[PDF] Comparison Of Ridge Regression And Neural Networks In Modeling Multicollinear Data eBook

Author : Arun Bansal
Publisher :
Page : 28 pages
File Size : 33,26 MB
Release : 2008
Category :
ISBN :

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Under circumstances where data quality may vary (due to inaccuracies or lack of timeliness,for example), knowledge about the potential performance of alternate predictive models can help adecision maker to design a business value-maximizing information system. This paper examines a real-worldexample from the field of finance to illustrate a comparison of alternative modeling tools. Twomodeling alternatives are used in this example: regression analysis and neural network analysis. Thereare two main results: (1) Linear regression outperformed neural nets in terms of forecasting accuracy,but the opposite was true when we considered the business value of the forecast. (2) Neural net-basedforecasts tended to be more robust than linear regression forecasts as data accuracy degraded.Managerial implications for financial risk management of MBS portfolios are drawn from the results.

Author : A. K. Md. Ehsanes Saleh
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 27,75 MB
Release : 2019-01-08
Category : Mathematics
ISBN : 1118644522

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A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.

Author : Kristine Joy Carpio
Publisher : LAP Lambert Academic Publishing
Page : 88 pages
File Size : 14,9 MB
Release : 2011-05
Category : Neural networks (Computer science)
ISBN : 9783844327090

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One of the many problems encountered in coming up with a multiple linear regression model is the presence of severe multicollinearity in the data set. In this work, the focus is on the mathematics of multicollinearity -- what it is, what it does to the model, how it can be detected and combated. Aside from the classical methods, artificial neural networks were also employed to combat multicollinearity. Softwares such as Statistical Package for the Social Science (SPPS) Release 7.0 and 10.0 for Windows, MATLAB version 5.3 and Stuttgart Neural Network Simulator (SNNS) version 4.1 were used to carry out the massive computations.

Author : A. K. Md. Ehsanes Saleh
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 22,2 MB
Release : 2019-02-12
Category : Mathematics
ISBN : 1118644611

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A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.

Author : Greg Qi Liu
Publisher :
Page : pages
File Size : 47,70 MB
Release : 2011
Category : Linear models (Statistics)
ISBN : 9781124782492

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Linear forecasting models have played major roles in many applications for over a century. If error terms in models are normally distributed, linear models are capable of producing the most accurate forecasting results. The central limit theorem (CLT) provides theoretical support in applying linear models. During the last two decades, nonlinear models such as neural network models have gradually emerged as alternatives in modeling and forecasting real processes. In hydrology, neural networks have been applied to rainfall-runoff estimation as well as stream and peak flow forecasting. Successful nonlinear methods rely on the generalized central limit theorem (GCLT), which provides theoretical justifications in applying nonlinear methods to real processes in impulsive environments. This dissertation will attempt to predict the daily stream flow of White Clay Creek by making intensive comparisons of linear and nonlinear forecasting methods. Data are modeled and forecasted by seven linear and nonlinear methods: The random walk with drift method; the ordinary least squares (OLS) regression method; the time series Autoregressive Integrated Moving Average (ARIMA) method; the feed-forward neural network (FNN) method; the recurrent neural network (RNN) method; the hybrid OLS regression and feed-forward neural network (OLS-FNN) method; and the hybrid ARIMA and recurrent neural network (ARIMA-RNN) method. The first three methods are linear methods and the remaining four are nonlinear methods. The OLS-FNN method and the ARIMA-RNN method are two completely new nonlinear methods proposed in this dissertation. These two hybrid methods have three special features that distinguish them from any existing hybrid method available in literature: (1) using the OLS or ARIMA residuals as the targets of followed neural networks; (2) training two neural networks in parallel for each hybrid method by two objective functions (the minimum mean squares error function and the minimum mean absolute error function); and (3) using two trained neural networks to obtain respective forecasting results and then combining the forecasting results by a Bayesian Model Averaging technique. Final forecasts from hybrid methods have linear components resulting from the regression method or the ARIMA method and nonlinear components resulting from feed-forward neural networks or recurrent neural networks. Forecasting performances are evaluated by both root of mean square errors (RMSE) and mean absolute errors (MAE). Forecasting results indicate that linear methods provide the lowest RMSE forecasts when data are normally distributed and data lengths are long enough, while nonlinear methods provide a more consistent RMSE and MAE forecasts when data are non-normally distributed. Nonlinear neural network methods also provide lower RMSE and MAE forecasts than linear methods even for data that are normally distributed but with small data samples. The hybrid methods provide the most consistent RMSE and MAE forecasts for data that are non-normally distributed. The original flow is differenced and log differenced to get two differenced series: The difference series and the log difference series. These two series are then decomposed based on stochastic process decomposition theorems to produce two, three and four variables that are used as input variables in regression models and neural network models. By working on an increment series, either difference series or log difference series, instead of the original flow series, we get two benefits: First we have a clear time series model. The secondary benefit is from the fact that the original flow series is an autocorrelated series and an increment series is approximately an independently ditributed series. For an independently ditributed series, parameters such as Mean and Standard Deviation can be calculated easily. The length of data during modeling is in practice very important. Model parameters and forecasts are estimated from 30 data samples (1 month), 90 data samples (3 months), 180 data samples (6 months), and 360 data samples (1 year).

Author : Aurélien Géron
Publisher : "O'Reilly Media, Inc."
Page : 851 pages
File Size : 46,93 MB
Release : 2019-09-05
Category : Computers
ISBN : 149203259X

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Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how. By using concrete examples, minimal theory, and two production-ready Python frameworks—Scikit-Learn and TensorFlow—author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You’ll learn a range of techniques, starting with simple linear regression and progressing to deep neural networks. With exercises in each chapter to help you apply what you’ve learned, all you need is programming experience to get started. Explore the machine learning landscape, particularly neural nets Use Scikit-Learn to track an example machine-learning project end-to-end Explore several training models, including support vector machines, decision trees, random forests, and ensemble methods Use the TensorFlow library to build and train neural nets Dive into neural net architectures, including convolutional nets, recurrent nets, and deep reinforcement learning Learn techniques for training and scaling deep neural nets

Author : Tomas Hrycej
Publisher : Springer Nature
Page : 218 pages
File Size : 49,93 MB
Release : 2023-04-14
Category : Computers
ISBN : 3031190742

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This textbook aims to point out the most important principles of data analysis from the mathematical point of view. Specifically, it selected these questions for exploring: Which are the principles necessary to understand the implications of an application, and which are necessary to understand the conditions for the success of methods used? Theory is presented only to the degree necessary to apply it properly, striving for the balance between excessive complexity and oversimplification. Its primary focus is on principles crucial for application success. Topics and features: Focuses on approaches supported by mathematical arguments, rather than sole computing experiences Investigates conditions under which numerical algorithms used in data science operate, and what performance can be expected from them Considers key data science problems: problem formulation including optimality measure; learning and generalization in relationships to training set size and number of free parameters; and convergence of numerical algorithms Examines original mathematical disciplines (statistics, numerical mathematics, system theory) as they are specifically relevant to a given problem Addresses the trade-off between model size and volume of data available for its identification and its consequences for model parametrization Investigates the mathematical principles involves with natural language processing and computer vision Keeps subject coverage intentionally compact, focusing on key issues of each topic to encourage full comprehension of the entire book Although this core textbook aims directly at students of computer science and/or data science, it will be of real appeal, too, to researchers in the field who want to gain a proper understanding of the mathematical foundations “beyond” the sole computing experience.

Author : James R. Makin
Publisher :
Page : 105 pages
File Size : 50,91 MB
Release : 1981
Category :
ISBN :

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The technique of linear regression has been applied as a tool for predicting the cost of an item based on its most important characteristics. Often these characteristics (variables) tend to be highly intercorrelated (the data are said to exhibit multicollinearity) causing least squares estimates of the regression coefficients to be unstable and possibly leading to erroneous predictions. Ridge regression, a possible remedy for the problems caused by multicollinearity proposed by Hoerl and Kennard, is a biased estimation technique which reduces the variance of estimators and provides more precision (as measured by mean square error of the coefficients) than ordinary least squares (OLS) estimators. A comparison was made between these techniques to determine when ridge regression provides better cost equation coefficient estimates than OLS as a function of the degree of multicollinearity in the data, the number of predictor variables in the model, the degree of model fit (R2), and the amount of bias (k) of the estimate. A regression analysis of both sets showed that the degree of multicollinearity and amount of bias interact in explaining the major part of the improvement (degradation) in the mean square coefficient error.