[PDF] Bayesian Learning For Parametric And Kernel Density Estimation eBook

Author : Estian Rademeyer
Publisher :
Page : 246 pages
File Size : 30,98 MB
Release : 2017
Category : Bayesian statistical decision theory
ISBN :

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This dissertation investigates the performance of two-class classi cation credit scoring data sets with low default ratios. The standard two-class parametric Gaussian and naive Bayes (NB), as well as the non-parametric Parzen classi ers are extended, using Bayes' rule, to include either a class imbalance or a Bernoulli prior. This is done with the aim of addressing the low default probability problem. Furthermore, the performance of Parzen classi cation with Silverman and Minimum Leave-one-out Entropy (MLE) Gaussian kernel bandwidth estimation is also investigated. It is shown that the non-parametric Parzen classi ers yield superior classi cation power. However, there is a longing for these non-parametric classi ers to posses a predictive power, such as exhibited by the odds ratio found in logistic regression (LR). The dissertation therefore dedicates a section to, amongst other things, study the paper entitled \Model-Free Objective Bayesian Prediction" (Bernardo 1999). Since this approach to Bayesian kernel density estimation is only developed for the univariate and the uncorrelated multivariate case, the section develops a theoretical multivariate approach to Bayesian kernel density estimation. This approach is theoretically capable of handling both correlated as well as uncorrelated features in data. This is done through the assumption of a multivariate Gaussian kernel function and the use of an inverse Wishart prior.

Author : Luc Devroye
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 13,19 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461301254

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Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Author : J.K. Ghosh
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 23,1 MB
Release : 2006-05-11
Category : Mathematics
ISBN : 0387226540

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This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.

Author : Jake VanderPlas
Publisher : "O'Reilly Media, Inc."
Page : 743 pages
File Size : 27,97 MB
Release : 2016-11-21
Category : Computers
ISBN : 1491912138

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For many researchers, Python is a first-class tool mainly because of its libraries for storing, manipulating, and gaining insight from data. Several resources exist for individual pieces of this data science stack, but only with the Python Data Science Handbook do you get them all—IPython, NumPy, Pandas, Matplotlib, Scikit-Learn, and other related tools. Working scientists and data crunchers familiar with reading and writing Python code will find this comprehensive desk reference ideal for tackling day-to-day issues: manipulating, transforming, and cleaning data; visualizing different types of data; and using data to build statistical or machine learning models. Quite simply, this is the must-have reference for scientific computing in Python. With this handbook, you’ll learn how to use: IPython and Jupyter: provide computational environments for data scientists using Python NumPy: includes the ndarray for efficient storage and manipulation of dense data arrays in Python Pandas: features the DataFrame for efficient storage and manipulation of labeled/columnar data in Python Matplotlib: includes capabilities for a flexible range of data visualizations in Python Scikit-Learn: for efficient and clean Python implementations of the most important and established machine learning algorithms

Author : Masashi Sugiyama
Publisher : Cambridge University Press
Page : 343 pages
File Size : 33,61 MB
Release : 2012-02-20
Category : Computers
ISBN : 0521190177

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This book introduces theories, methods and applications of density ratio estimation, a newly emerging paradigm in the machine learning community.