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Author : 曾奕齊
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (122 download)
Download or read book Variable Selection for High-dimensional Spatial Linear Models written by 曾奕齊 and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Author : Jinzhu Jiang
Publisher :
ISBN 13 :
Total Pages : 105 pages
Book Rating : 4.:/5 (126 download)
Download or read book Feature Screening for High-dimensional Variable Selection in Generalized Linear Models written by Jinzhu Jiang and published by . This book was released on 2021 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional data are widely encountered in a great variety of areas such as bioinformatics, medicine, marketing, and finance over the past few decades. The curse of high-dimensionality presents a challenge in both methodological and computational aspects. Many traditional statistical modeling techniques perform well for low-dimensional data, but their performance begin to deteriorate when being extended to high-dimensional data. Among all modeling techniques, variable selection plays a fundamental role in high-dimensional data modeling. To deal with the high-dimensionality problem, a large amount of variable selection approaches based on regularization have been developed, including but not limited to LASSO (Tibshirani, 1996), SCAD (Fan and Li, 2001), Dantzig selector (Candes and Tao, 2007). However, as the dimensionality getting higher and higher, those regularization approaches may not perform well due to the simultaneous challenges in computational expediency, statistical accuracy, and algorithm stability (Fan et al., 2009). To address those challenges, a series of feature screening procedures have been proposed. Sure independence screening (SIS) is a well-known procedure for variable selection in linear models with high and ultrahigh dimensional data based on the Pearson correlation (Fan and Lv, 2008). Yet, the original SIS procedure mainly focused on linear models with the continuous response variable. Fan and Song (2010) also extended this method to generalized linear models by ranking the maximum marginal likelihood estimator (MMLE) or maximum marginal likelihood itself. In this dissertation, we consider extending the SIS procedure to high-dimensional generalized linear models with binary response variable. We propose a two-stage feature screening procedure for generalized linear models with a binary response based on point-biserial correlation. The point-biserial correlation is an estimate of the correlation between one continuous variable and one binary variable. The two-stage point-biserial sure independence screening (PB-SIS) can be implemented in a straightforward way as the original SIS procedure, but it targets more specifically on high-dimensional generalized linear models with the binary response variable. In the first stage, we perform the SIS procedure by using point-biserial correlation to reduce the high dimensionality of a model to a moderate size. In the second stage, we apply a regularization method, such as LASSO, SCAD, or MCP, to further select important variables and find the final spare model. We establish the sure screening property under certain conditions for the PB-SIS method for high-dimensional generalized linear models with the binary response variable. The sure independence property for PB-SIS shows that our proposed method can select all the important variables in the screened submodel with probability very close to one. We also conduct simulation studies for generalized linear models with binary response variable by generating data from different link functions. To evaluate the performance of our proposed method, we compare the proportion of submodel with size d that contains all the true predictors among 1000 simulations, P , and computing time for our proposed method with MMLE and Kolmogorov filter methods after the first stage screening. We also compare the performance of two-stage PB-SIS methods with different penalized methods by using different tuning parameter selection criteria. The simulation results demonstrate that PB-SIS outperforms the Kolmogorov filter methods in both the selection accuracy and computational cost in different settings and has almost the same selection accuracy as MMLE but with much lower computational cost. A real data application is given to illustrate the performance of the proposed two-stage PB-SIS method.
Author : Cristina Davino
Publisher : John Wiley & Sons
ISBN 13 : 111997528X
Total Pages : 288 pages
Book Rating : 4.1/5 (199 download)
Download or read book Quantile Regression written by Cristina Davino and published by John Wiley & Sons. This book was released on 2013-12-31 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. Delivers a balance between methodolgy and application Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.
Author : Hossein Moradi Rekabdarkolaee
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (982 download)
Download or read book Dimension Reduction and Variable Selection written by Hossein Moradi Rekabdarkolaee and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional data are becoming increasingly available as data collection technology advances. Over the last decade, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics, signal processing, and environmental studies. Statistical techniques such as dimension reduction and variable selection play important roles in high dimensional data analysis. Sufficient dimension reduction provides a way to find the reduced space of the original space without a parametric model. This method has been widely applied in many scientific fields such as genetics, brain imaging analysis, econometrics, environmental sciences, etc. in recent years. In this dissertation, we worked on three projects. The first one combines local modal regression and Minimum Average Variance Estimation (MAVE) to introduce a robust dimension reduction approach. In addition to being robust to outliers or heavy-tailed distribution, our proposed method has the same convergence rate as the original MAVE. Furthermore, we combine local modal base MAVE with a $L_1$ penalty to select informative covariates in a regression setting. This new approach can exhaustively estimate directions in the regression mean function and select informative covariates simultaneously, while being robust to the existence of possible outliers in the dependent variable. The second project develops sparse adaptive MAVE (saMAVE). SaMAVE has advantages over adaptive LASSO because it extends adaptive LASSO to multi-dimensional and nonlinear settings, without any model assumption, and has advantages over sparse inverse dimension reduction methods in that it does not require any particular probability distribution on \textbf{X}. In addition, saMAVE can exhaustively estimate the dimensions in the conditional mean function. The third project extends the envelope method to multivariate spatial data. The envelope technique is a new version of the classical multivariate linear model. The estimator from envelope asymptotically has less variation compare to the Maximum Likelihood Estimator (MLE). The current envelope methodology is for independent observations. While the assumption of independence is convenient, this does not address the additional complication associated with a spatial correlation. This work extends the idea of the envelope method to cases where independence is an unreasonable assumption, specifically multivariate data from spatially correlated process. This novel approach provides estimates for the parameters of interest with smaller variance compared to maximum likelihood estimator while still being able to capture the spatial structure in the data.
Author : Jia Wang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (127 download)
Download or read book Topics on Variable Selection in High-Dimensional Data written by Jia Wang and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection has been extensively studied in the last few decades as it provides a principled solution to high dimensionality arising in a broad spectrum of real applications, such as bioinformatics, health studies, social science and econometrics. This dissertation is concerned with variable selection for ultrahigh-dimensional data when the dimension is allowed to grow with the sample size or the network size at an exponential rate. We propose new Bayesian approaches to selecting variables under several model frameworks, including (1) partially linear models (2) static social network models with degree heterogeneity and (3) time-varying network models. Firstly for partially linear models, we develop a procedure which employs the difference-based method to reduce the impact from the estimation of the nonparametric component, and incorporates Bayesian subset modeling with diffusing prior (BSM-DP) to shrink the corresponding estimator in the linear component. Secondly, a class of network models where the connection probability depends on ultrahigh-dimensional nodal covariates (homophily) and node-specific popularity (degree heterogeneity) is considered. We propose a Bayesian method to select nodal features in both dense and sparse networks under a relaxed assumption on popularity parameters. To alleviate the computational burden for large sparse networks, we particularly develop another working model in which parameters are updated based on a dense sub-graph at each step. Lastly, we extend the static model to time-varying cases, where the connection probability at time t is modeled based on observed nodal attributes at time t and node-specific continuous-time baseline functions evaluated at time t. Those Bayesian proposals are shown to be analogous to a mixture of L0 and L2 penalized methods and work well in the setting of highly correlated predictors. Corresponding model selection consistency is studied for all aforementioned models, in the sense that the probability of the true model being selected converges to one asymptotically. The finite sample performance of the proposed models is further examined by simulation studies and analyses on social-media and financial datasets.
Author : Mahlet G. Tadesse
Publisher : CRC Press
ISBN 13 : 1000510255
Total Pages : 762 pages
Book Rating : 4.0/5 (5 download)
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 762 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
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:
Author : Joel Horowitz
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (931 download)
Download or read book Variable Selection and Estimation in High-dimensional Models written by Joel Horowitz and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models with high-dimensional covariates arise frequently in economics and other fields. Often, only a few covariates have important effects on the dependent variable. When this happens, the model is said to be sparse. In applications, however, it is not known which covariates are important and which are not. This paper reviews methods for discriminating between important and unimportant covariates with particular attention given to methods that discriminate correctly with probability approaching 1 as the sample size increases. Methods are available for a wide variety of linear, nonlinear, semiparametric, and nonparametric models. The performance of some of these methods in finite samples is illustrated through Monte Carlo simulations and an empirical example.
Author : Daniele Bianchi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book Dynamic Variable Selection in High-Dimensional Predictive Regressions written by Daniele Bianchi and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop methodology and theory for a general Bayesian approach towards dynamic variable selection in high-dimensional regression models with time-varying parameters. Specifically, we propose a variational inference scheme which features dynamic sparsity-inducing properties so that different subsets of "active'' predictors can be identified over different time periods. We compare our modeling framework against established static and dynamic variable selection methods both in simulation and within the context of two common problems in macroeconomics and finance: inflation forecasting and equity returns predictability. The results show that our approach helps to tease out more accurately the dynamic impact of different predictors over time. This translates into significant gains in terms of out-of-sample point and density forecasting accuracy. We believe our results highlight the importance of taking a dynamic approach towards variable selection for economic modeling and forecasting.
Author : Toshio Honda
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book Forward Variable Selection for Ultra-high Dimensional Quantile Regression Models written by Toshio Honda and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hassan Pazira
Publisher :
ISBN 13 : 9789036799539
Total Pages : 177 pages
Book Rating : 4.7/5 (995 download)
Download or read book High-dimensional Variable Selection for GLMs and Survival Models written by Hassan Pazira and published by . This book was released on 2017 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chi Chen
Publisher :
ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.:/5 (893 download)
Download or read book Variable Selection in High Dimensional Semi-varying Coefficienct Models written by Chi Chen and published by . This book was released on 2013 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mahlet G. Tadesse
Publisher : CRC Press
ISBN 13 : 1000510204
Total Pages : 491 pages
Book Rating : 4.0/5 (5 download)
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
Author : Vivian Wai Ying Ng
Publisher :
ISBN 13 :
Total Pages : 470 pages
Book Rating : 4.:/5 (34 download)
Download or read book Univariate and Bivariate Variable Selection in High Dimensional Data written by Vivian Wai Ying Ng and published by . This book was released on 2004 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shibasish Dasgupta
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (888 download)
Download or read book High Dimensional Inference and Variable Selection written by Shibasish Dasgupta and published by . This book was released on 2013 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three research projects. The first project focuses on asymptotic expansions of posteriors for generalized linear models (GLM) with canonical link functions when the number of regressors grows to infinity at a certain rate relative to the growth of the sample size. As a side result, we have also proved asymptotic normality of the maximum likelihood estimator in a high-dimensional GLM set up. The second project considers posterior consistency in the context of high dimensional variable selection using the Bayesian lasso algorithm. In a frequentist setting, consistency is perhaps the most basic property that we expect any reasonable estimator to achieve. However, in a Bayesian setting, consistency is often ignored or taken for granted, especially in more complex hierarchical Bayesian models. We have derived sufficient conditions for posterior consistency in the Bayesian lasso model (with orthogonal design), where the number of parameters grows with the sample size. The last part of my thesis proposes a new variable selection technique using the Kullback-Leibler (KL) divergence loss and establishes related asymptotic properties.
Author : Yiheng Liu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book Ultra High Dimension Variable Selection with Threshold Partial Correlations written by Yiheng Liu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With respect to variable selection in linear regression, partial correlation for normal models (Buhlmann, Kalisch and Maathuis, 2010), was a powerful alternative method to penalized least squares approaches (LASSO, SCAD, etc.). The method was improved by Li, Liu, Lou (2015) with the concept of threshold partial correlation (TPC) and extension to elliptical contoured dis- tributions. The TPC procedure is endowed with its dominant advantages over the simple partial correlation in high or ultrahigh dimensional cases (where the dimension of predictors increases in an exponential rate of the sample size). However, the convergence rate for TPC is not very satis- fying since it usually takes substantial amount of time for the procedure to reach the final solution, especially in high or even ultrahigh dimensional scenarios. Besides, the model assumptions on the TPC are too strong, which suggest the approach might not be conveniently used in practice. To address these two important issues, this dissertation puts forward an innovative model selection al- gorithm. It starts with an alternative definition of elliptical contoured distributions, which restricts the impact of the marginal kurtosis. This posts a relatively weaker condition for the validity of the model selection algorithm. Based on the simulation results, the new approach demonstrates not only competitive outcomes with established methods such as LASSO and SCAD, but also advan- tages in terms of computing efficiency. The idea of the algorithm is extended to survival data and nonparametric inference by exploring various measurements on correlations between the response variable and predictors.
