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Author : Chen Xu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Applications of Penalized Likelihood Methods for Feature Selection in Statistical Modeling written by Chen Xu and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 121 pages
Book Rating : 4.:/5 (881 download)
Download or read book Variable Selection Via Penalized Likelihood written by and published by . This book was released on 2014 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection via penalized likelihood plays an important role in high dimensional statistical modeling and it has attracted great attention in recent literature. This thesis is devoted to the study of variable selection problem. It consists of three major parts, all of which fall within the framework of penalized least squares regression setting. In the first part of this thesis, we propose a family of nonconvex penalties named the K-Smallest Items (KSI) penalty for variable selection, which is able to improve the performance of variable selection and reduce estimation bias on the estimates of the important coefficients. We fully investigate the theoretical properties of the KSI method and show that it possesses the weak oracle property and the oracle property in the high-dimensional setting where the number of coefficients is allowed to be much larger than the sample size. To demonstrate its numerical performance, we applied the KSI method to several simulation examples as well as the well known Boston housing dataset. We also extend the idea of the KSI method to handle the group variable selection problem. In the second part of this thesis, we propose another nonconvex penalty named Self-adaptive penalty (SAP) for variable selection. It is distinguished from other existing methods in the sense that the penalization on each individual coefficient takes into account directly the influence of other estimated coefficients. We also thoroughly study the theoretical properties of the SAP method and show that it possesses the weak oracle property under desirable conditions. The proposed method is applied to the glioblastoma cancer data obtained from The Cancer Genome Atlas. In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. In statistics, this is a group variable selection problem. In the third part of this thesis, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and may help design intervention programs to improve the quality of life for breast cancer survivors.
Author : Tharshanna Nadarajah
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.:/5 (773 download)
Download or read book Penalized Empirical Likelihood Based Variable Selection written by Tharshanna Nadarajah and published by . This book was released on 2011 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jianqing Fan
Publisher : CRC Press
ISBN 13 : 0429527616
Total Pages : 942 pages
Book Rating : 4.4/5 (295 download)
Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Author : Arie Preminger
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Using the Penalized Likelihood Method for Model Selection with Nuisance Parameters Present Only Under the Alternative written by Arie Preminger and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the problem of model selection with nuisance parameters present only under the alternative. The common approach for testing in this case is to determine the true model through the use of some functionals over the nuisance parameters space. Since in such cases the distribution of these statistics is not known, critical values had to be approximated usually through computationally intensive simulations. Furthermore, the computed critical values are data and model dependent and hence cannot be tabulated. We address this problem by using the penalized likelihood method to choose the correct model. We start by viewing the likelihood ratio as a function of the unidentified parameters. By using the empirical process theory and the uniform law of the iterated logarithm (LIL) together with sufficient conditions on the penalty term, we derive the consistency properties of this method. Our approach generates a simple and consistent procedure for model selection. This methodology is presented in the context of switching regression models. We also provide some Monte Carlo simulations to analyze the finite sample performance of our procedure.
Author : Jan C. Willems
Publisher : Springer Science & Business Media
ISBN 13 : 3642750079
Total Pages : 254 pages
Book Rating : 4.6/5 (427 download)
Download or read book From Data to Model written by Jan C. Willems and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of obtaining dynamical models directly from an observed time-series occurs in many fields of application. There are a number of possible approaches to this problem. In this volume a number of such points of view are exposed: the statistical time series approach, a theory of guaranted performance, and finally a deterministic approximation approach. This volume is an out-growth of a number of get-togethers sponsered by the Systems and Decision Sciences group of the International Institute of Applied Systems Analysis (IIASA) in Laxenburg, Austria. The hospitality and support of this organization is gratefully acknowledged. Jan Willems Groningen, the Netherlands May 1989 TABLE OF CONTENTS Linear System Identification- A Survey page 1 M. Deistler A Tutorial on Hankel-Norm Approximation 26 K. Glover A Deterministic Approach to Approximate Modelling 49 C. Heij and J. C. Willems Identification - a Theory of Guaranteed Estimates 135 A. B. Kurzhanski Statistical Aspects of Model Selection 215 R. Shibata Index 241 Addresses of Authors 246 LINEAR SYSTEM IDENTIFICATION· A SURVEY M. DEISTLER Abstract In this paper we give an introductory survey on the theory of identification of (in general MIMO) linear systems from (discrete) time series data. The main parts are: Structure theory for linear systems, asymptotic properties of maximum likelihood type estimators, estimation of the dynamic specification by methods based on information criteria and finally, extensions and alternative approaches such as identification of unstable systems and errors-in-variables. Keywords Linear systems, parametrization, maximum likelihood estimation, information criteria, errors-in-variables.
Author : Syed Ejaz Ahmed
Publisher : CRC Press
ISBN 13 : 1000876659
Total Pages : 409 pages
Book Rating : 4.0/5 (8 download)
Download or read book Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data written by Syed Ejaz Ahmed and published by CRC Press. This book was released on 2023-05-25 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some post-estimation and predictions strategies for the host of useful statistical models with applications in data science. It combines statistical learning and machine learning techniques in a unique and optimal way. It is well-known that machine learning methods are subject to many issues relating to bias, and consequently the mean squared error and prediction error may explode. For this reason, we suggest shrinkage strategies to control the bias by combining a submodel selected by a penalized method with a model with many features. Further, the suggested shrinkage methodology can be successfully implemented for high dimensional data analysis. Many researchers in statistics and medical sciences work with big data. They need to analyse this data through statistical modelling. Estimating the model parameters accurately is an important part of the data analysis. This book may be a repository for developing improve estimation strategies for statisticians. This book will help researchers and practitioners for their teaching and advanced research, and is an excellent textbook for advanced undergraduate and graduate courses involving shrinkage, statistical, and machine learning. The book succinctly reveals the bias inherited in machine learning method and successfully provides tools, tricks and tips to deal with the bias issue. Expertly sheds light on the fundamental reasoning for model selection and post estimation using shrinkage and related strategies. This presentation is fundamental, because shrinkage and other methods appropriate for model selection and estimation problems and there is a growing interest in this area to fill the gap between competitive strategies. Application of these strategies to real life data set from many walks of life. Analytical results are fully corroborated by numerical work and numerous worked examples are included in each chapter with numerous graphs for data visualization. The presentation and style of the book clearly makes it accessible to a broad audience. It offers rich, concise expositions of each strategy and clearly describes how to use each estimation strategy for the problem at hand. This book emphasizes that statistics/statisticians can play a dominant role in solving Big Data problems, and will put them on the precipice of scientific discovery. The book contributes novel methodologies for HDDA and will open a door for continued research in this hot area. The practical impact of the proposed work stems from wide applications. The developed computational packages will aid in analyzing a broad range of applications in many walks of life.
Author : Max Kuhn
Publisher : CRC Press
ISBN 13 : 1351609467
Total Pages : 266 pages
Book Rating : 4.3/5 (516 download)
Download or read book Feature Engineering and Selection written by Max Kuhn and published by CRC Press. This book was released on 2019-07-25 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.
Author : Ludwig Fahrmeir
Publisher : Springer Science & Business Media
ISBN 13 : 3642343333
Total Pages : 768 pages
Book Rating : 4.6/5 (423 download)
Download or read book Regression written by Ludwig Fahrmeir and published by Springer Science & Business Media. This book was released on 2013-05-09 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is an applied and unified introduction into parametric, non- and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through many real data examples and case studies. Availability of (user-friendly) software has been a major criterion for the methods selected and presented. Thus, the book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written on an intermediate mathematical level and assumes only knowledge of basic probability, calculus, and statistics. The most important definitions and statements are concisely summarized in boxes. Two appendices describe required matrix algebra, as well as elements of probability calculus and statistical inference.
Author : Ricardo López-Ruiz
Publisher : BoD – Books on Demand
ISBN 13 : 1839697822
Total Pages : 207 pages
Book Rating : 4.8/5 (396 download)
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.
Author : Yichuan Zhao
Publisher : Springer Nature
ISBN 13 : 3030334163
Total Pages : 495 pages
Book Rating : 4.0/5 (33 download)
Download or read book Statistical Modeling in Biomedical Research written by Yichuan Zhao and published by Springer Nature. This book was released on 2020-03-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection discusses the emerging topics in statistical modeling for biomedical research. Leading experts in the frontiers of biostatistics and biomedical research discuss the statistical procedures, useful methods, and their novel applications in biostatistics research. Interdisciplinary in scope, the volume as a whole reflects the latest advances in statistical modeling in biomedical research, identifies impactful new directions, and seeks to drive the field forward. It also fosters the interaction of scholars in the arena, offering great opportunities to stimulate further collaborations. This book will appeal to industry data scientists and statisticians, researchers, and graduate students in biostatistics and biomedical science. It covers topics in: Next generation sequence data analysis Deep learning, precision medicine, and their applications Large scale data analysis and its applications Biomedical research and modeling Survival analysis with complex data structure and its applications.
Author : Ganggang Xu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (812 download)
Download or read book Variable Selection and Function Estimation Using Penalized Methods written by Ganggang Xu and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Penalized methods are becoming more and more popular in statistical research. This dissertation research covers two major aspects of applications of penalized methods: variable selection and nonparametric function estimation. The following two paragraphs give brief introductions to each of the two topics. Infinite variance autoregressive models are important for modeling heavy-tailed time series. We use a penalty method to conduct model selection for autoregressive models with innovations in the domain of attraction of a stable law indexed by alpha is an element of (0, 2). We show that by combining the least absolute deviation loss function and the adaptive lasso penalty, we can consistently identify the true model. At the same time, the resulting coefficient estimator converges at a rate of n(1/alpha) . The proposed approach gives a unified variable selection procedure for both the finite and infinite variance autoregressive models. While automatic smoothing parameter selection for nonparametric function estimation has been extensively researched for independent data, it is much less so for clustered and longitudinal data. Although leave-subject-out cross-validation (CV) has been widely used, its theoretical property is unknown and its minimization is computationally expensive, especially when there are multiple smoothing parameters. By focusing on penalized modeling methods, we show that leave-subject-out CV is optimal in that its minimization is asymptotically equivalent to the minimization of the true loss function. We develop an efficient Newton-type algorithm to compute the smoothing parameters that minimize the CV criterion. Furthermore, we derive one simplification of the leave-subject-out CV, which leads to a more efficient algorithm for selecting the smoothing parameters. We show that the simplified version of CV criteria is asymptotically equivalent to the unsimplified one and thus enjoys the same optimality property. This CV criterion also provides a completely data driven approach to select working covariance structure using generalized estimating equations in longitudinal data analysis. Our results are applicable to additive, linear varying-coefficient, nonlinear models with data from exponential families.
Author : Wai Keung Li
Publisher : Springer
ISBN 13 : 1493965689
Total Pages : 298 pages
Book Rating : 4.4/5 (939 download)
Download or read book Advances in Time Series Methods and Applications written by Wai Keung Li and published by Springer. This book was released on 2016-12-02 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reviews and summarizes some of A. I. McLeod's significant contributions to time series analysis. It also contains original contributions to the field and to related areas by participants of the festschrift held in June 2014 and friends of Dr. McLeod. Covering a diverse range of state-of-the-art topics, this volume well balances applied and theoretical research across fourteen contributions by experts in the field. It will be of interest to researchers and practitioners in time series, econometricians, and graduate students in time series or econometrics, as well as environmental statisticians, data scientists, statisticians interested in graphical models, and researchers in quantitative risk management.
Author : Kaitai Fang
Publisher : World Scientific
ISBN 13 : 9812567763
Total Pages : 470 pages
Book Rating : 4.8/5 (125 download)
Download or read book Contemporary Multivariate Analysis and Design of Experiments written by Kaitai Fang and published by World Scientific. This book was released on 2005 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Index. Subject index -- Author index
Author : Ying Yu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)
Download or read book Penalized Likelihood Methods for Sparse Datasets, with Applications to Genetic Epidemiology written by Ying Yu and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Increasingly, logistic regression methods for genetic association studies of binary phenotypes must be able to accommodate data sparsity, which arises from unbalanced case-control ratios and/or rare exposures. Sparseness leads to maximum likelihood estimates (MLEs) of log odds-ratio parameters that are biased away from their null value of zero and tests with inflated type I errors. Different penalized-likelihood methods have been developed to mitigate sparse-data bias. We study penalized logistic and conditional regression using a class of log-F priors indexed by a shrinkage parameter m to shrink the biased MLE towards zero. The thesis is organized in three parts. First, we propose a two-step methodology for implementing log-F penalization for inference of regression parameters from logistic regression, with application to genome-wide association studies. In the first step we estimate the shrinkage parameter, and in the second step we use the penalized regression estimator to estimate single-variant associations across the genome. Next, we explore log-F penalization for inference of regression parameters from conditional logistic regression, with application to data from matched case-control and case-parent trio studies. In the first two projects we use simulation to study the statistical properties of our methods and make comparisons to methods that use Firth penalization. Finally, we apply log-F-penalized logistic regression to data from the UK Biobank, to investigate the method's feasibility for genome-wide, biobank-scale data. The complexity and size of biobank data present unique challenges, and we make modifications to our methodology to increase its flexibility and adaptability to such datasets.
Author : Hulin Wu
Publisher : CRC Press
ISBN 13 : 1000260968
Total Pages : 268 pages
Book Rating : 4.0/5 (2 download)
Download or read book Statistics and Machine Learning Methods for EHR Data written by Hulin Wu and published by CRC Press. This book was released on 2020-12-10 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Electronic Health Records (EHR)/Electronic Medical Records (EMR) data is becoming more prevalent for research. However, analysis of this type of data has many unique complications due to how they are collected, processed and types of questions that can be answered. This book covers many important topics related to using EHR/EMR data for research including data extraction, cleaning, processing, analysis, inference, and predictions based on many years of practical experience of the authors. The book carefully evaluates and compares the standard statistical models and approaches with those of machine learning and deep learning methods and reports the unbiased comparison results for these methods in predicting clinical outcomes based on the EHR data. Key Features: Written based on hands-on experience of contributors from multidisciplinary EHR research projects, which include methods and approaches from statistics, computing, informatics, data science and clinical/epidemiological domains. Documents the detailed experience on EHR data extraction, cleaning and preparation Provides a broad view of statistical approaches and machine learning prediction models to deal with the challenges and limitations of EHR data. Considers the complete cycle of EHR data analysis. The use of EHR/EMR analysis requires close collaborations between statisticians, informaticians, data scientists and clinical/epidemiological investigators. This book reflects that multidisciplinary perspective.
Author : Yibo Zhao
Publisher :
ISBN 13 :
Total Pages : 64 pages
Book Rating : 4.:/5 (13 download)
Download or read book New Models and Methods for Applied Statistics written by Yibo Zhao and published by . This book was released on 2017 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applied statistics, people develop models to solve real world problems based on data. However, the data is growing fast and become more and more massive and complex. Conventional models are limited in the capability of dealing with the fast growing data. This dissertation develops two new models in computer experiments and time series analysis. The new models are developed based on the special features of two real-world problems. The two datasets are from an IBM data thermal study and a biological cell adhesion experiment. For computer experiment, we address two important issues in Gaussian process (GP) modeling. One is how to reduce the computational complexity in GP modeling and the other is how to simultaneous perform variable selection and estimation for the mean function of GP models. Estimation is computationally intensive for GP models because it heavily involves manipulations of an n-by-n correlation matrix, where n is the sample size. Conventional penalized likelihood approaches are widely used for variable selection. However, the computational cost of the penalized likelihood estimation (PMLE) or the corresponding one-step sparse estimation (OSE) can be prohibitively high as the sample size becomes large, especially for GP models. To address both issues, this article proposes an efficient subsample aggregating (subagging) approach with an experimental design-based subsampling scheme. The proposed method is computationally cheaper, yet it can be shown that the resulting subagging estimators achieve the same efficiency as the original PMLE and OSE asymptotically. The finite-sample performance is examined through simulation studies. Application of the proposed methodology to a data center thermal study reveals some interesting information, including identifying an efficient cooling mechanism. Motivated by an analysis of cell adhesion experiments, we introduce a new statistical framework within which the unique features are incorporated and the molecular binding mechanism can be studied. This framework is based upon an extension of Markov switching autoregressive (MSAR) models, a regime-switching type of time series model generalized from hidden Markov models. Standard MSAR models are developed for the analysis of individual stochastic process. To handle multiple time series processes, we introduce Markov switching autoregressive mixed (MSARM) model that simultaneously models multiple time series processes collected from different experimental subjects as in the longitudinal data setting. More than a simple extension, the MSARM model posts statistical challenges in the theoretical developments as well as computational efficiency in high-dimensional integration.
