Proceedings Article•
EfficientL 1 regularized logistic regression
16 Jul 2006-pp 401-408
TL;DR: Theoretical results show that the proposed efficient algorithm for L1 regularized logistic regression is guaranteed to converge to the global optimum, and experiments show that it significantly outperforms standard algorithms for solving convex optimization problems.
Abstract: L1 regularized logistic regression is now a workhorse of machine learning: it is widely used for many classification problems, particularly ones with many features. L1 regularized logistic regression requires solving a convex optimization problem. However, standard algorithms for solving convex optimization problems do not scale well enough to handle the large datasets encountered in many practical settings. In this paper, we propose an efficient algorithm for L1 regularized logistic regression. Our algorithm iteratively approximates the objective function by a quadratic approximation at the current point, while maintaining the L1 constraint. In each iteration, it uses the efficient LARS (Least Angle Regression) algorithm to solve the resulting L1 constrained quadratic optimization problem. Our theoretical results show that our algorithm is guaranteed to converge to the global optimum. Our experiments show that our algorithm significantly outperforms standard algorithms for solving convex optimization problems. Moreover, our algorithm outperforms four previously published algorithms that were specifically designed to solve the L1 regularized logistic regression problem.
Citations
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TL;DR: The proposed method overcomes the limitations of applying multiple-instance learning to visual object localization using region weighting and is capable of distinguishing object and non-object regions, and generating irregular-shape object localization.
Abstract: In this paper, we address the problem of weakly supervised object localization using region weighting. For a weakly labelled image/video, the inside regions have different relevance to its semantic label. We first over-segment an image/video to get super-pixel/voxel regions, and assign each region with a latent weight to represent its support to the semantic label, then regress the weights to right values by optimizing the classification according to the weak labels. We adopt logistic regression as our base model due to its good performance in multiple-instance setting. The latent region weights are incorporated into the objective function as an interpretation of region combination at feature-level. The weights and the model parameters are optimized in an alternate manner. With the updates of the weights, the model is trained on the semantic regions independently of the background, therefore the learned model is capable of distinguishing object and non-object regions, and generating irregular-shape object localization. The method overcomes the limitations of applying multiple-instance learning to visual object localization. Experimental results on three datasets validates the effectiveness of the proposed method.
4 citations
Cites methods from "EfficientL 1 regularized logistic r..."
...Inspired by [32], we rewrite the Newton-Raphson update to derive a quadratic programming solution, which will play a key role in our region weighting optimization where there are constraints on the parameter....
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...Onemore efficient strategy tominimize the cross entropy loss is Newton-Raphson scheme [32]....
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01 Jan 2012
TL;DR: This research trained an off-task speech detector that yielded 87% detection rate at a cost of 10% false positives on children's oral reading, and studied the generality of features by detecting off- task speech in the data from four tutorial tasks ranging from oral 3 reading to prompted free-form responses.
Abstract: Off-task speech is speech that strays away from an intended task. It occurs in many dialog applications, such as intelligent tutors, virtual games, health communication systems and human-robot cooperation. Off-task speech input to computers presents both challenges and opportunities for such dialog systems. On the one hand, off-task speech contains informal conversational style and potentially unbounded scope that hamper accurate speech recognition. On the other hand, an automated agent capable of detecting off-task speech could track users' attention and thereby maintain the intended conversation by bringing a user back on task; also, knowledge of where off-task speech events are likely to occur can help the analysis of automatic speech recognition (ASR) errors. Related work has been done in confidence measures for dialog systems and detecting out-of-domain utterances. However, there is a lack of systematic study on the type of off-task speech being detected and generality of features capturing off-task speech. In addition, we know of no published research on detecting off-task speech in children's interactions with an automated agent. The goal of this research is to fill in these blanks to provide a systematic study of off-task speech, with an emphasis on child-machine interactions. To characterize off-task speech quantitatively, we used acoustic features to capture its speaking style; we used lexical features to capture its linguistic content; and we used contextual features to capture the relations of off-task speech to nearby utterances. Using these features, we trained an off-task speech detector that yielded 87% detection rate at a cost of 10% false positives on children's oral reading. Furthermore, we studied the generality of these types of features by detecting off-task speech in the data from four tutorial tasks ranging from oral 3 reading to prompted free-form responses. In additional, we examined how the features help detect adults' off-task speech in the data from the CMU Let's Go bus information system. We show that lexical features detect more task-related off-task speech such as complaints about the system, whereas acoustic features detect more unintelligible speech and non-speech events such as mumbling and humming. Moreover, acoustic features tend to be more robust than lexical features when switching domains. Finally, we demonstrate how off-task speech detection can improve the performance on application-relevant metrics such as predicting fluency test scores and understanding utterances in the CMU Let's Go bus information system.
4 citations
Book•
26 Oct 2016TL;DR: This chapter will first give an overview on the systems in terms of the input features and common applications, and provide a self-contained introduction to some discriminative learning tools that are commonly used in biometrics.
Abstract: Biometrics, similar to other pattern recognition systems, are essentially based on data collection and learning techniques In this chapter, we will first give an overview on the systems in terms of the input features and common applications After that, we will provide a self-contained introduction to some discriminative learning tools that are commonly used in biometrics A clear understanding of these techniques could be of essential importance in the sense that it forms the foundation for much of the subsequent parts in this book
4 citations
Posted Content•
TL;DR: This paper develops a new penalized regression model for the NBA, uses cross-validation to select its tuning parameters, and then uses it to produce ratings of player ability, and applies it to the 2010-2011 NBA season to predict the outcome of games.
Abstract: In the National Basketball Association (NBA), teams must make choices about which players to acquire, how much to pay them, and other decisions that are fundamentally dependent on player effectiveness Thus, there is great interest in quantitatively understanding the impact of each player In this paper we develop a new penalized regression model for the NBA, use cross-validation to select its tuning parameters, and then use it to produce ratings of player ability We then apply the model to the 2010-2011 NBA season to predict the outcome of games We compare the performance of our procedure to other known regression techniques for this problem, and demonstrate empirically that our model produces substantially better predictions We evaluate the performance of our procedure against the Las Vegas gambling lines, and show that with a sufficiently large number of games to train on our model outperforms those lines Finally, we demonstrate how the technique developed in this paper can be used to quantitively identify "overrated" players who are less impactful than common wisdom might suggest
4 citations
16 Mar 2020
TL;DR: Experimental results show that, in high privacy regimes (small ε), ssADMM and mpADMM outperform baseline algorithms in terms of classification and feature selection performance, respectively.
Abstract: In this paper we consider the problem of minimizing composite objective functions consisting of a convex differentiable loss function plus a non-smooth regularization term, such as $L_1$ norm or nuclear norm, under Renyi differential privacy (RDP). To solve the problem, we propose two stochastic alternating direction method of multipliers (ADMM) algorithms: ssADMM based on gradient perturbation and mpADMM based on output perturbation. Both algorithms decompose the original problem into sub-problems that have closed-form solutions. The first algorithm, ssADMM, applies the recent privacy amplification result for RDP to reduce the amount of noise to add. The second algorithm, mpADMM, numerically computes the sensitivity of ADMM variable updates and releases the updated parameter vector at the end of each epoch. We compare the performance of our algorithms with several baseline algorithms on both real and simulated datasets. Experimental results show that, in high privacy regimes (small e), ssADMM and mpADMM outperform baseline algorithms in terms of classification and feature selection performance, respectively.
4 citations
Cites methods from "EfficientL 1 regularized logistic r..."
...It has been used for classification problems, and many algorithms for solving L1 regularized generalized linear models were presented, such as [32], [33], and [34]....
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References
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TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.
40,785 citations
"EfficientL 1 regularized logistic r..." refers methods in this paper
...(Tibshirani 1996) Several algorithms have been developed to solve L1 constrained least squares problems....
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...See, Tibshirani (1996) for details.)...
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...(Tibshirani 1996) Several algorithms have been developed to solve L1 constrained least squares problems....
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Book•
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TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Abstract: Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
33,341 citations
Book•
01 Jan 1983TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).
23,215 citations
01 Jan 1998
12,940 citations
"EfficientL 1 regularized logistic r..." refers methods in this paper
...We tested each algorithm’s performance on 12 different datasets, consisting of 9 UCI datasets (Newman et al. 1998), one artificial dataset called Madelon from the NIPS 2003 workshop on feature extraction,3 and two gene expression datasets (Microarray 1 and 2).4 Table 2 gives details on the number…...
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...We tested each algorithm’s performance on 12 different real datasets, consisting of 9 UCI datasets (Newman et al. 1998) and 3 gene expression datasets (Microarray 1, 2 and 3) 3....
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TL;DR: This is the rst book on generalized linear models written by authors not mostly associated with the biological sciences, and it is thoroughly enjoyable to read.
Abstract: This is the rst book on generalized linear models written by authors not mostly associated with the biological sciences. Subtitled “With Applications in Engineering and the Sciences,” this book’s authors all specialize primarily in engineering statistics. The rst author has produced several recent editions of Walpole, Myers, and Myers (1998), the last reported by Ziegel (1999). The second author has had several editions of Montgomery and Runger (1999), recently reported by Ziegel (2002). All of the authors are renowned experts in modeling. The rst two authors collaborated on a seminal volume in applied modeling (Myers and Montgomery 2002), which had its recent revised edition reported by Ziegel (2002). The last two authors collaborated on the most recent edition of a book on regression analysis (Montgomery, Peck, and Vining (2001), reported by Gray (2002), and the rst author has had multiple editions of his own regression analysis book (Myers 1990), the latest of which was reported by Ziegel (1991). A comparable book with similar objectives and a more speci c focus on logistic regression, Hosmer and Lemeshow (2000), reported by Conklin (2002), presumed a background in regression analysis and began with generalized linear models. The Preface here (p. xi) indicates an identical requirement but nonetheless begins with 100 pages of material on linear and nonlinear regression. Most of this will probably be a review for the readers of the book. Chapter 2, “Linear Regression Model,” begins with 50 pages of familiar material on estimation, inference, and diagnostic checking for multiple regression. The approach is very traditional, including the use of formal hypothesis tests. In industrial settings, use of p values as part of a risk-weighted decision is generally more appropriate. The pedagologic approach includes formulas and demonstrations for computations, although computing by Minitab is eventually illustrated. Less-familiar material on maximum likelihood estimation, scaled residuals, and weighted least squares provides more speci c background for subsequent estimation methods for generalized linear models. This review is not meant to be disparaging. The authors have packed a wealth of useful nuggets for any practitioner in this chapter. It is thoroughly enjoyable to read. Chapter 3, “Nonlinear Regression Models,” is arguably less of a review, because regression analysis courses often give short shrift to nonlinear models. The chapter begins with a great example on the pitfalls of linearizing a nonlinear model for parameter estimation. It continues with the effective balancing of explicit statements concerning the theoretical basis for computations versus the application and demonstration of their use. The details of maximum likelihood estimation are again provided, and weighted and generalized regression estimation are discussed. Chapter 4 is titled “Logistic and Poisson Regression Models.” Logistic regression provides the basic model for generalized linear models. The prior development for weighted regression is used to motivate maximum likelihood estimation for the parameters in the logistic model. The algebraic details are provided. As in the development for linear models, some of the details are pushed into an appendix. In addition to connecting to the foregoing material on regression on several occasions, the authors link their development forward to their following chapter on the entire family of generalized linear models. They discuss score functions, the variance-covariance matrix, Wald inference, likelihood inference, deviance, and overdispersion. Careful explanations are given for the values provided in standard computer software, here PROC LOGISTIC in SAS. The value in having the book begin with familiar regression concepts is clearly realized when the analogies are drawn between overdispersion and nonhomogenous variance, or analysis of deviance and analysis of variance. The authors rely on the similarity of Poisson regression methods to logistic regression methods and mostly present illustrations for Poisson regression. These use PROC GENMOD in SAS. The book does not give any of the SAS code that produces the results. Two of the examples illustrate designed experiments and modeling. They include discussion of subset selection and adjustment for overdispersion. The mathematic level of the presentation is elevated in Chapter 5, “The Family of Generalized Linear Models.” First, the authors unify the two preceding chapters under the exponential distribution. The material on the formal structure for generalized linear models (GLMs), likelihood equations, quasilikelihood, the gamma distribution family, and power functions as links is some of the most advanced material in the book. Most of the computational details are relegated to appendixes. A discussion of residuals returns one to a more practical perspective, and two long examples on gamma distribution applications provide excellent guidance on how to put this material into practice. One example is a contrast to the use of linear regression with a log transformation of the response, and the other is a comparison to the use of a different link function in the previous chapter. Chapter 6 considers generalized estimating equations (GEEs) for longitudinal and analogous studies. The rst half of the chapter presents the methodology, and the second half demonstrates its application through ve different examples. The basis for the general situation is rst established using the case with a normal distribution for the response and an identity link. The importance of the correlation structure is explained, the iterative estimation procedure is shown, and estimation for the scale parameters and the standard errors of the coef cients is discussed. The procedures are then generalized for the exponential family of distributions and quasi-likelihood estimation. Two of the examples are standard repeated-measures illustrations from biostatistical applications, but the last three illustrations are all interesting reworkings of industrial applications. The GEE computations in PROC GENMOD are applied to account for correlations that occur with multiple measurements on the subjects or restrictions to randomizations. The examples show that accounting for correlation structure can result in different conclusions. Chapter 7, “Further Advances and Applications in GLM,” discusses several additional topics. These are experimental designs for GLMs, asymptotic results, analysis of screening experiments, data transformation, modeling for both a process mean and variance, and generalized additive models. The material on experimental designs is more discursive than prescriptive and as a result is also somewhat theoretical. Similar comments apply for the discussion on the quality of the asymptotic results, which wallows a little too much in reports on various simulation studies. The examples on screening and data transformations experiments are again reworkings of analyses of familiar industrial examples and another obvious motivation for the enthusiasm that the authors have developed for using the GLM toolkit. One can hope that subsequent editions will similarly contain new examples that will have caused the authors to expand the material on generalized additive models and other topics in this chapter. Designating myself to review a book that I know I will love to read is one of the rewards of being editor. I read both of the editions of McCullagh and Nelder (1989), which was reviewed by Schuenemeyer (1992). That book was not fun to read. The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities.
10,520 citations
Additional excerpts
...(Nelder & Wedderbum 1972; McCullagh & Nelder 1989)...
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...(Nelder & Wedderbum 1972; McCullagh & Nelder 1989 )...
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