Methods and Theory for Nonparametric Inference In High-dimensional Settings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods and Theory for Nonparametric Inference In High-dimensional Settings write by Yunhua Xiang. This book was released on 2021. Methods and Theory for Nonparametric Inference In High-dimensional Settings available in PDF, EPUB and Kindle. This dissertation addresses nonparametric estimation and inference problems of graphical modeling, linear association assessment, and matrix completion. First, we introduce a flexible framework for nonparametric graphical modeling. We propose three nonparametric measures of conditional dependence, which have theoretically optimal estimators that allow incorporation of flexible machine learning techniques and yield wald-type confidence intervals. In the second project, we propose a nonparametric parameter to measure the linear association between the outcome and explanatory variables. This parameter is always explicitly defined even when the true relationship is nonlinear and is equivalent with the regression coefficient under a linear model space. Thus, its estimator can be a more robust alternative to the standard model-based techniques to estimate the coefficients of a linear model. In the final project, we theoretically show that nuclear-norm penalization used for recovering low-rank matrices, remains effective even when the underlying matrices are generated by a low-dimensional non-linear manifold. The convergence rate can be expressed as a function of the size of the matrix, as well as the smoothness and dimension of the manifold, which is minimax optimal (up to a log term).
Nonparametric Inference for High Dimensional Data
Nonparametric Inference for High Dimensional Data - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonparametric Inference for High Dimensional Data write by Subhadeep Mukhopadhyay. This book was released on 2013. Nonparametric Inference for High Dimensional Data available in PDF, EPUB and Kindle. Learning from data, especially 'Big Data', is becoming increasingly popular under names such as Data Mining, Data Science, Machine Learning, Statistical Learning and High Dimensional Data Analysis. In this dissertation we propose a new related field, which we call 'United Nonparametric Data Science' - applied statistics with "just in time" theory. It integrates the practice of traditional and novel statistical methods for nonparametric exploratory data modeling, and it is applicable to teaching introductory statistics courses that are closer to modern frontiers of scientific research. Our framework includes small data analysis (combining traditional and modern nonparametric statistical inference), big and high dimensional data analysis (by statistical modeling methods that extend our unified framework for small data analysis). The first part of the dissertation (Chapters 2 and 3) has been oriented by the goal of developing a new theoretical foundation to unify many cultures of statistical science and statistical learning methods using mid-distribution function, custom made orthonormal score function, comparison density, copula density, LP moments and comoments. It is also examined how this elegant theory yields solution to many important applied problems. In the second part (Chapter 4) we extend the traditional empirical likelihood (EL), a versatile tool for nonparametric inference, in the high dimensional context. We introduce a modified version of the EL method that is computationally simpler and applicable to a large class of "large p small n" problems, allowing p to grow faster than n. This is an important step in generalizing the EL in high dimensions beyond the p ≤ n threshold where the standard EL and its existing variants fail. We also present detailed theoretical study of the proposed method. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/149430
Statistics for High-Dimensional Data
Statistics for High-Dimensional Data - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Statistics for High-Dimensional Data write by Peter Bühlmann. This book was released on 2011-06-08. Statistics for High-Dimensional Data available in PDF, EPUB and Kindle. 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.
Nonparametric Learning in High Dimensions
Nonparametric Learning in High Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonparametric Learning in High Dimensions write by Han Liu. This book was released on 2010. Nonparametric Learning in High Dimensions available in PDF, EPUB and Kindle. Abstract: "This thesis develops flexible and principled nonparametric learning algorithms to explore, understand, and predict high dimensional and complex datasets. Such data appear frequently in modern scientific domains and lead to numerous important applications. For example, exploring high dimensional functional magnetic resonance imaging data helps us to better understand brain functionalities; inferring large-scale gene regulatory network is crucial for new drug design and development; detecting anomalies in high dimensional transaction databases is vital for corporate and government security. Our main results include a rigorous theoretical framework and efficient nonparametric learning algorithms that exploit hidden structures to overcome the curse of dimensionality when analyzing massive high dimensional datasets. These algorithms have strong theoretical guarantees and provide high dimensional nonparametric recipes for many important learning tasks, ranging from unsupervised exploratory data analysis to supervised predictive modeling. In this thesis, we address three aspects: 1 Understanding the statistical theories of high dimensional nonparametric inference, including risk, estimation, and model selection consistency; 2 Designing new methods for different data-analysis tasks, including regression classification, density estimation, graphical model learning, multi-task learning, spatial-temporal adaptive learning; 3 Demonstrating the usefulness of these methods in scientific applications, including functional genomics, cognitive neuroscience, and meteorology. In the last part of this thesis, we also present the future vision of high dimensional and large-scale nonparametric inference."
High-Dimensional Statistics
High-Dimensional Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High-Dimensional Statistics write by Martin J. Wainwright. This book was released on 2019-02-21. High-Dimensional Statistics available in PDF, EPUB and Kindle. A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
