifolds by
John Lafferty(
Book
)
2 editions published in 2004 in English and held by 1 WorldCat member library worldwide
Abstract: "A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian kernel of Euclidean space. As an important special case, kernels based on the geometry of multinomial families are derived, leading to kernelbased learning algorithms that apply naturally to discrete data. Bounds on covering numbers and Rademacher averages for the kernels are proved using bounds on the eigenvalues of the Laplacian on Riemannian manifolds. Experimental results are presented for document classification, for which the use of multinomial geometry is natural and well motivated, and improvements are obtained over the standard use of Gaussian or linear kernels, which have been the standard for text classification."
2 editions published in 2004 in English and held by 1 WorldCat member library worldwide
Abstract: "A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian kernel of Euclidean space. As an important special case, kernels based on the geometry of multinomial families are derived, leading to kernelbased learning algorithms that apply naturally to discrete data. Bounds on covering numbers and Rademacher averages for the kernels are proved using bounds on the eigenvalues of the Laplacian on Riemannian manifolds. Experimental results are presented for document classification, for which the use of multinomial geometry is natural and well motivated, and improvements are obtained over the standard use of Gaussian or linear kernels, which have been the standard for text classification."
Preface intelligent interactive data visualization by Barbara Hammer(
)
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
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