DOCSLIB.ORG

Bagging and the Bayesian Bootstrap

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bagging and the Bayesian Bootstrap Bagging and the Bayesian Bootstrap Merlise A. Clyde and Herbert K. H. Lee Institute of Statistics & Decision Sciences Duke University Durham, NC 27708 Abstract reduction in mean-squared prediction error for unsta- ble procedures. Bagging is a method of obtaining more ro- In this paper, we consider a Bayesian version of bag- bust predictions when the model class under ging based on Rubin’s Bayesian bootstrap (1981). consideration is unstable with respect to the This overcomes a technical difficulty with the usual data, i.e., small changes in the data can cause bootstrap in bagging, and it leads to a reduction the predicted values to change significantly. in variance over the bootstrap for certain classes of In this paper, we introduce a Bayesian ver- estimators. Another Bayesian approach for dealing sion of bagging based on the Bayesian boot- with unstable procedures is Bayesian model averaging strap. The Bayesian bootstrap resolves a the- (BMA) (Hoeting et al., 1999). In BMA, one fits sev- oretical problem with ordinary bagging and eral models to the data and makes predictions by tak- often results in more efficient estimators. We ing the weighted average of the predictions from each show how model averaging can be combined of the fitted models, where the weights are posterior within the Bayesian bootstrap and illustrate probabilities of models. We show that the Bayesian the procedure with several examples. bootstrap and Bayesian model averaging can be com- bined. We illustrate Bayesian bagging in a regression problem with variable selection and a highly influen- 1INTRODUCTION tial data point, a classification problem using logistic regression, and a CART model. In a typical prediction problem, there is a trade-offbe- tween bias and variance, in that after a certain amount of fitting, any increase in the precision of the fit will 2 BOOTSTRAPPING cause an increase in the prediction variance on future observations. Similarly, any reduction in the predic- Suppose we have a sample of size n,withobserved data Z ,...,Z where Z is a vector in p+1 and the tion variance causes an increase in the expected bias 1 n i R for future predictions. Breiman (1996a) introduced Zi are independent, identically distributed realizations bagging as a method of reducing the prediction vari- from some distribution F .Here is the class of ∈Fp+1 F ance without affecting the prediction bias. all distribution functions on .Theparameterof interest is a functional T (F )whereR T is a mapping Bagging is short for “Bootstrap AGGregatING” which from to or k in the case of vectored valued describes how it works. The idea is straightforward. functions,F forR example,R the p +1 dimensionalmeanof Instead of making predictions from a single model fit the distribution, µ = zdF. to the observed data, bootstrap samples are taken of the data, the model is fit to each sample, and the pre- In Efron’s bootstrap and! the Bayesian bootstrap, the dictions are averaged over all of the fitted models to get class of distribution functions is restricted to a para- metric model by restricting estimation to F , the bagged prediction. Breiman explains that bagging n ∈Fn works well for unstable modeling procedures, i.e. those where Fn is represented as for which the conclusions are sensitive to small changes n in the data, such as neural networks, classification and Fn = ωiδZi , i=1 regression trees (CART), and variable selection for re- " gression (Breiman, 1996b). He also gives a theoretical δZi is a degenerate probability measure at Zi,andωi explanation of how bagging works, demonstrating the is the weight associated with Z , ω 0, ω =1. i i ≥ i # In the bootstrap, the distribution of T (F )isob- variance under the ordinary bootstrap. This applies tained by repeatedly generating bootstrap replicates, directly for CART models; for other estimators that where one bootstrap replicate is a sample drawn with are not necessarily linear in the weights, in our ex- replacement of size n from Z1,...,Zn.Theboot- perience the Bayesian bootstrap has also empirically strap distribution of T (F )isbasedonconsideringall exhibited less variability than the ordinary bootstrap. (r) (r) We illustrate this reduction in the rat liver example. possible bootstrap replications T (Fn )whereωi in (r) Fn corresponds to the proportion of times Zi ap- (r) pears in the rth bootstrap replicate, with ωi tak- 4BAGGINGVIATHEBAYESIAN ing on values in 0, 1/n, . ., n/n .Forexample,the BOOTSTRAP bootstrap mean{ for the rth replicate} is calculated ˆ(r) n (r) Bagging is used primarily in prediction problems, and as Z = i=1 ωi Zi,andthebaggedestimateof the mean is the average over all bootstrap replicates, with that in mind we partition each Zi into a response R ˆ(r) # Y (which could be continuous or categorical) and a p r=1 Z /R,whereR is the number of bootstrap i replicates. Of course, one cannot usually consider all dimensional vector of input variables xi for predicting 2n 1 # Y .Inmatrixform,thedataareY =(y1,...,yn)′ with possible bootstrap samples, which is n− ,andbag- ging is often based on a much smaller set of bootstrap a n p matrix of covariates X with rows xi. $ % × replicates, say 25 to 50 (Breiman, 1996a). Under the nonparametric model for the data, the only unknown quantity is the distribution F ,ortheparam- 3 BAYESIAN BOOTSTRAP eters ω under the restricted class of distribution func- tions. The posterior distribution on ω induces a poste- The Bayesian bootstrap was introduced by Rubin rior distribution on a functional T (F )forpredictingY (1981) as a Bayesian analog of the original bootstrap. given X.Wefirstconsiderthecasewhereinterestisin Instead of drawing weights ωi from the discrete set regression-type estimates, then extend the procedure 0, 1 ,..., n ,theBayesianapproachtreatsthevector to allow for variable selection, nonlinear functions, cat- { n n } of weights ω in Fn as unknown parameters and derives egorical responses and model uncertainty. aposteriordistributionforω,andhenceT (F ). Rubin n 1 (1981) used a non-informative prior, i=1 ωi− ,which 4.1 LINEAR REGRESSION when combined with the multinomial likelihood for Z, leads to a Dirichlet(1,...,1) distribution& for the pos- For making predictions based on linear combinations terior distribution of ω.Theposteriordistributionof of Y ,weconsiderfunctionalsoftheform T (F )isestimatedbyMonteCarlomethods:generate ˆ 2 (b) β = T (F )=argmin Y Xβ dF (1) ω from a Dirichlet(1,...,1) distribution and then β || − || (b) (b) 'n calculate T (Fn )foreachsampleω .Theaverage 2 (b) =argmin ωi(yi xiβ) of T (Fn )overthesamplescorrespondstotheMonte β − Carlo estimate of the posterior mean of T (F )andcan i=1 "1 be viewed as a Bayesian analog of bagging. =(X′WX)− X′WY Although there are differences in interpretation, op- where W is a diagonal matrix of weights ω.Thevalues of βˆ,thatminimize(1)withtherestrictionto ,are erationally the ordinary bootstrap and Bayesian boot- Fn strap differ primarily in how the values of ω are drawn. equivalent to weighted leastsquaresestimatesusing As Rubin (1981) shows, the expected values of the weights ω. weights ω are equal to 1/n under both bootstrap meth- Operationally, Bayesian bagging (BB) proceeds by ods. As the expectations of the weights are the same, taking a sample ω(b),fromaDirichlet(1,...,1) distri- both ordinary bagging and Bayesian bagging will have bution, and then using weighted least squares to obtain the same expectation for functions T (F )thatarelin- n ˆ(b) (b) 1 (b) ear in the weights ω,suchasmeans.Therearesit- β =(X′W X)− X′W Y uations, which will be discussed later, where the or- where W (b) is a diagonal matrix of weights ω(b).Thisis dinary bootstrap distribution is not well defined, and repeated for b =1,...,B,whereB is the total number the two approaches may yield different answers. Both of Monte Carlo samples, to obtain the posterior distri- approaches also lead to the same correlation between bution of βˆ,andtheposteriordistributionofYˆ = Xβˆ weights. However, the variability of the weights ω or other functions of ω.LetYˆ (b) = Xβˆ(b).TheBB under the ordinary bootstrap is (n +1)/n times the estimate of Yˆ given X is the Monte Carlo average variance of ω under the Bayesian bootstrap. For lin- B 1 ear functionals, the variance of the estimate under the Yˆ = Yˆ (b) . (2) Bayesian bootstrap is therefore strictly less than the B "b=1 4.2 VARIABLE SELECTION 4.4 NEURAL NETWORKS AND OTHER NONLINEAR ESTIMATORS While linear regression is a stable procedure, where bagging does not lead to substantial improvements, For continuous responses, the linear predictor Xβ in variable selection is viewed as being unstable. The BB (1) can be replaced by nonlinear functions as in neu- procedure is modified to combine model selection with ral nets or generalized additive models. While we no parameter estimation, where for each sample of ω(b), longer have an explicit solution for βˆ(b),anycodefor one selects a model M (b) using an appropriate model fitting neural networks (or other nonlinear models) ˆ(b) selection criterion and then estimates βM under model that allows weights can be used to construct the BB ˆ (b) M (b).TheposteriordistributionforYˆ and the pos- predictions, where one substitutes Y using predic- terior mean are now based on multiple models where tions from the neural network in (2). For model aver- the BB estimate of Y given X is aging with neural networks with continuous responses, model probabilities based on (4-5) are still appropri- B 1 (r) ate. Yˆ = Yˆ B M b=1 " 4.5 EXPONENTIAL FAMILY MODELS, ˆ (r) ˆ(r) where YM = XM (r) βM is the prediction using de- GLMS AND CART sign matrix XM (r) based on model M.Althoughnot equivalent to Bayesian model averaging as described For continuous responses, linear regression predictions in Hoeting et al.
Load more

Recommended publications
  • Ranking and Automatic Selection of Machine Learning Models Abstract Sandro Feuz
    Technical Disclosure Commons Defensive Publications Series December 13, 2017 Ranking and automatic selection of machine learning models Abstract Sandro Feuz Victor Carbune Follow this and additional works at: http://www.tdcommons.org/dpubs_series Recommended Citation Feuz, Sandro and Carbune, Victor, "Ranking and automatic selection of machine learning models Abstract", Technical Disclosure Commons, (December 13, 2017) http://www.tdcommons.org/dpubs_series/982 This work is licensed under a Creative Commons Attribution 4.0 License. This Article is brought to you for free and open access by Technical Disclosure Commons. It has been accepted for inclusion in Defensive Publications Series by an authorized administrator of Technical Disclosure Commons. Feuz and Carbune: Ranking and automatic selection of machine learning models Abstra Ranking and automatic selection of machine learning models Abstract Generally, the present disclosure is directed to an API for ranking and automatic selection from competing machine learning models that can perform a particular task. In particular, in some implementations, the systems and methods of the present disclosure can include or otherwise leverage one or more machine-learned models to provide to a software application one or more machine learning models from different providers. The trained models are suited to a task or data type specified by the developer. The one or more models are selected from a registry of machine learning models, their task specialties, cost, and performance, such that the application specified cost and performance requirements are met. An application processor interface (API) maintains a registry of various machine learning models, their task specialties, costs and/or performances. A third-party developer can make a call to the API to select one or more machine learning models.
    [Show full text]
  • A Robust Deep Learning Approach for Spatiotemporal Estimation of Satellite AOD and PM2.5
    remote sensing Article A Robust Deep Learning Approach for Spatiotemporal Estimation of Satellite AOD and PM2.5 Lianfa Li 1,2,3 1 State Key Laboratory of Resources and Environmental Information Systems, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Datun Road, Beijing 100101, China; [email protected]; Tel.: +86-10-648888362 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Spatial Data Intelligence Lab Ltd. Liability Co., Casper, WY 82609, USA Received: 22 November 2019; Accepted: 7 January 2020; Published: 13 January 2020 Abstract: Accurate estimation of fine particulate matter with diameter 2.5 µm (PM ) at a high ≤ 2.5 spatiotemporal resolution is crucial for the evaluation of its health effects. Previous studies face multiple challenges including limited ground measurements and availability of spatiotemporal covariates. Although the multiangle implementation of atmospheric correction (MAIAC) retrieves satellite aerosol optical depth (AOD) at a high spatiotemporal resolution, massive non-random missingness considerably limits its application in PM2.5 estimation. Here, a deep learning approach, i.e., bootstrap aggregating (bagging) of autoencoder-based residual deep networks, was developed to make robust imputation of MAIAC AOD and further estimate PM2.5 at a high spatial (1 km) and temporal (daily) resolution. The base model consisted of autoencoder-based residual networks where residual connections were introduced to improve learning performance. Bagging of residual networks was used to generate ensemble predictions for better accuracy and uncertainty estimates. As a case study, the proposed approach was applied to impute daily satellite AOD and subsequently estimate daily PM2.5 in the Jing-Jin-Ji metropolitan region of China in 2015.
    [Show full text]
  • An Evaluation of Machine Learning Approaches to Natural Language Processing for Legal Text Classification
    Imperial College London Department of Computing An Evaluation of Machine Learning Approaches to Natural Language Processing for Legal Text Classification Supervisors: Author: Prof Alessandra Russo Clavance Lim Nuri Cingillioglu Submitted in partial fulfillment of the requirements for the MSc degree in Computing Science of Imperial College London September 2019 Contents Abstract 1 Acknowledgements 2 1 Introduction 3 1.1 Motivation .................................. 3 1.2 Aims and objectives ............................ 4 1.3 Outline .................................... 5 2 Background 6 2.1 Overview ................................... 6 2.1.1 Text classification .......................... 6 2.1.2 Training, validation and test sets ................. 6 2.1.3 Cross validation ........................... 7 2.1.4 Hyperparameter optimization ................... 8 2.1.5 Evaluation metrics ......................... 9 2.2 Text classification pipeline ......................... 14 2.3 Feature extraction ............................. 15 2.3.1 Count vectorizer .......................... 15 2.3.2 TF-IDF vectorizer ......................... 16 2.3.3 Word embeddings .......................... 17 2.4 Classifiers .................................. 18 2.4.1 Naive Bayes classifier ........................ 18 2.4.2 Decision tree ............................ 20 2.4.3 Random forest ........................... 21 2.4.4 Logistic regression ......................... 21 2.4.5 Support vector machines ...................... 22 2.4.6 k-Nearest Neighbours .......................
    [Show full text]
  • Predicting Construction Cost and Schedule Success Using Artificial
    Available online at www.sciencedirect.com International Journal of Project Management 30 (2012) 470–478 www.elsevier.com/locate/ijproman Predicting construction cost and schedule success using artificial neural networks ensemble and support vector machines classification models ⁎ Yu-Ren Wang , Chung-Ying Yu, Hsun-Hsi Chan Dept. of Civil Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung, 807, Taiwan Received 11 May 2011; received in revised form 2 August 2011; accepted 15 September 2011 Abstract It is commonly perceived that how well the planning is performed during the early stage will have significant impact on final project outcome. This paper outlines the development of artificial neural networks ensemble and support vector machines classification models to predict project cost and schedule success, using status of early planning as the model inputs. Through industry survey, early planning and project performance information from a total of 92 building projects is collected. The results show that early planning status can be effectively used to predict project success and the proposed artificial intelligence models produce satisfactory prediction results. © 2011 Elsevier Ltd. APM and IPMA. All rights reserved. Keywords: Project success; Early planning; Classification model; ANNs ensemble; Support vector machines 1. Introduction Menches and Hanna, 2006). In particular, researches have indi- cated that project definition in the early planning process is an im- In the past few decades, the researchers and industry prac- portant factor leading to project success (Le et al., 2010; Thomas titioners have recognized the potential impact of early plan- and Fernández, 2008; Younga and Samson, 2008). Based on ning to final project outcomes and started to put more these results, this research intends to further investigate this rela- emphasis on early planning process (Dvir, 2005; Gibson et tionship and to examine if the status of early planning can be used al., 2006; Hartman and Ashrafi, 2004).
    [Show full text]
  • A Taxonomy of Massive Data for Optimal Predictive Machine Learning and Data Mining Ernest Fokoue
    Rochester Institute of Technology RIT Scholar Works Articles 2013 A Taxonomy of Massive Data for Optimal Predictive Machine Learning and Data Mining Ernest Fokoue Follow this and additional works at: http://scholarworks.rit.edu/article Recommended Citation Fokoue, Ernest, "A Taxonomy of Massive Data for Optimal Predictive Machine Learning and Data Mining" (2013). Accessed from http://scholarworks.rit.edu/article/1750 This Article is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Articles by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. A Taxonomy of Massive Data for Optimal Predictive Machine Learning and Data Mining Ernest Fokoué Center for Quality and Applied Statistics Rochester Institute of Technology 98 Lomb Memorial Drive, Rochester, NY 14623, USA [email protected] Abstract Massive data, also known as big data, come in various ways, types, shapes, forms and sizes. In this paper, we propose a rough idea of a possible taxonomy of massive data, along with some of the most commonly used tools for handling each particular category of massiveness. The dimensionality p of the input space and the sample size n are usually the main ingredients in the characterization of data massiveness. The specific statistical machine learning technique used to handle a particular massive data set will depend on which category it falls in within the massiveness taxonomy. Large p small n data sets for instance require a different set of tools from the large n small p variety. Among other tools, we discuss Prepro- cessing, Standardization, Imputation, Projection, Regularization, Penalization, Compression, Reduction, Selection, Kernelization, Hybridization, Parallelization, Aggregation, Randomization, Replication, Se- quentialization.
    [Show full text]
  • A Comparison of Artificial Neural Networks and Bootstrap
    Journal of Risk and Financial Management Article A Comparison of Artificial Neural Networks and Bootstrap Aggregating Ensembles in a Modern Financial Derivative Pricing Framework Ryno du Plooy * and Pierre J. Venter Department of Finance and Investment Management, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa; [email protected] * Correspondence: [email protected] Abstract: In this paper, the pricing performances of two learning networks, namely an artificial neural network and a bootstrap aggregating ensemble network, were compared when pricing the Johannesburg Stock Exchange (JSE) Top 40 European call options in a modern option pricing framework using a constructed implied volatility surface. In addition to this, the numerical accuracy of the better performing network was compared to a Monte Carlo simulation in a separate numerical experiment. It was found that the bootstrap aggregating ensemble network outperformed the artificial neural network and produced price estimates within the error bounds of a Monte Carlo simulation when pricing derivatives in a multi-curve framework setting. Keywords: artificial neural networks; vanilla option pricing; multi-curve framework; collateral; funding Citation: du Plooy, Ryno, and Pierre J. Venter. 2021. A Comparison of Artificial Neural Networks and Bootstrap Aggregating Ensembles in 1. Introduction a Modern Financial Derivative Black and Scholes(1973) established the foundation for modern option pricing the- Pricing Framework. Journal of Risk ory by showing that under certain ideal market conditions, it is possible to derive an and Financial Management 14: 254. analytically tractable solution for the price of a financial derivative. Industry practition- https://doi.org/10.3390/jrfm14060254 ers however quickly discovered that certain assumptions underlying the Black–Scholes (BS) model such as constant volatility and the existence of a unique risk-free interest rate Academic Editor: Jakub Horak were fundamentally flawed.
    [Show full text]
  • Tensor Ensemble Learning for Multidimensional Data
    Tensor Ensemble Learning for Multidimensional Data Ilia Kisil1, Ahmad Moniri1, and Danilo P. Mandic1 1Electrical and Electronic Engineering Department, Imperial College London, SW7 2AZ, UK, E-mails: fi.kisil15, ahmad.moniri13, [email protected] Abstract In big data applications, classical ensemble learning is typically infeasible on the raw input data and dimensionality reduction techniques are necessary. To this end, novel framework that generalises classic flat-view ensemble learning to multidimensional tensor- valued data is introduced. This is achieved by virtue of tensor decompositions, whereby the proposed method, referred to as tensor ensemble learning (TEL), decomposes every input data sample into multiple factors which allows for a flexibility in the choice of multiple learning algorithms in order to improve test performance. The TEL framework is shown to naturally compress multidimensional data in order to take advantage of the inherent multi-way data structure and exploit the benefit of ensemble learning. The proposed framework is verified through the application of Higher Order Singular Value Decomposition (HOSVD) to the ETH-80 dataset and is shown to outperform the classical ensemble learning approach of bootstrap aggregating. Index terms| Tensor Decomposition, Multidimensional Data, Ensemble Learning, Clas- sification, Bagging 1 Introduction The phenomenon of the wisdom of the crowd has been known for a very long time and was originally formulated by Aristotle. It simply states that the collective answer of a group of peo- ple to questions related to common world knowledge, spatial reasoning, and general estimation tasks, is often superior to the judgement of a particular person within this group. With the advent of computer, the machine learning community have adopted this concept under the framework of ensemble learning [1].
    [Show full text]
  • Some Enhancements of Decision Tree Bagging
    Some Enhancements of Decision Tree Bagging Pierre Geurts University of Li`ege, Department of Electrical and Computer Engineering Institut Montefiore, Sart-Tilman B28, B4000 Li`ege, Belgium [email protected] Abstract. This paper investigates enhancements of decision tree bag- ging which mainly aim at improving computation times, but also accu- racy. The three questions which are reconsidered are: discretization of continuous attributes, tree pruning, and sampling schemes. A very sim- ple discretization procedure is proposed, resulting in a dramatic speedup without significant decrease in accuracy. Then a new method is pro- posed to prune an ensemble of trees in a combined fashion, which is significantly more effective than individual pruning. Finally, different re- sampling schemes are considered leading to different CPU time/accuracy tradeoffs. Combining all these enhancements makes it possible to apply tree bagging to very large datasets, with computational performances similar to single tree induction. Simulations are carried out on two syn- thetic databases and four real-life datasets. 1 Introduction The bias/variance tradeoff is a well known problem in machine learning. Bias relates to the systematic error component, whereas variance relates to the varia- bility resulting from the randomness of the learning sample and both contribute to prediction errors. Decision tree induction [5] is among the machine learning methods which present the higher variance. This variance is mainly due to the recursive partitioning of the input space, which is highly unstable with respect to small perturbations of the learning set. Bagging [2] consists in aggregating predictions produced by several classifiers generated from different bootstrap samples drawn from the original learning set.
    [Show full text]
  • Bootstrap Aggregating and Random Forest
    Bootstrap Aggregating and Random Forest Tae-Hwy Lee, Aman Ullah and Ran Wang Abstract Bootstrap Aggregating (Bagging) is an ensemble technique for improving the robustness of forecasts. Random Forest is a successful method based on Bagging and Decision Trees. In this chapter, we explore Bagging, Random Forest, and their variants in various aspects of theory and practice. We also discuss applications based on these methods in economic forecasting and inference. 1 Introduction The last 30 years witnessed the dramatic developments and applications of Bag- ging and Random Forests. The core idea of Bagging is model averaging. Instead of choosing one estimator, Bagging considers a set of estimators trained on the boot- strap samples and then takes the average output of them, which is helpful in improv- ing the robustness of an estimator. In Random Forest, we grow a set of Decision Trees to construct a ‘forest’ to balance the accuracy and robustness for forecasting. This chapter is organized as follows. First, we introduce Bagging and some vari- ants. Second, we discuss Decision Trees in details. Then, we move to Random Forest which is one of the most attractive machine learning algorithms combining Decision Trees and Bagging. Finally, several economic applications of Bagging and Random Forest are discussed. As we mainly focus on the regression problems rather than classification problems, the response y is a real number, unless otherwise mentioned. Tae-Hwy Lee Department of Economics, University of California, Riverside, e-mail: [email protected] Aman Ullah Department of Economics, University of California, Riverside, e-mail: [email protected] Ran Wang Department of Economics, University of California, Riverside, e-mail: ran.wang@email.
    [Show full text]
  • Accelerated Training of Bootstrap Aggregation-Based Deep Information Extraction Systems from Cancer Pathology Reports
    HHS Public Access Author manuscript Author ManuscriptAuthor Manuscript Author J Biomed Manuscript Author Inform. Author Manuscript Author manuscript; available in PMC 2021 July 13. Published in final edited form as: J Biomed Inform. 2020 October ; 110: 103564. doi:10.1016/j.jbi.2020.103564. Accelerated training of bootstrap aggregation-based deep information extraction systems from cancer pathology reports Hong-Jun Yoona,*, Hilda B. Klaskya, John P. Gounleya, Mohammed Alawada, Shang Gaoa, Eric B. Durbinb, Xiao-Cheng Wuc, Antoinette Stroupd, Jennifer Dohertye, Linda Coylef, Lynne Penberthyg, J. Blair Christiana, Georgia D. Tourassih aComputational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, United States of America bCollege of Medicine, University of Kentucky, Lexington, KY 40536, United States of America cLouisiana Tumor Registry, Louisiana State University Health Sciences Center, School of Public Health, New Orleans, LA 70112, United States of America dNew Jersey State Cancer Registry, Rutgers Cancer Institute of New Jersey, New Brunswick, NJ, 08901, United States of America eUtah Cancer Registry, University of Utah School of Medicine, Salt Lake City, UT 84132, United States of America fInformation Management Services Inc., Calverton, MD 20705, United States of America gSurveillance Research Program, Division of Cancer Control and Population Sciences, National Cancer Institute, Bethesda, MD 20814, United States of America hNational Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37830, United States of America Abstract Objective: In machine learning, it is evident that the classification of the task performance increases if bootstrap aggregation (bagging) is applied. However, the bagging of deep neural networks takes tremendous amounts of computational resources and training time.
    [Show full text]
  • Convolutional Neural Network-Based Ensemble Methods to Recognize Bangla Handwritten Character
    Convolutional neural network-based ensemble methods to recognize Bangla handwritten character Mir Moynuddin Ahmed Shibly*, Tahmina Akter Tisha*, Tanzina Akter Tani and Shamim Ripon Department of Computer Science and Engineering, East West University, Dhaka, Bangladesh * These authors contributed equally to this work. ABSTRACT In this era of advancements in deep learning, an autonomous system that recognizes handwritten characters and texts can be eventually integrated with the software to provide better user experience. Like other languages, Bangla handwritten text extraction also has various applications such as post-office automation, signboard recognition, and many more. A large-scale and efficient isolated Bangla handwritten character classifier can be the first building block to create such a system. This study aims to classify the handwritten Bangla characters. The proposed methods of this study are divided into three phases. In the first phase, seven convolutional neural networks i.e., CNN-based architectures are created. After that, the best performing CNN model is identified, and it is used as a feature extractor. Classifiers are then obtained by using shallow machine learning algorithms. In the last phase, five ensemble methods have been used to achieve better performance in the classification task. To systematically assess the outcomes of this study, a comparative analysis of the performances has also been carried out. Among all the methods, the stacked generalization ensemble method has achieved better performance than the other implemented methods. It has obtained accuracy, precision, and recall of 98.68%, 98.69%, and 98.68%, respectively on the Ekush dataset. Moreover, the use of CNN architectures and ensemble methods in large-scale Bangla handwritten character fi 22 January 2021 recognition has also been justi ed by obtaining consistent results on the Submitted fi Accepted 6 May 2021 BanglaLekha-Isolated dataset.
    [Show full text]
  • SAS Visual Data Mining and Machine Learning Procedures
    SAS® Visual Data Mining and Machine Learning 8.1 Data Mining and Machine Learning Procedures The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2016. SAS® Visual Data Mining and Machine Learning 8.1: Data Mining and Machine Learning Procedures. Cary, NC: SAS Institute Inc. SAS® Visual Data Mining and Machine Learning 8.1: Data Mining and Machine Learning Procedures Copyright © 2016, SAS Institute Inc., Cary, NC, USA All Rights Reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others’ rights is appreciated. U.S. Government License Rights; Restricted Rights: The Software and its documentation is commercial computer software developed at private expense and is provided with RESTRICTED RIGHTS to the United States Government. Use, duplication, or disclosure of the Software by the United States Government is subject to the license terms of this Agreement pursuant to, as applicable, FAR 12.212, DFAR 227.7202-1(a), DFAR 227.7202-3(a), and DFAR 227.7202-4, and, to the extent required under U.S.
    [Show full text]