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2275 results in Pattern Recognition and Machine Learning

Page 80 of 114

  • Preface

  • Jianfeng Yao, The University of Hong Kong, Shurong Zheng, Zhidong Bai
  • Book:
    Large Sample Covariance Matrices and High-Dimensional Data Analysis
    Published online:
    05 April 2015
    Print publication:
    26 March 2015, pp xiii-xiv

  • Summary

    Dempster (1958, 1960) proposed a non-exact test for the two-sample significance test when the dimension of data is larger than the degrees of freedom. He raised the question of what statisticians should do if traditional multivariate statistical theory does not apply when the dimension of data is too large. Later, Bai and Saranadasa (1996) found that even when traditional approaches can be applied, they are much less powerful than the non-exact test when the dimension of data is large. This raised another question of how classical multivariate statistical procedures could be adapted and improved when the data dimension is large. These problems have attracted considerable attention since the middle of the first decade of this century. Efforts towards solving these problems have been made along two directions: the first is to propose special statistical procedures to solve ad hoc large-dimensional statistical problems where traditional multivariate statistical procedures are inapplicable or perform poorly, for some specific large-dimensional hypotheses. The family of various non-exact tests follows this approach. The second direction, following the work of Bai et al. (2009a), is to make systematic corrections to the classical multivariate statistical procedures so that the effect of large dimension is overcome. This goal is achieved by employing new and powerful asymptotic tools borrowed from the theory of random matrices, such as the central limit theorems in Bai and Silverstein (2004) and Zheng (2012).

    Recently, research along these two directions has become very active in response to an increasingly important need for analysis of massive and large-dimensional data. Indeed, such “big data” are nowadays routinely collected owing to rapid advances in computer-based or web-based commerce and data-collection technology.

    To accommodate such need, this monograph collects existing results along the aforementioned second direction of large-dimensional data analysis. In Chapters 2 and 3, the core of fundamental results from random matrix theory about sample covariance matrices and random Fisher matrices is presented in detail. Chapters 4–12 collect large-dimensional statistical problems in which the classical large sample methods fail and the new asymptotic methods, based on the fundamental results of the preceding chapters, provide a valuable remedy.

Pattern Recognition and Neural Networks
  • Brian D. Ripley
  • Published online:
    05 August 2014
    Print publication:
    18 January 1996
  • This 1996 book is a reliable account of the statistical framework for pattern recognition and machine learning. With unparalleled coverage and a wealth of case-studies this book gives valuable insight into both the theory and the enormously diverse applications (which can be found in remote sensing, astrophysics, engineering and medicine, for example). So that readers can develop their skills and understanding, many of the real data sets used in the book are available from the author's website: www.stats.ox.ac.uk/~ripley/PRbook/. For the same reason, many examples are included to illustrate real problems in pattern recognition. Unifying principles are highlighted, and the author gives an overview of the state of the subject, making the book valuable to experienced researchers in statistics, machine learning/artificial intelligence and engineering. The clear writing style means that the book is also a superb introduction for non-specialists.

Grammatical Inference
  • Learning Automata and Grammars
  • Colin de la Higuera
  • Published online:
    05 July 2014
    Print publication:
    01 April 2010
  • The problem of inducing, learning or inferring grammars has been studied for decades, but only in recent years has grammatical inference emerged as an independent field with connections to many scientific disciplines, including bio-informatics, computational linguistics and pattern recognition. This book meets the need for a comprehensive and unified summary of the basic techniques and results, suitable for researchers working in these various areas. In Part I, the objects of use for grammatical inference are studied in detail: strings and their topology, automata and grammars, whether probabilistic or not. Part II carefully explores the main questions in the field: What does learning mean? How can we associate complexity theory with learning? In Part III the author describes a number of techniques and algorithms that allow us to learn from text, from an informant, or through interaction with the environment. These concern automata, grammars, rewriting systems, pattern languages or transducers.

Independent Component Analysis
  • Principles and Practice
  • Edited by Stephen Roberts, Richard Everson
  • Published online:
    05 July 2014
    Print publication:
    01 March 2001
  • Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

Page 80 of 114