The Solution Path of the Generalized Lasso

The Solution Path of the Generalized Lasso

Author: Ryan Joseph Tibshirani

Publisher: Stanford University

Published: 2011

Total Pages: 95

ISBN-13:

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We present a path algorithm for the generalized lasso problem. This problem penalizes the l1 norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which facilitates computation and conceptual understanding of the path. For D=I (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary D, we derive an unbiased estimate of the degrees of freedom of the generalized lasso fit. This estimate turns out to be quite intuitive in many applications.


The Solution Path of the Generalized Lasso

The Solution Path of the Generalized Lasso

Author: Ryan Joseph Tibshirani

Publisher:

Published: 2011

Total Pages:

ISBN-13:

DOWNLOAD EBOOK

We present a path algorithm for the generalized lasso problem. This problem penalizes the l1 norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which facilitates computation and conceptual understanding of the path. For D=I (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary D, we derive an unbiased estimate of the degrees of freedom of the generalized lasso fit. This estimate turns out to be quite intuitive in many applications.


Intelligent Decision Technologies

Intelligent Decision Technologies

Author: Ireneusz Czarnowski

Publisher: Springer Nature

Published: 2023-05-29

Total Pages: 324

ISBN-13: 9819929695

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This book gathers selected papers from the KES-IDT 2023 Conference, held in Rome, Italy, on June 14–16, 2023. The book presents and discusses the latest research results and generates new ideas in the field of intelligent decision-making. The range of topics discussed is classification, prediction, data analysis, big data, data science, decision support, knowledge engineering and modeling in diverse areas such as finance, cybersecurity, economics, health, management and transportation. The problems in industry 4.0 and IoT are also addressed. The book contains several sections devoted to specific topics, such as intelligent data processing and its applications, high-dimensional data analysis and its applications, multi-criteria decision analysis—theory and applications, large-scale systems for intelligent decision-making and knowledge engineering, decision technologies and related topics in big data analysis of social and financial issues and decision-making theory for economics.


Statistics in Action

Statistics in Action

Author: Jerald F. Lawless

Publisher: CRC Press

Published: 2014-03-03

Total Pages: 382

ISBN-13: 1482236249

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Commissioned by the Statistical Society of Canada (SSC), Statistics in Action: A Canadian Outlook helps both general readers and users of statistics better appreciate the scope and importance of statistics. It presents the ways in which statistics is used while highlighting key contributions that Canadian statisticians are making to science, techno


Statistical Process Monitoring Using Advanced Data-Driven and Deep Learning Approaches

Statistical Process Monitoring Using Advanced Data-Driven and Deep Learning Approaches

Author: Fouzi Harrou

Publisher: Elsevier

Published: 2020-07-03

Total Pages: 330

ISBN-13: 0128193662

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Statistical Process Monitoring Using Advanced Data-Driven and Deep Learning Approaches tackles multivariate challenges in process monitoring by merging the advantages of univariate and traditional multivariate techniques to enhance their performance and widen their practical applicability. The book proceeds with merging the desirable properties of shallow learning approaches – such as a one-class support vector machine and k-nearest neighbours and unsupervised deep learning approaches – to develop more sophisticated and efficient monitoring techniques. Finally, the developed approaches are applied to monitor many processes, such as waste-water treatment plants, detection of obstacles in driving environments for autonomous robots and vehicles, robot swarm, chemical processes (continuous stirred tank reactor, plug flow rector, and distillation columns), ozone pollution, road traffic congestion, and solar photovoltaic systems. Uses a data-driven based approach to fault detection and attribution Provides an in-depth understanding of fault detection and attribution in complex and multivariate systems Familiarises you with the most suitable data-driven based techniques including multivariate statistical techniques and deep learning-based methods Includes case studies and comparison of different methods


Information Processing in Medical Imaging

Information Processing in Medical Imaging

Author: Gábor Székely

Publisher: Springer

Published: 2011-06-17

Total Pages: 806

ISBN-13: 3642220924

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This book constitutes the refereed proceedings of the 22nd International Conference on Information Processing in Medical Imaging, IPMI 2011, held at Kloster Irsee, Germany, in July 2011. The 24 full papers and 39 poster papers included in this volume were carefully reviewed and selected from 224 submissions. The papers are organized in topical sections on segmentation, statistical methods, shape analysis, registration, diffusion imaging, disease progression modeling, and computer aided diagnosis. The poster sessions deal with segmentation, shape analysis, statistical methods, image reconstruction, microscopic image analysis, computer aided diagnosis, diffusion imaging, functional brain analysis, registration and other related topics.


Handbook of Bayesian, Fiducial, and Frequentist Inference

Handbook of Bayesian, Fiducial, and Frequentist Inference

Author: James Berger

Publisher: CRC Press

Published: 2024-02-26

Total Pages: 421

ISBN-13: 1003837646

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The emergence of data science, in recent decades, has magnified the need for efficient methodology for analyzing data and highlighted the importance of statistical inference. Despite the tremendous progress that has been made, statistical science is still a young discipline and continues to have several different and competing paths in its approaches and its foundations. While the emergence of competing approaches is a natural progression of any scientific discipline, differences in the foundations of statistical inference can sometimes lead to different interpretations and conclusions from the same dataset. The increased interest in the foundations of statistical inference has led to many publications, and recent vibrant research activities in statistics, applied mathematics, philosophy and other fields of science reflect the importance of this development. The BFF approaches not only bridge foundations and scientific learning, but also facilitate objective and replicable scientific research, and provide scalable computing methodologies for the analysis of big data. Most of the published work typically focusses on a single topic or theme, and the body of work is scattered in different journals. This handbook provides a comprehensive introduction and broad overview of the key developments in the BFF schools of inference. It is intended for researchers and students who wish for an overview of foundations of inference from the BFF perspective and provides a general reference for BFF inference. Key Features: Provides a comprehensive introduction to the key developments in the BFF schools of inference Gives an overview of modern inferential methods, allowing scientists in other fields to expand their knowledge Is accessible for readers with different perspectives and backgrounds


Sparse Estimation with Math and R

Sparse Estimation with Math and R

Author: Joe Suzuki

Publisher: Springer Nature

Published: 2021-08-04

Total Pages: 234

ISBN-13: 9811614466

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The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of sparse estimation by considering math problems and building R programs. Each chapter introduces the notion of sparsity and provides procedures followed by mathematical derivations and source programs with examples of execution. To maximize readers’ insights into sparsity, mathematical proofs are presented for almost all propositions, and programs are described without depending on any packages. The book is carefully organized to provide the solutions to the exercises in each chapter so that readers can solve the total of 100 exercises by simply following the contents of each chapter. This textbook is suitable for an undergraduate or graduate course consisting of about 15 lectures (90 mins each). Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning by data scientists, machine learning engineers, and researchers interested in linear regression, generalized linear lasso, group lasso, fused lasso, graphical models, matrix decomposition, and multivariate analysis. This book is one of a series of textbooks in machine learning by the same author. Other titles are: - Statistical Learning with Math and R (https://www.springer.com/gp/book/9789811575679) - Statistical Learning with Math and Python (https://www.springer.com/gp/book/9789811578762) - Sparse Estimation with Math and Python


Sampling Theory, a Renaissance

Sampling Theory, a Renaissance

Author: Götz E. Pfander

Publisher: Birkhäuser

Published: 2015-12-08

Total Pages: 532

ISBN-13: 3319197495

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Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.


Mathematical Methods in Engineering

Mathematical Methods in Engineering

Author: Kenan Taş

Publisher: Springer

Published: 2018-08-02

Total Pages: 266

ISBN-13: 331990972X

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This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.