Download or read book Methods for Interquantile Shrinkage and Variable Selection in Linear Regression Models written by Liewen Jiang and published by . This book was released on 2012 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shrinkage Based Variable Selection Methods for Linear Regression and Mixed Effects Models written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: KRISHNA, ARUN. Shrinkage-Based Variable Selection Methods for Linear Regression and Mixed-Effects Models. (Under the direction of Professors H.D. Bondell and S.K. Ghosh). In this dissertation we propose two new shrinkage-based variable selection approaches. We first propose a Bayesian selection technique for linear regression models, which allows for highly correlated predictors to enter or exit the model, simultaneously. The second variable selection method proposed is for linear mixed-effects models, where we develop a new technique to jointly select the important fixed and random effects parameters. We briefly summarize each of these methods below. The problem of selecting the correct subset of predictors within a linear model has received much attention in recent literature. Within the Bayesian framework, a popular choice of prior has been Zellnerâ€"! g-prior which is based on the inverse of empirical covariance matrix of the predictors. We propose an extension of Zellnerâ€"! gprior which allow for a power parameter on the empirical covariance of the predictors. The power parameter helps control the degree to which correlated predictors are smoothed towards or away from one another. In addition, the empirical covariance of the predictors is used to obtain suitable priors over model space. In this manner, the power parameter also helps to determine whether models containing highly collinear predictors are preferred or avoided. The proposed power parameter can be chosen via an empirical Bayes method which leads to a data adaptive choice of prior. Simulation studies and a real data example are presented to show how the power parameter is well determined from the degree of cross-correlation within predictors. The proposed modification compares favorably to the standard use of Zellnerâ€"! prior and an intrinsic prior in these examples. We propose a new method of simultaneously identifying the important predictors that correspond to both the fixed and random effects.
Download or read book Shrinkage based Variable Selection Methods for Linear Regression and Mixed effects Models written by Arun Krishna and published by . This book was released on 2009 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: shrinkage techniques, powered correlation prior, Zellner's prior, mixed-models.
Download or read book Alternative Methods of Variable Selection in Linear Regression Models for Incomplete Multivariate Normal Data written by Xiaowei Yang and published by . This book was released on 2002 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variable Screening and Model Selection in Censored Quantile Regression Via Sparse Penalties and Stepwise Refinement written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transplant Rejection and Tolerance Advancing the Field through Integration of Computational and Experimental Investigations written by Giorgio Raimondi and published by Frontiers Media SA. This book was released on 2017-12-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Organ transplantation is a life-saving surgical procedure through which the functionality of a failing organ system can be restored. However, without the life-long administration of immunosuppressive drugs, the recipient’s immune system will launch a massive immune attack that will ultimately destroy the graft. Although successful at protecting the graft from an immune attack, long-term use of immunosuppressive drugs leads to serious complications (e.g., increased risk of infection, diabetes, hypertension, cardiovascular disease, and cancer). Moreover, recipients suffer from limited long-term graft survival rates due to the inability of current treatments to establish tolerance to the transplanted tissues. Thus, there is a great medical need to understand the complex network of immune system interactions that lead to transplant rejection so that new strategies of intervention can be determined that will redirect the system toward transplant acceptance while preserving immune competence against offending agents. In the past 20 years, the discovery and growing understanding of the positive and negative regulators of the activation of the immune system have fostered new interventional procedures targeting one or the other. While pre-clinical results proved the validity of these strategies, their clinical implementation has been troublesome. These results underscore the need for additional methods to determine the most effective interventions to prevent long-term transplant rejection. New tools of genomics, proteomics and metabolomics are being implemented in powerful analyses that promise the development of better, safer personalized treatments. In parallel, theoretical modeling has emerged as a tool that transcends investigations of individual mechanistic processes and instead unravels the relevant mechanisms of complex systems such as the immune response triggered by a transplant. In this way, theoretical models can be used to identify important behavior that arises from complex systems and thereby delineate emergent properties of biological systems that could not be identified studying single components. Employing this approach, interdisciplinary collaborations among immunologists, mathematicians, and system biologists will yield novel perspectives in the development of more effective strategies of intervention. The aim of this Research Topic is to demonstrate how new insight and methods from theoretical and experimental studies of the immune response can aid in identifying new research directions in transplant immunology. First, techniques from various theoretical and experimental studies with applications to the immune response will be reviewed to determine how they can be adapted to explore the complexity of transplant rejection. Second, recent advances in the acquisition and mining of large data sets related to transplant genomics, proteomics, and metabolomics will be discussed in the context of their predictive power and potential for optimizing and personalizing patient treatment. Last, new perspectives will be offered on the integration of computational immune modeling with transplant and omics data to establish more effective strategies of intervention that promote transplant tolerance.
Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Download or read book Quantile Regression for Cross Sectional and Time Series Data written by Jorge M. Uribe and published by Springer Nature. This book was released on 2020-03-30 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief addresses the estimation of quantile regression models from a practical perspective, which will support researchers who need to use conditional quantile regression to measure economic relationships among a set of variables. It will also benefit students using the methodology for the first time, and practitioners at private or public organizations who are interested in modeling different fragments of the conditional distribution of a given variable. The book pursues a practical approach with reference to energy markets, helping readers learn the main features of the technique more quickly. Emphasis is placed on the implementation details and the correct interpretation of the quantile regression coefficients rather than on the technicalities of the method, unlike the approach used in the majority of the literature. All applications are illustrated with R.
Download or read book Variable Selection Methods in Multiple Linear Regression written by Tsung-Sheng Hu and published by . This book was released on 1993 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shrinkage Methods for Variable Selection and Prediction with Applications to Genetic Data written by Erika Cule and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interpretable Machine Learning written by Christoph Molnar and published by Lulu.com. This book was released on 2020 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.
Download or read book Tree Based Methods for Statistical Learning in R written by Brandon M. Greenwell and published by CRC Press. This book was released on 2022-06-23 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Distributed Quantile Regression Analysis and a Group Variable Selection Method written by Liqun Yu (Mathematician) and published by . This book was released on 2018 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation develops novel methodologies for distributed quantile regression analysis for big data by utilizing a distributed optimization algorithm called the alternating direction method of multipliers (ADMM). Specifically, we first write the penalized quantile regression into a specific form that can be solved by the ADMM and propose numerical algorithms for solving the ADMM subproblems. This results in the distributed QR-ADMM algorithm. Then, to further reduce the computational time, we formulate the penalized quantile regression into another equivalent ADMM form in which all the subproblems have exact closed-form solutions and hence avoid iterative numerical methods. This results in the single-loop QPADM algorithm that further improve on the computational efficiency of the QR-ADMM. Both QR-ADMM and QPADM enjoy flexible parallelization by enabling data splitting across both sample space and feature space, which make them especially appealing for the case when both sample size n and feature dimension p are large. Besides the QR-ADMM and QPADM algorithms for penalized quantile regression, we also develop a group variable selection method by approximating the Bayesian information criterion. Unlike existing penalization methods for feature selection, our proposed gMIC algorithm is free of parameter tuning and hence enjoys greater computational efficiency. Although the current version of gMIC focuses on the generalized linear model, it can be naturally extended to the quantile regression for feature selection. We provide theoretical analysis for our proposed methods. Specifically, we conduct numerical convergence analysis for the QR-ADMM and QPADM algorithms, and provide asymptotical theories and oracle property of feature selection for the gMIC method. All our methods are evaluated with simulation studies and real data analysis.
Download or read book Variable selection and parameter estimation for normal linear regression models written by Peter J. Kempthorne and published by . This book was released on 1985 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Input Variable Selection Methods for Construction of Interpretable Regression Models written by Jarkko Tikka and published by . This book was released on 2008 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tiivistelmä: Syötemuuttujanvalintamenetelmiä tulkittavien regressiomallien konstruoimiseen.
Download or read book Variable Selection in Clusterwise switching Regression written by Minhee Kang and published by . This book was released on 1995 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical and Modern Variable Selection Methods in Regression Analysis written by Anna Tivy and published by . This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
