Discrepancy Based Algorithms For Best Subset Model Selection
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Discrepancy Based Algorithms For Best Subset Model Selection
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Author : Tao Zhang
language : en
Publisher:
Release Date : 2013
Discrepancy Based Algorithms For Best Subset Model Selection written by Tao Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Akaike Information Criterion categories.
The selection of a best-subset regression model from a candidate family is a common problem that arises in many analyses. In best-subset model selection, we consider all possible subsets of regressor variables; thus, numerous candidate models may need to be fit and compared. One of the main challenges of best-subset selection arises from the size of the candidate model family: specifically, the probability of selecting an inappropriate model generally increases as the size of the family increases. For this reason, it is usually difficult to select an optimal model when best-subset selection is attempted based on a moderate to large number of regressor variables. Model selection criteria are often constructed to estimate discrepancy measures used to assess the disparity between each fitted candidate model and the generating model. The Akaike information criterion (AIC) and the corrected AIC (AICc) are designed to estimate the expected Kullback-Leibler (K-L) discrepancy. For best-subset selection, both AIC and AICc are negatively biased, and the use of either criterion will lead to overfitted models. To correct for this bias, we introduce a criterion AICi, which has a penalty term evaluated from Monte Carlo simulation. A multistage model selection procedure AICaps, which utilizes AICi, is proposed for best-subset selection. In the framework of linear regression models, the Gauss discrepancy is another frequently applied measure of proximity between a fitted candidate model and the generating model. Mallows' conceptual predictive statistic (Cp) and the modified Cp (MCp) are designed to estimate the expected Gauss discrepancy. For best-subset selection, Cp and MCp exhibit negative estimation bias. To correct for this bias, we propose a criterion CPSi that again employs a penalty term evaluated from Monte Carlo simulation. We further devise a multistage procedure, CPSaps, which selectively utilizes CPSi. In this thesis, we consider best-subset selection in two different modeling frameworks: linear models and generalized linear models. Extensive simulation studies are compiled to compare the selection behavior of our methods and other traditional model selection criteria. We also apply our methods to a model selection problem in a study of bipolar disorder.
Computational Subset Model Selection Algorithms And Applications
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Author :
language : en
Publisher:
Release Date : 2004
Computational Subset Model Selection Algorithms And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
This dissertation develops new computationally efficient algorithms for identifying the subset of variables that minimizes any desired information criteria in model selection. In recent years, the statistical literature has placed more and more emphasis on information theoretic model selection criteria. A model selection criterion chooses model that "closely" approximates the true underlying model. Recent years have also seen many exciting developments in the model selection techniques. As demand increases for data mining of massive datasets with many variables, the demand for model selection techniques are becoming much stronger and needed. To this end, we introduce a new Implicit Enumeration (IE) algorithm and a hybridized IE with the Genetic Algorithm (GA) in this dissertation. The proposed Implicit Enumeration algorithm is the first algorithm that explicitly uses an information criterion as the objective function. The algorithm works with a variety of information criteria including some for which the existing branch and bound algorithms developed by Furnival and Wilson (1974) and Gatu and Kontoghiorghies (2003) are not applicable. It also finds the "best" subset model directly without the need of finding the "best" subset of each size as the branch and bound techniques do. The proposed methods are demonstrated in multiple, multivariate, logistic regression and discriminant analysis problems. The implicit enumeration algorithm converged to the optimal solution on real and simulated data sets with up to 80 predictors, thus having 280 = 1,208,925,819,614,630,000,000,000 possible subset models in the model portfolio. To our knowledge, none of the existing exact algorithms have the capability of optimally solving such problems of this size.
Basic Guide For Machine Learning Algorithms And Models
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Author : Ms.G.Vanitha
language : en
Publisher: SK Research Group of Companies
Release Date : 2024-07-10
Basic Guide For Machine Learning Algorithms And Models written by Ms.G.Vanitha and has been published by SK Research Group of Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-10 with Computers categories.
Ms.G.Vanitha, Associate Professor, Department of Information Technology, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India. Dr.M.Kasthuri, Associate Professor, Department of Computer Science, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India.
Expert Clouds And Applications
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Author : I. Jeena Jacob
language : en
Publisher: Springer Nature
Release Date : 2022-08-17
Expert Clouds And Applications written by I. Jeena Jacob and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-17 with Technology & Engineering categories.
The book features original papers from International Conference on Expert Clouds and Applications (ICOECA 2022), organized by GITAM School of Technology, Bangalore, India, during 3–4 February 2022. It covers new research insights on artificial intelligence, big data, cloud computing, sustainability, knowledge-based expert systems. The book discusses innovative research from all aspects including theoretical, practical, and experimental domains that pertain to the expert systems, sustainable clouds, and artificial intelligence technologies.
Machine Learning Under A Modern Optimization Lens
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Author : Dimitris Bertsimas
language : en
Publisher:
Release Date : 2019
Machine Learning Under A Modern Optimization Lens written by Dimitris Bertsimas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Machine learning categories.
The General Linear Model
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Author : Alexander von Eye
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-30
The General Linear Model written by Alexander von Eye and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-30 with Psychology categories.
General Linear Model methods are the most widely used in data analysis in applied empirical research. Still, there exists no compact text that can be used in statistics courses and as a guide in data analysis. This volume fills this void by introducing the General Linear Model (GLM), whose basic concept is that an observed variable can be explained from weighted independent variables plus an additive error term that reflects imperfections of the model and measurement error. It also covers multivariate regression, analysis of variance, analysis under consideration of covariates, variable selection methods, symmetric regression, and the recently developed methods of recursive partitioning and direction dependence analysis. Each method is formally derived and embedded in the GLM, and characteristics of these methods are highlighted. Real-world data examples illustrate the application of each of these methods, and it is shown how results can be interpreted.
Subspace Latent Structure And Feature Selection
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Author : Craig Saunders
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-16
Subspace Latent Structure And Feature Selection written by Craig Saunders and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-16 with Computers categories.
Many of the papers in this proceedings volume were presented at the PASCAL Workshop entitled Subspace, Latent Structure and Feature Selection Techniques: Statistical and Optimization Perspectives which took place in Bohinj, Slovenia during February, 23–25 2005.
Tree Based Methods For Statistical Learning In R
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Author : Brandon M. Greenwell
language : en
Publisher: CRC Press
Release Date : 2022-06-23
Tree Based Methods For Statistical Learning In R written by Brandon M. Greenwell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-23 with Business & Economics categories.
Tree-based Methods for Statistical Learning in R provides a thorough introduction to both individual decision tree algorithms (Part I) and ensembles thereof (Part II). Part I of the book brings several different tree algorithms into focus, both conventional and contemporary. Building a strong foundation for how individual decision trees work will help readers better understand tree-based ensembles at a deeper level, which lie at the cutting edge of modern statistical and machine learning methodology. The book follows up most ideas and mathematical concepts with code-based examples in the R statistical language; with an emphasis on using as few external packages as possible. For example, users will be exposed to writing their own random forest and gradient tree boosting functions using simple for loops and basic tree fitting software (like rpart and party/partykit), and more. The core chapters also end with a detailed section on relevant software in both R and other opensource alternatives (e.g., Python, Spark, and Julia), and example usage on real data sets. While the book mostly uses R, it is meant to be equally accessible and useful to non-R programmers. Consumers of this book will have gained a solid foundation (and appreciation) for tree-based methods and how they can be used to solve practical problems and challenges data scientists often face in applied work. Features: Thorough coverage, from the ground up, of tree-based methods (e.g., CART, conditional inference trees, bagging, boosting, and random forests). A companion website containing additional supplementary material and the code to reproduce every example and figure in the book. A companion R package, called treemisc, which contains several data sets and functions used throughout the book (e.g., there’s an implementation of gradient tree boosting with LAD loss that shows how to perform the line search step by updating the terminal node estimates of a fitted rpart tree). Interesting examples that are of practical use; for example, how to construct partial dependence plots from a fitted model in Spark MLlib (using only Spark operations), or post-processing tree ensembles via the LASSO to reduce the number of trees while maintaining, or even improving performance.
Best Practices In Quantitative Methods
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Author : Jason W. Osborne
language : en
Publisher: SAGE
Release Date : 2008
Best Practices In Quantitative Methods written by Jason W. Osborne and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Social Science categories.
The contributors to Best Practices in Quantitative Methods envision quantitative methods in the 21st century, identify the best practices, and, where possible, demonstrate the superiority of their recommendations empirically. Editor Jason W. Osborne designed this book with the goal of providing readers with the most effective, evidence-based, modern quantitative methods and quantitative data analysis across the social and behavioral sciences. The text is divided into five main sections covering select best practices in Measurement, Research Design, Basics of Data Analysis, Quantitative Methods, and Advanced Quantitative Methods. Each chapter contains a current and expansive review of the literature, a case for best practices in terms of method, outcomes, inferences, etc., and broad-ranging examples along with any empirical evidence to show why certain techniques are better. Key Features: Describes important implicit knowledge to readers: The chapters in this volume explain the important details of seemingly mundane aspects of quantitative research, making them accessible to readers and demonstrating why it is important to pay attention to these details. Compares and contrasts analytic techniques: The book examines instances where there are multiple options for doing things, and make recommendations as to what is the "best" choice—or choices, as what is best often depends on the circumstances. Offers new procedures to update and explicate traditional techniques: The featured scholars present and explain new options for data analysis, discussing the advantages and disadvantages of the new procedures in depth, describing how to perform them, and demonstrating their use. Intended Audience: Representing the vanguard of research methods for the 21st century, this book is an invaluable resource for graduate students and researchers who want a comprehensive, authoritative resource for practical and sound advice from leading experts in quantitative methods.
Empirical Model Discovery And Theory Evaluation
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Author : David F. Hendry
language : en
Publisher: MIT Press
Release Date : 2014-07-03
Empirical Model Discovery And Theory Evaluation written by David F. Hendry and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Business & Economics categories.
A synthesis of the authors' groundbreaking econometric research on automatic model selection, which uses powerful computational algorithms and theory evaluation. Economic models of empirical phenomena are developed for a variety of reasons, the most obvious of which is the numerical characterization of available evidence, in a suitably parsimonious form. Another is to test a theory, or evaluate it against the evidence; still another is to forecast future outcomes. Building such models involves a multitude of decisions, and the large number of features that need to be taken into account can overwhelm the researcher. Automatic model selection, which draws on recent advances in computation and search algorithms, can create, and then empirically investigate, a vastly wider range of possibilities than even the greatest expert. In this book, leading econometricians David Hendry and Jurgen Doornik report on their several decades of innovative research on automatic model selection. After introducing the principles of empirical model discovery and the role of model selection, Hendry and Doornik outline the stages of developing a viable model of a complicated evolving process. They discuss the discovery stages in detail, considering both the theory of model selection and the performance of several algorithms. They describe extensions to tackling outliers and multiple breaks, leading to the general case of more candidate variables than observations. Finally, they briefly consider selecting models specifically for forecasting.