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Minimax Estimation With Structured Data
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Book Synopsis Minimax Estimation with Structured Data by : Jan-Christian Klaus Hütter
Download or read book Minimax Estimation with Structured Data written by Jan-Christian Klaus Hütter and published by . This book was released on 2019 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistics often deals with high-dimensional problems that suffer from poor performance guarantees and from the curse of dimensionality. In this thesis, we study how structural assumptions can be used to overcome these difficulties in several estimation problems, spanning three different areas of statistics: shape-constrained estimation, causal discovery, and optimal transport. In the area of shape-constrained estimation, we study the estimation of matrices, first under the assumption of bounded total-variation (TV) and second under the assumption that the underlying matrix is Monge, or supermodular. While the first problem has a long history in image denoising, the latter structure has so far been mainly investigated in the context of computer science and optimization. For TV denoising, we provide fast rates that are adaptive to the underlying edge sparsity of the image, as well as generalizations to other graph structures, including higher-dimensional grid-graphs. For the estimation of Monge matrices, we give near minimax rates for their estimation, including the case where latent permutations act on the rows and columns of the matrix. In the latter case, we also give two computationally efficient and consistent estimators. Moreover, we show how to obtain estimation rates in the related problem of estimating continuous totally positive distributions in 2D. In the area of causal discovery, we investigate a linear cyclic causal model and give an estimator that is near minimax optimal for causal graphs of bounded in-degree. In the area of optimal transport, we introduce the notion of the transport rank of a coupling and provide empirical and theoretical evidence that it can be used to significantly improve rates of estimation of Wasserstein distances and optimal transport plans. Finally, we give near minimax optimal rates for the estimation of smooth optimal transport maps based on a wavelet regularization of the semi-dual objective.
Book Synopsis Minimax Estimation of the Mode of Functional Data by : Dennis Müller
Download or read book Minimax Estimation of the Mode of Functional Data written by Dennis Müller and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the mode of a distribution defined on a function space, e.g. the space of integrable functions. We give a definition of the mode using small ball probabilities. We use entropy methods, e.g. finite covers, to define an estimator of the mode and to deduce its asymptotic behaviour. We show strong consistency and continue to derive the optimal rate of convergence over a class of distributions whose modes are contained in a totally bounded subset of the function space.eng
Book Synopsis Minimax Estimation by : Workshop on Linear Minimax Estimation - Theory and Practice
Download or read book Minimax Estimation written by Workshop on Linear Minimax Estimation - Theory and Practice and published by . This book was released on 1996 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotically Local Minimax Estimation of Infinitely Smooth Density with Censored Data by : E. N. Belitser
Download or read book Asymptotically Local Minimax Estimation of Infinitely Smooth Density with Censored Data written by E. N. Belitser and published by . This book was released on 1996 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation in Regression and Random Censorship Models by : Eduard N. Belitser
Download or read book Minimax Estimation in Regression and Random Censorship Models written by Eduard N. Belitser and published by . This book was released on 2000 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robustness in Data Analysis by : Georgy L. Shevlyakov
Download or read book Robustness in Data Analysis written by Georgy L. Shevlyakov and published by Walter de Gruyter. This book was released on 2011-12-07 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Book Synopsis Ten Lectures on Statistical and Structural Pattern Recognition by : M.I. Schlesinger
Download or read book Ten Lectures on Statistical and Structural Pattern Recognition written by M.I. Schlesinger and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface to the English edition This monograph Ten Lectur,es on Statistical and Structural Pattern Recognition uncovers the close relationship between various well known pattern recognition problems that have so far been considered independent. These relationships became apparent when formal procedures addressing not only known prob lems but also their generalisations were discovered. The generalised problem formulations were analysed mathematically and unified algorithms were found. The book unifies of two main streams ill pattern recognition-the statisti cal a11d structural ones. In addition to this bridging on the uppermost level, the book mentions several other unexpected relations within statistical and structural methods. The monograph is intended for experts, for students, as well as for those who want to enter the field of pattern recognition. The theory is built up from scratch with almost no assumptions about any prior knowledge of the reader. Even when rigorous mathematical language is used we make an effort to keep the text easy to comprehend. This approach makes the book suitable for students at the beginning of their scientific career. Basic building blocks are explained in a style of an accessible intellectual exercise, thus promoting good practice in reading mathematical text. The paradoxes, beauty, and pitfalls of scientific research are shown on examples from pattern recognition. Each lecture is amended by a discussion with an inquisitive student that elucidates and deepens the explanation, providing additional pointers to computational procedures and deep rooted errors.
Book Synopsis Minimax Estimation with Side Conditions by : Michael William Trosset
Download or read book Minimax Estimation with Side Conditions written by Michael William Trosset and published by . This book was released on 1983 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Minimax Parameter Estimation with Loss Functions That Exhibit a Product Structure by : David John Stelte
Download or read book On Minimax Parameter Estimation with Loss Functions That Exhibit a Product Structure written by David John Stelte and published by . This book was released on 1973 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report treats minimax parameter estimation problems. Chapters 1 and 2 contain introductory material. Chapter 3 deals with several parameter estimation problems.
Book Synopsis Kernels for Structured Data by : Thomas Grtner
Download or read book Kernels for Structured Data written by Thomas Grtner and published by World Scientific. This book was released on 2008 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique treatment of an important area of machine learning and answers the question of how kernel methods can be applied to structured data. Kernel methods are a class of state-of-the-art learning algorithms that exhibit excellent learning results in several application domains. Originally, kernel methods were developed with data in mind that can easily be embedded in a Euclidean vector space. Much real-world data does not have this property but is inherently structured. An example of such data, often consulted in the book, is the (2D) graph structure of molecules formed by their atoms and bonds. The book guides the reader from the basics of kernel methods to advanced algorithms and kernel design for structured data. It is thus useful for readers who seek an entry point into the field as well as experienced researchers.
Book Synopsis Minimax Estimation with Respect to Restricted Parameter Sets by : Soebanar
Download or read book Minimax Estimation with Respect to Restricted Parameter Sets written by Soebanar and published by . This book was released on 1987 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation for Bounded Parameters by : Sherif Farouk Niazi Ali
Download or read book Minimax Estimation for Bounded Parameters written by Sherif Farouk Niazi Ali and published by . This book was released on 2010 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Structural Analysis by : Anatoly Perelmuter
Download or read book Numerical Structural Analysis written by Anatoly Perelmuter and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: To our sons, Mike, Andrew, Alex, who did not inherit their fathers' level of interest in applied mechanics, but who became sophisticated in software development and in this regard surpassed their parents. A.P., V.S. Hard times came, the god5 got angry. Children do not behave themselves and everybody wishes to write a book. Ancient Babylonian inscription X Preface Preface to the English Edition The book you are reading is a translation from Russian into English. Within a pretty short term this book saw two editions in Russian. The authors received in spiring responses from readers that both stimulated our continuing and improving this work and made sure it would not be in vain of us to try to multiply our readers by covering the English-speaking engineering community. When we prepared the present edition, we took into account interests of the Western readers, so we had to make some changes to our text published earlier. These changes include the following aspects. First, we excluded a lot of references and discussions regarding Russian engi neering codes. It seems to us those are of no real interest for Western engineers oriented at Eurocode or national construction design regulations.
Book Synopsis Minimax Estimation and Model Identification for High-dimensional Regression by : Zhan Wang
Download or read book Minimax Estimation and Model Identification for High-dimensional Regression written by Zhan Wang and published by . This book was released on 2012 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Alexandre B. Tsybakov Publisher :Springer Science & Business Media ISBN 13 :0387790527 Total Pages :222 pages Book Rating :4.3/5 (877 download)
Book Synopsis Introduction to Nonparametric Estimation by : Alexandre B. Tsybakov
Download or read book Introduction to Nonparametric Estimation written by Alexandre B. Tsybakov and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field.
Book Synopsis Minimax Estimation of the Mean of a Normal Distribution Subject to Doing Well at a Point by :
Download or read book Minimax Estimation of the Mean of a Normal Distribution Subject to Doing Well at a Point written by and published by . This book was released on 1982 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation on Subsets of Parameters by : Zakhar G. Maymin
Download or read book Minimax Estimation on Subsets of Parameters written by Zakhar G. Maymin and published by . This book was released on 1981 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
