Statistical Inference and Resampling Statistics
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Analysis of Imbalance Strategies Recommendation Using a Meta-Learning Approach
7th ICML Workshop on Automated Machine Learning (2020) Analysis of Imbalance Strategies Recommendation using a Meta-Learning Approach Afonso Jos´eCosta [email protected] CISUC, Department of Informatics Engineering, University of Coimbra, Portugal Miriam Seoane Santos [email protected] CISUC, Department of Informatics Engineering, University of Coimbra, Portugal Carlos Soares [email protected] Fraunhofer AICOS and LIACC, Faculty of Engineering, University of Porto, Portugal Pedro Henriques Abreu [email protected] CISUC, Department of Informatics Engineering, University of Coimbra, Portugal Abstract Class imbalance is known to degrade the performance of classifiers. To address this is- sue, imbalance strategies, such as oversampling or undersampling, are often employed to balance the class distribution of datasets. However, although several strategies have been proposed throughout the years, there is no one-fits-all solution for imbalanced datasets. In this context, meta-learning arises a way to recommend proper strategies to handle class imbalance, based on data characteristics. Nonetheless, in related work, recommendation- based systems do not focus on how the recommendation process is conducted, thus lacking interpretable knowledge. In this paper, several meta-characteristics are identified in order to provide interpretable knowledge to guide the selection of imbalance strategies, using Ex- ceptional Preferences Mining. The experimental setup considers 163 real-world imbalanced datasets, preprocessed with 9 well-known resampling algorithms. Our findings elaborate on the identification of meta-characteristics that demonstrate when using preprocessing algo- rithms is advantageous for the problem and when maintaining the original dataset benefits classification performance. 1. Introduction Class imbalance is known to severely affect the data quality. -
Memorial Resolution George Bernard Dantzig (1914–2005)
MEMORIAL RESOLUTION GEORGE BERNARD DANTZIG (1914–2005) George Bernard Dantzig, the C. A. Criley Professor of Transportation Sciences and Professor of Operations Research and of Computer Science, Emeritus, died at his campus home on May 13, 2005 at age 90. Born on November 8, 1914 in Portland, Oregon, George Dantzig was given the middle name “Bernard” as an expression of his parents’ hope that he would become a writer. This was not to be, even though late in his life George was engaged in writing a novel. Instead, George became a mathematician. He graduated from the University of Maryland with an A.B. in mathematics and physics (1936) and took his M.A. in mathematics from the University of Michigan (1938). After a two-year period at the Bureau of Labor Statistics, he enrolled in the doctoral program in mathematics at the University of California, Berkeley, with the intention of writing his dissertation on mathematical statistics under the supervision of Jerzy Neyman. Arriving late to one of Neyman’s lectures, George copied down two problem statements from the blackboard thinking they were a homework assignment. George found these problems challenging. After a while though, he was able to solve them both and turned them in to the professor. As it happened, the problems were not just exercises but open questions in the field. The solutions to these problems became the two independent parts of George’s doctoral dissertation. With the outbreak of World War II, George took a leave of absence from the doctoral program at Berkeley to join the U.S. -
The Meaning of Probability
CHAPTER 2 THE MEANING OF PROBABILITY INTRODUCTION by Glenn Shafer The meaning of probability has been debated since the mathematical theory of probability was formulated in the late 1600s. The five articles in this section have been selected to provide perspective on the history and present state of this debate. Mathematical statistics provided the main arena for debating the meaning of probability during the nineteenth and early twentieth centuries. The debate was conducted mainly between two camps, the subjectivists and the frequentists. The subjectivists contended that the probability of an event is the degree to which someone believes it, as indicated by their willingness to bet or take other actions. The frequentists contended that probability of an event is the frequency with which it occurs. Leonard J. Savage (1917-1971), the author of our first article, was an influential subjectivist. Bradley Efron, the author of our second article, is a leading contemporary frequentist. A newer debate, dating only from the 1950s and conducted more by psychologists and economists than by statisticians, has been concerned with whether the rules of probability are descriptive of human behavior or instead normative for human and machine reasoning. This debate has inspired empirical studies of the ways people violate the rules. In our third article, Amos Tversky and Daniel Kahneman report on some of the results of these studies. In our fourth article, Amos Tversky and I propose that we resolve both debates by formalizing a constructive interpretation of probability. According to this interpretation, probabilities are degrees of belief deliberately constructed and adopted on the basis of evidence, and frequencies are only one among many types of evidence. -
Notes on Jackknife
Stat 427/627 (Statistical Machine Learning, Baron) Notes on Jackknife Jackknife is an effective resampling method that was proposed by Morris Quenouille to estimate and reduce the bias of parameter estimates. 1.1 Jackknife resampling Resampling refers to sampling from the original sample S with certain weights. The original weights are (1/n) for each units in the sample, and the original empirical distribution is 1 mass at each observation x , i ∈ S ˆ i F = n 0 elsewhere Resampling schemes assign different weights. Jackknife re-assigns weights as follows, 1 mass at each observation x , i ∈ S, i =6 j ˆ i FJK = n − 1 0 elsewhere, including xj That is, Jackknife removes unit j from the sample, and the new jackknife sample is S(j) =(x1,...,xj−1, xj+1,...,xn). 1.2 Jackknife estimator ˆ ˆ ˆ Suppose we estimate parameter θ with an estimator θ = θ(x1,...,xn). The bias of θ is Bias(θˆ)= Eθ(θˆ) − θ. • How to estimate Bias(θˆ)? • How to reduce |Bias(θˆ)|? • If the bias is not zero, how to find an estimator with a smaller bias? For almost all reasonable and practical estimates, Bias(θˆ) → 0, as n →∞. Then, it is reasonable to assume a power series of the type a a a E (θˆ)= θ + 1 + 2 + 3 + ..., θ n n2 n3 with some coefficients {ak}. 1 1.2.1 Delete one Based on a Jackknife sample S(j), we compute the Jackknife version of the estimator, ˆ ˆ ˆ θ(j) = θ(S(j))= θ(x1,...,xj−1, xj+1,...,xn), whose expected value admits representation a a E (θˆ )= θ + 1 + 2 + ... -
Particle Filtering-Based Maximum Likelihood Estimation for Financial Parameter Estimation
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Spiral - Imperial College Digital Repository Particle Filtering-based Maximum Likelihood Estimation for Financial Parameter Estimation Jinzhe Yang Binghuan Lin Wayne Luk Terence Nahar Imperial College & SWIP Techila Technologies Ltd Imperial College SWIP London & Edinburgh, UK Tampere University of Technology London, UK London, UK [email protected] Tampere, Finland [email protected] [email protected] [email protected] Abstract—This paper presents a novel method for estimating result, which cannot meet runtime requirement in practice. In parameters of financial models with jump diffusions. It is a addition, high performance computing (HPC) technologies are Particle Filter based Maximum Likelihood Estimation process, still new to the finance industry. We provide a PF based MLE which uses particle streams to enable efficient evaluation of con- straints and weights. We also provide a CPU-FPGA collaborative solution to estimate parameters of jump diffusion models, and design for parameter estimation of Stochastic Volatility with we utilise HPC technology to speedup the estimation scheme Correlated and Contemporaneous Jumps model as a case study. so that it would be acceptable for practical use. The result is evaluated by comparing with a CPU and a cloud This paper presents the algorithm development, as well computing platform. We show 14 times speed up for the FPGA as the pipeline design solution in FPGA technology, of PF design compared with the CPU, and similar speedup but better convergence compared with an alternative parallelisation scheme based MLE for parameter estimation of Stochastic Volatility using Techila Middleware on a multi-CPU environment. -
Resampling Hypothesis Tests for Autocorrelated Fields
JANUARY 1997 WILKS 65 Resampling Hypothesis Tests for Autocorrelated Fields D. S. WILKS Department of Soil, Crop and Atmospheric Sciences, Cornell University, Ithaca, New York (Manuscript received 5 March 1996, in ®nal form 10 May 1996) ABSTRACT Presently employed hypothesis tests for multivariate geophysical data (e.g., climatic ®elds) require the as- sumption that either the data are serially uncorrelated, or spatially uncorrelated, or both. Good methods have been developed to deal with temporal correlation, but generalization of these methods to multivariate problems involving spatial correlation has been problematic, particularly when (as is often the case) sample sizes are small relative to the dimension of the data vectors. Spatial correlation has been handled successfully by resampling methods when the temporal correlation can be neglected, at least according to the null hypothesis. This paper describes the construction of resampling tests for differences of means that account simultaneously for temporal and spatial correlation. First, univariate tests are derived that respect temporal correlation in the data, using the relatively new concept of ``moving blocks'' bootstrap resampling. These tests perform accurately for small samples and are nearly as powerful as existing alternatives. Simultaneous application of these univariate resam- pling tests to elements of data vectors (or ®elds) yields a powerful (i.e., sensitive) multivariate test in which the cross correlation between elements of the data vectors is successfully captured by the resampling, rather than through explicit modeling and estimation. 1. Introduction dle portion of Fig. 1. First, standard tests, including the t test, rest on the assumption that the underlying data It is often of interest to compare two datasets for are composed of independent samples from their parent differences with respect to particular attributes. -
Strength in Numbers: the Rising of Academic Statistics Departments In
Agresti · Meng Agresti Eds. Alan Agresti · Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics DepartmentsStatistics in the U.S. Rising of Academic The in Numbers: Strength Statistics Departments in the U.S. Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. Alan Agresti • Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. 123 Editors Alan Agresti Xiao-Li Meng Department of Statistics Department of Statistics University of Florida Harvard University Gainesville, FL Cambridge, MA USA USA ISBN 978-1-4614-3648-5 ISBN 978-1-4614-3649-2 (eBook) DOI 10.1007/978-1-4614-3649-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942702 Ó Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. -
Cramer, and Rao
2000 PARZEN PRIZE FOR STATISTICAL INNOVATION awarded by TEXAS A&M UNIVERSITY DEPARTMENT OF STATISTICS to C. R. RAO April 24, 2000 292 Breezeway MSC 4 pm Pictures from Parzen Prize Presentation and Reception, 4/24/2000 The 2000 EMANUEL AND CAROL PARZEN PRIZE FOR STATISTICAL INNOVATION is awarded to C. Radhakrishna Rao (Eberly Professor of Statistics, and Director of the Center for Multivariate Analysis, at the Pennsylvania State University, University Park, PA 16802) for outstanding distinction and eminence in research on the theory of statistics, in applications of statistical methods in diverse fields, in providing international leadership for 55 years in directing statistical research centers, in continuing impact through his vision and effectiveness as a scholar and teacher, and in extensive service to American and international society. The year 2000 motivates us to plan for the future of the discipline of statistics which emerged in the 20th century as a firmly grounded mathematical science due to the pioneering research of Pearson, Gossett, Fisher, Neyman, Hotelling, Wald, Cramer, and Rao. Numerous honors and awards to Rao demonstrate the esteem in which he is held throughout the world for his unusually distinguished and productive life. C. R. Rao was born September 10, 1920, received his Ph.D. from Cambridge University (England) in 1948, and has been awarded 22 honorary doctorates. He has worked at the Indian Statistical Institute (1944-1992), University of Pittsburgh (1979- 1988), and Pennsylvania State University (1988- ). Professor Rao is the author (or co-author) of 14 books and over 300 publications. His pioneering contributions (in linear models, multivariate analysis, design of experiments and combinatorics, probability distribution characterizations, generalized inverses, and robust inference) are taught in statistics textbooks. -
Sampling and Resampling
Sampling and Resampling Thomas Lumley Biostatistics 2005-11-3 Basic Problem (Frequentist) statistics is based on the sampling distribution of statistics: Given a statistic Tn and a true data distribution, what is the distribution of Tn • The mean of samples of size 10 from an Exponential • The median of samples of size 20 from a Cauchy • The difference in Pearson’s coefficient of skewness ((X¯ − m)/s) between two samples of size 40 from a Weibull(3,7). This is easy: you have written programs to do it. In 512-3 you learn how to do it analytically in some cases. But... We really want to know: What is the distribution of Tn in sampling from the true data distribution But we don’t know the true data distribution. Empirical distribution On the other hand, we do have an estimate of the true data distribution. It should look like the sample data distribution. (we write Fn for the sample data distribution and F for the true data distribution). The Glivenko–Cantelli theorem says that the cumulative distribution function of the sample converges uniformly to the true cumulative distribution. We can work out the sampling distribution of Tn(Fn) by simulation, and hope that this is close to that of Tn(F ). Simulating from Fn just involves taking a sample, with replace- ment, from the observed data. This is called the bootstrap. We ∗ write Fn for the data distribution of a resample. Too good to be true? There are obviously some limits to this • It requires large enough samples for Fn to be close to F . -
Proceedings of the Fourth Berkeley Symposium
PROCEEDINGS OF THE FOURTH BERKELEY SYMPOSIUM VOLUME III PROCEEDINGS of the FOURTH BERKELEY SYMPOSIUM ON MATHEMATICAL STATISTICS AND PROBABILITY Held at the Statistical Laboratory University of California June 20-jtuly 30, 1960, with the support of University of California National Science Foundation Office of Naval Research Office of Ordnance Research Air Force Office of Research National Institutes of Health VOLUME III CONTRIBUTIONS TO ASTRONOMY, METEOROLOGY, AND PHYSICS EDITED BY JERZY NEYMAN UNIVERSITY OF CALIFORNIA PRESS BERKELEY AND LOS ANGELES 1961 UNIVERSITY OF CALIFORNIA PRESS BERKELEY AND LOS ANGELES CALIFORNIA CAMBRIDGE UNIVERSITY PRESS LONDON, ENGLAND © 1961, BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA The United States Government and its offices, agents, an I em- ployees, acting within the scope of their duties, may reproduce, publish, and use this material in whole or in part for governmental purposes without payment of royalties thereon or therefor. The publication or republication by the government either separately or in a public document of any material in which copyright subsists shall not be taken to cause any abridgment or annulment of the copyright or to authorize any use or appropriation of such copy- right material without the consent of the copyright proprietor. LIBRARY OF CONGRESS CATALOG CARD NUMBER: 49-8189 PRINTED IN THE UNITED STATES OF AMERICA CONTENTS OF PROCEEDINGS, VOLUMES I, II, AND IV Volume I-Theory of Statistics F. J. ANSCOMBE, Examination of residuals. RICHARD BELLMAN, A mathematical formulation of variational processes of adaptive type. Z. W. BIRNBAUM, On the probabil- istic theory of complex structuires. DAVID BLACKWELL, Exponential error bounds for finite state channels. -
Academic Genealogy of the Oakland University Department Of
Basilios Bessarion Mystras 1436 Guarino da Verona Johannes Argyropoulos 1408 Università di Padova 1444 Academic Genealogy of the Oakland University Vittorino da Feltre Marsilio Ficino Cristoforo Landino Università di Padova 1416 Università di Firenze 1462 Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo Angelo Poliziano Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Università di Mantova 1433 Università di Mantova Università di Firenze 1477 Constantinople 1433 DepartmentThe Mathematics Genealogy Project of is a serviceMathematics of North Dakota State University and and the American Statistics Mathematical Society. Demetrios Chalcocondyles http://www.mathgenealogy.org/ Heinrich von Langenstein Gaetano da Thiene Sigismondo Polcastro Leo Outers Moses Perez Scipione Fortiguerra Rudolf Agricola Thomas von Kempen à Kempis Jacob ben Jehiel Loans Accademia Romana 1452 Université de Paris 1363, 1375 Université Catholique de Louvain 1485 Università di Firenze 1493 Università degli Studi di Ferrara 1478 Mystras 1452 Jan Standonck Johann (Johannes Kapnion) Reuchlin Johannes von Gmunden Nicoletto Vernia Pietro Roccabonella Pelope Maarten (Martinus Dorpius) van Dorp Jean Tagault François Dubois Janus Lascaris Girolamo (Hieronymus Aleander) Aleandro Matthaeus Adrianus Alexander Hegius Johannes Stöffler Collège Sainte-Barbe 1474 Universität Basel 1477 Universität Wien 1406 Università di Padova Università di Padova Université Catholique de Louvain 1504, 1515 Université de Paris 1516 Università di Padova 1472 Università -
Efficient Computation of Adjusted P-Values for Resampling-Based Stepdown Multiple Testing
University of Zurich Department of Economics Working Paper Series ISSN 1664-7041 (print) ISSN 1664-705X (online) Working Paper No. 219 Efficient Computation of Adjusted p-Values for Resampling-Based Stepdown Multiple Testing Joseph P. Romano and Michael Wolf February 2016 Efficient Computation of Adjusted p-Values for Resampling-Based Stepdown Multiple Testing∗ Joseph P. Romano† Michael Wolf Departments of Statistics and Economics Department of Economics Stanford University University of Zurich Stanford, CA 94305, USA 8032 Zurich, Switzerland [email protected] [email protected] February 2016 Abstract There has been a recent interest in reporting p-values adjusted for resampling-based stepdown multiple testing procedures proposed in Romano and Wolf (2005a,b). The original papers only describe how to carry out multiple testing at a fixed significance level. Computing adjusted p-values instead in an efficient manner is not entirely trivial. Therefore, this paper fills an apparent gap by detailing such an algorithm. KEY WORDS: Adjusted p-values; Multiple testing; Resampling; Stepdown procedure. JEL classification code: C12. ∗We thank Henning M¨uller for helpful comments. †Research supported by NSF Grant DMS-1307973. 1 1 Introduction Romano and Wolf (2005a,b) propose resampling-based stepdown multiple testing procedures to control the familywise error rate (FWE); also see Romano et al. (2008, Section 3). The procedures as described are designed to be carried out at a fixed significance level α. Therefore, the result of applying such a procedure to a set of data will be a ‘list’ of binary decisions concerning the individual null hypotheses under study: reject or do not reject a given null hypothesis at the chosen significance level α.