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Boosting Methods For Variable Selection In High Dimensional Sparse Models
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Book Synopsis Boosting Methods for Variable Selection in High Dimensional Sparse Models by :
Download or read book Boosting Methods for Variable Selection in High Dimensional Sparse Models written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Firstly, we propose new variable selection techniques for regression in high dimensional linear models based on a forward selection version of the LASSO, adaptive LASSO or elastic net, respectively to be called as forward iterative regression and shrinkage technique (FIRST), adaptive FIRST and elastic FIRST. These methods seem to work better for an extremely sparse high dimensional linear regression model. We exploit the fact that the LASSO, adaptive LASSO and elastic net have closed form solutions when the predictor is one-dimensional. The explicit formula is then repeatedly used in an iterative fashion until convergence occurs. By carefully considering the relationship between estimators at successive stages, we develop fast algorithms to compute our estimators. The performance of our new estimators is compared with commonly used estimators in terms of predictive accuracy and errors in variable selection. It is observed that our approach has better prediction performance for highly sparse high dimensional linear regression models. Secondly, we propose a new variable selection technique for binary classification in high dimensional models based on a forward selection version of the Squared Support Vector Machines or one-norm Support Vector Machines, to be called as forward iterative selection and classification algorithm (FISCAL). This methods seem to work better for a highly sparse high dimensional binary classification model. We suggest the squared support vector machines using 1-norm and 2-norm simultaneously. The squared support vector machines are convex and differentiable except at zero when the predictor is one-dimensional. Then an iterative forward selection approach is applied along with the squared support vector machines until a stopping rule is satisfied. Also, we develop a recursive algorithm for the FISCAL to save computational burdens. We apply the processes to the original onenorm Support Vector Machines. We compare the FISCAL with other widely used.
Book Synopsis L'usage des terrains dans les villes by :
Download or read book L'usage des terrains dans les villes written by and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sparse Boosting Based Machine Learning Methods for High-Dimensional Data by : Mu Yue
Download or read book Sparse Boosting Based Machine Learning Methods for High-Dimensional Data written by Mu Yue and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In high-dimensional data, penalized regression is often used for variable selection and parameter estimation. However, these methods typically require time-consuming cross-validation methods to select tuning parameters and retain more false positives under high dimensionality. This chapter discusses sparse boosting based machine learning methods in the following high-dimensional problems. First, a sparse boosting method to select important biomarkers is studied for the right censored survival data with high-dimensional biomarkers. Then, a two-step sparse boosting method to carry out the variable selection and the model-based prediction is studied for the high-dimensional longitudinal observations measured repeatedly over time. Finally, a multi-step sparse boosting method to identify patient subgroups that exhibit different treatment effects is studied for the high-dimensional dense longitudinal observations. This chapter intends to solve the problem of how to improve the accuracy and calculation speed of variable selection and parameter estimation in high-dimensional data. It aims to expand the application scope of sparse boosting and develop new methods of high-dimensional survival analysis, longitudinal data analysis, and subgroup analysis, which has great application prospects.
Book Synopsis Cross-validation and Regression Analysis in High-dimensional Sparse Linear Models by : Feng Zhang
Download or read book Cross-validation and Regression Analysis in High-dimensional Sparse Linear Models written by Feng Zhang and published by Stanford University. This book was released on 2011 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern scientific research often involves experiments with at most hundreds of subjects but with tens of thousands of variables for every subject. The challenge of high dimensionality has reshaped statistical thinking and modeling. Variable selection plays a pivotal role in the high-dimensional data analysis, and the combination of sparsity and accuracy is crucial for statistical theory and practical applications. Regularization methods are attractive for tackling these sparsity and accuracy issues. The first part of this thesis studies two regularization methods. First, we consider the orthogonal greedy algorithm (OGA) used in conjunction with a high-dimensional information criterion introduced by Ing& Lai (2011). Although it has been shown to have excellent performance for weakly sparse regression models, one does not know a priori in practice that the actual model is weakly sparse, and we address this problem by developing a new cross-validation approach. OGA can be viewed as L0 regularization for weakly sparse regression models. When such sparsity fails, as revealed by the cross-validation analysis, we propose to use a new way to combine L1 and L2 penalties, which we show to have important advantages over previous regularization methods. The second part of the thesis develops a Monte Carlo Cross-Validation (MCCV) method to estimate the distribution of out-of-sample prediction errors when a training sample is used to build a regression model for prediction. Asymptotic theory and simulation studies show that the proposed MCCV method mimics the actual (but unknown) prediction error distribution even when the number of regressors exceeds the sample size. Therefore MCCV provides a useful tool for comparing the predictive performance of different regularization methods for real (rather than simulated) data sets.
Book Synopsis Computational Statistics and Applications by : Ricardo López-Ruiz
Download or read book Computational Statistics and Applications written by Ricardo López-Ruiz and published by BoD – Books on Demand. This book was released on 2022-04-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nature evolves mainly in a statistical way. Different strategies, formulas, and conformations are continuously confronted in the natural processes. Some of them are selected and then the evolution continues with a new loop of confrontation for the next generation of phenomena and living beings. Failings are corrected without a previous program or design. The new options generated by different statistical and random scenarios lead to solutions for surviving the present conditions. This is the general panorama for all scrutiny levels of the life cycles. Over three sections, this book examines different statistical questions and techniques in the context of machine learning and clustering methods, the frailty models used in survival analysis, and other studies of statistics applied to diverse problems.
Book Synopsis High Dimensional Classification and Variable Selection by :
Download or read book High Dimensional Classification and Variable Selection written by and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in biotechnology and other disciplines have led to the generation of many high-dimensional data, which raises challenges to develop new statistical methodologies to handle them. This dissertation focuses on two aspects of high-dimensional data inference: (1) classification based on high-dimensional covariates; (2) variable selection of high-dimensional linear regression model. Both aspects have great importance in high-dimensional data inference and are related with each other. Variable selection plays a critical rule to reduce the dimension of data. It usually boosts the signal to noise ratio and results in a simpler model that becomes much easier to interpret. Classification has many important applications in practice, such as face detection, hand-writing recognition, etc. For the high-dimensional classification problem, I have developed a new Sparse Quadratic Discriminant Analysis (SQDA) approach, which extends the application of traditional low-dimensional Quadratic Discriminant Analysis. The theoretical properties of the new SQDA approach is thoroughly addressed. Simulation studies have been conducted to compare SQDA with many other well-known classifiers in the literature. This new approach has also been applied to analyze one dataset from a colon cancer study. For the variable selection problem, a Regularized LASSO approach has been proposed, which alleviates the strong conditions for the classical LASSO method to perform well. It has been found that the new Regularized LASSO approach includes many other well-known variable selection methods as its special cases, which makes it a very general approach. The asymptotic properties of Regularized LASSO is thoroughly studied. It has been shown that the Regularized LASSO asymptotically identifies the correct model under mild assumptions. The new method has also been investigated through simulation studies, where it outperforms many other variable selection methods.
Book Synopsis Statistics for High-Dimensional Data by : Peter Bühlmann
Download or read book Statistics for High-Dimensional Data written by Peter Bühlmann and published by Springer Science & Business Media. This book was released on 2011-06-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.
Book Synopsis Advanced Data Mining and Applications by : Shuigeng Zhou
Download or read book Advanced Data Mining and Applications written by Shuigeng Zhou and published by Springer Science & Business Media. This book was released on 2012-12-09 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Advanced Data Mining and Applications, ADMA 2012, held in Nanjing, China, in December 2012. The 32 regular papers and 32 short papers presented in this volume were carefully reviewed and selected from 168 submissions. They are organized in topical sections named: social media mining; clustering; machine learning: algorithms and applications; classification; prediction, regression and recognition; optimization and approximation; mining time series and streaming data; Web mining and semantic analysis; data mining applications; search and retrieval; information recommendation and hiding; outlier detection; topic modeling; and data cube computing.
Book Synopsis Machine Learning Under a Modern Optimization Lens by : Dimitris Bertsimas
Download or read book Machine Learning Under a Modern Optimization Lens written by Dimitris Bertsimas and published by . This book was released on 2019 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Bayesian Variable Selection by : Mahlet G. Tadesse
Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Book Synopsis Large Dimensional Factor Analysis by : Jushan Bai
Download or read book Large Dimensional Factor Analysis written by Jushan Bai and published by Now Publishers Inc. This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Dimensional Factor Analysis provides a survey of the main theoretical results for large dimensional factor models, emphasizing results that have implications for empirical work. The authors focus on the development of the static factor models and on the use of estimated factors in subsequent estimation and inference. Large Dimensional Factor Analysis discusses how to determine the number of factors, how to conduct inference when estimated factors are used in regressions, how to assess the adequacy pf observed variables as proxies for latent factors, how to exploit the estimated factors to test unit root tests and common trends, and how to estimate panel cointegration models.
Book Synopsis Prediction and Variable Selection in Sparse Ultrahigh Dimensional Additive Models by : Girly Manguba Ramirez
Download or read book Prediction and Variable Selection in Sparse Ultrahigh Dimensional Additive Models written by Girly Manguba Ramirez and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The advance in technologies has enabled many fields to collect datasets where the number of covariates (p) tends to be much bigger than the number of observations (n), the so-called ultrahigh dimensionality. In this setting, classical regression methodologies are invalid. There is a great need to develop methods that can explain the variations of the response variable using only a parsimonious set of covariates. In the recent years, there have been significant developments of variable selection procedures. However, these available procedures usually result in the selection of too many false variables. In addition, most of the available procedures are appropriate only when the response variable is linearly associated with the covariates. Motivated by these concerns, we propose another procedure for variable selection in ultrahigh dimensional setting which has the ability to reduce the number of false positive variables. Moreover, this procedure can be applied when the response variable is continuous or binary, and when the response variable is linearly or non-linearly related to the covariates. Inspired by the Least Angle Regression approach, we develop two multi-step algorithms to select variables in sparse ultrahigh dimensional additive models. The variables go through a series of nonlinear dependence evaluation following a Most Significant Regression (MSR) algorithm. In addition, the MSR algorithm is also designed to implement prediction of the response variable. The first algorithm called MSR-continuous (MSRc) is appropriate for a dataset with a response variable that is continuous. Simulation results demonstrate that this algorithm works well. Comparisons with other methods such as greedy-INIS by Fan et al. (2011) and generalized correlation procedure by Hall and Miller (2009) showed that MSRc not only has false positive rate that is significantly less than both methods, but also has accuracy and true positive rate comparable with greedy-INIS. The second algorithm called MSR-binary (MSRb) is appropriate when the response variable is binary. Simulations demonstrate that MSRb is competitive in terms of prediction accuracy and true positive rate, and better than GLMNET in terms of false positive rate. Application of MSRb to real datasets is also presented. In general, MSR algorithm usually selects fewer variables while preserving the accuracy of predictions.
Book Synopsis Forward Variable Selection for Sparse Ultra-high Dimensional Generalized Varying Coefficient Models by : Toshio Honda
Download or read book Forward Variable Selection for Sparse Ultra-high Dimensional Generalized Varying Coefficient Models written by Toshio Honda and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Graphs and Networks by : Stefan Bornholdt
Download or read book Handbook of Graphs and Networks written by Stefan Bornholdt and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs. This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines. The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field. Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.
Book Synopsis Statistical Learning with Sparsity by : Trevor Hastie
Download or read book Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl
Book Synopsis Issues in Life Sciences: Molecular Biology: 2011 Edition by :
Download or read book Issues in Life Sciences: Molecular Biology: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 3332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Life Sciences: Molecular Biology / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Life Sciences—Molecular Biology. The editors have built Issues in Life Sciences: Molecular Biology: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Life Sciences—Molecular Biology in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Life Sciences: Molecular Biology: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Book Synopsis New Frontiers of Biostatistics and Bioinformatics by : Yichuan Zhao
Download or read book New Frontiers of Biostatistics and Bioinformatics written by Yichuan Zhao and published by Springer. This book was released on 2018-12-05 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is comprised of presentations delivered at the 5th Workshop on Biostatistics and Bioinformatics held in Atlanta on May 5-7, 2017. Featuring twenty-two selected papers from the workshop, this book showcases the most current advances in the field, presenting new methods, theories, and case applications at the frontiers of biostatistics, bioinformatics, and interdisciplinary areas. Biostatistics and bioinformatics have been playing a key role in statistics and other scientific research fields in recent years. The goal of the 5th Workshop on Biostatistics and Bioinformatics was to stimulate research, foster interaction among researchers in field, and offer opportunities for learning and facilitating research collaborations in the era of big data. The resulting volume offers timely insights for researchers, students, and industry practitioners.
