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Hellinger Distance Based Drift Detection for Nonstationary Environments
Hellinger Distance Based Drift Detection for Nonstationary Environments Gregory Ditzler and Robi Polikar Dept. of Electrical & Computer Engineering Rowan University Glassboro, NJ, USA [email protected], [email protected] Abstract—Most machine learning algorithms, including many sion boundaries as a concept change, whereas gradual changes online learners, assume that the data distribution to be learned is in the data distribution as a concept drift. However, when the fixed. There are many real-world problems where the distribu- context does not require us to distinguish between the two, we tion of the data changes as a function of time. Changes in use the term concept drift to encompass both scenarios, as it is nonstationary data distributions can significantly reduce the ge- usually the more difficult one to detect. neralization ability of the learning algorithm on new or field data, if the algorithm is not equipped to track such changes. When the Learning from drifting environments is usually associated stationary data distribution assumption does not hold, the learner with a stream of incoming data, either one instance or one must take appropriate actions to ensure that the new/relevant in- batch at a time. There are two types of approaches for drift de- formation is learned. On the other hand, data distributions do tection in such streaming data: in passive drift detection, the not necessarily change continuously, necessitating the ability to learner assumes – every time new data become available – that monitor the distribution and detect when a significant change in some drift may have occurred, and updates the classifier ac- distribution has occurred. -
Report for the Academic Year 1995
Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1994 - 95 PRINCETON NEW JERSEY Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1 994 - 95 OLDEN LANE PRINCETON • NEW JERSEY 08540-0631 609-734-8000 609-924-8399 (Fax) Extract from the letter addressed by the Founders to the Institute's Trustees, dated June 6, 1930. Newark, New jersey. It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. TABLE OF CONTENTS 4 BACKGROUND AND PURPOSE 5 • FOUNDERS, TRUSTEES AND OFFICERS OF THE BOARD AND OF THE CORPORATION 8 • ADMINISTRATION 11 REPORT OF THE CHAIRMAN 15 REPORT OF THE DIRECTOR 23 • ACKNOWLEDGMENTS 27 • REPORT OF THE SCHOOL OF HISTORICAL STUDIES ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 36 • REPORT OF THE SCHOOL OF MATHEMATICS ACADEMIC ACTIVITIES MEMBERS AND VISITORS 42 • REPORT OF THE SCHOOL OF NATURAL SCIENCES ACADEMIC ACTIVITIES MEMBERS AND VISITORS 50 • REPORT OF THE SCHOOL OF SOCIAL SCIENCE ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 55 • REPORT OF THE INSTITUTE LIBRARIES 57 • RECORD OF INSTITUTE EVENTS IN THE ACADEMIC YEAR 1994-95 85 • INDEPENDENT AUDITORS' REPORT INSTITUTE FOR ADVANCED STUDY: BACKGROUND AND PURPOSE The Institute for Advanced Study is an independent, nonprofit institution devoted to the encouragement of learning and scholarship. -
Hellinger Distance-Based Similarity Measures for Recommender Systems
Hellinger Distance-based Similarity Measures for Recommender Systems Roma Goussakov One year master thesis Ume˚aUniversity Abstract Recommender systems are used in online sales and e-commerce for recommend- ing potential items/products for customers to buy based on their previous buy- ing preferences and related behaviours. Collaborative filtering is a popular computational technique that has been used worldwide for such personalized recommendations. Among two forms of collaborative filtering, neighbourhood and model-based, the neighbourhood-based collaborative filtering is more pop- ular yet relatively simple. It relies on the concept that a certain item might be of interest to a given customer (active user) if, either he appreciated sim- ilar items in the buying space, or if the item is appreciated by similar users (neighbours). To implement this concept different kinds of similarity measures are used. This thesis is set to compare different user-based similarity measures along with defining meaningful measures based on Hellinger distance that is a metric in the space of probability distributions. Data from a popular database MovieLens will be used to show the effectiveness of different Hellinger distance- based measures compared to other popular measures such as Pearson correlation (PC), cosine similarity, constrained PC and JMSD. The performance of differ- ent similarity measures will then be evaluated with the help of mean absolute error, root mean squared error and F-score. From the results, no evidence were found to claim that Hellinger distance-based measures performed better than more popular similarity measures for the given dataset. Abstrakt Titel: Hellinger distance-baserad similaritetsm˚attf¨orrekomendationsystem Rekomendationsystem ¨aroftast anv¨andainom e-handel f¨orrekomenderingar av potentiella varor/produkter som en kund kommer att vara intresserad av att k¨opabaserat p˚aderas tidigare k¨oppreferenseroch relaterat beteende. -
Institut Des Hautes Ét Udes Scientifiques
InstItut des Hautes É t u d e s scIentIfIques A foundation in the public interest since 1981 2 | IHES IHES | 3 Contents A VISIONARY PROJECT, FOR EXCELLENCE IN SCIENCE P. 5 Editorial P. 6 Founder P. 7 Permanent professors A MODERN-DAY THELEMA FOR A GLOBAL SCIENTIFIC COMMUNITY P. 8 Research P. 9 Visitors P. 10 Events P. 11 International INDEPENDENCE AND FREEDOM, THE INSTITUTE’S TWO OPERATIONAL PILLARS P. 12 Finance P. 13 Governance P. 14 Members P. 15 Tax benefits The Marilyn and James Simons Conference Center The aim of the Foundation known as ‘Institut des Hautes Études Scientifiques’ is to enable and encourage theoretical scientific research (…). [Its] activity consists mainly in providing the Institute’s professors and researchers, both permanent and invited, with the resources required to undertake disinterested IHES February 2016 Content: IHES Communication Department – Translation: Hélène Wilkinson – Design: blossom-creation.com research. Photo Credits: Valérie Touchant-Landais / IHES, Marie-Claude Vergne / IHES – Cover: unigma All rights reserved Extract from the statutes of the Institut des Hautes Études Scientifiques, 1958. 4 | IHES IHES | 5 A visionary project, for excellence in science Editorial Emmanuel Ullmo, Mathematician, IHES Director A single scientific program: curiosity. A single selection criterion: excellence. The Institut des Hautes Études Scientifiques is an international mathematics and theoretical physics research center. Free of teaching duties and administrative tasks, its professors and visitors undertake research in complete independence and total freedom, at the highest international level. Ever since it was created, IHES has cultivated interdisciplinarity. The constant dialogue between mathematicians and theoretical physicists has led to particularly rich interactions. -
Biographical Sketch of Jean Bourgain Born
Biographical Sketch of Jean Bourgain Born: February 28, 1954 in Ostende, Belgium Citizenship: Citizen of Belgium Education: 1977 - Ph.D., Free University of Brussels 1979 - Habilitation Degree, Free University of Brussels Appointments: Research Fellowship in Belgium NSF (NFWO), 1975-1981 Professor at Free University of Brussels, 1981-1985 J.L. Doob Professor of Mathematics, University of Illinois, 1985-2006 Professor a IHES (France), 1985-1995 Lady Davis Professor of Mathematics, Hebrew University of Jerusalem, 1988 Fairchild Distinguished Professor, Caltech, 1991 Professor IAS, 1994- IBM, Von Neumann Professor IAS, 2010– Honors: Alumni Prize, Belgium NSF, 1979 Empain Prize, Belgium NSF, 1983 Salem Prize, 1983 Damry-Deleeuw-Bourlart Prize (awarded by Belgian NSF), 1985 (quintesimal Belgian Science Prize) Langevin Prize (French Academy), 1985 E. Cartan Prize (French Academy), 1990 (quintesimal) Ostrowski Prize, Ostrowski Foundation (Basel-Switzerland), 1991 (biannual) Fields Medal, ICM Zurich, 1994 I.V. Vernadski Gold Medal, National Academy of Sciences of Ukraine, 2010 Shaw Prize, 2010 Crafoord Prize 2012, The Royal Swedish Academy of Sciences Dr. H.C. Hebrew University, 1991 Dr. H.C. Universit´eMarne-la-Vallee (France), 1994 Dr. H.C. Free University of Brussels (Belgium), 1995 Associ´eEtranger de l’Academie des Sciences, 2000 Foreign Member of the Polish Academy, 2000 Foreign Member Academia Europaea, 2008 Foreign Member Royal Swedish Academy of Sciences, 2009 Foreign Associate National Academy of Sciences, 2011 International Congress of Mathematics, Warsaw (1983), Berkeley (1986), Zurich (1994) - plenary International Congress on Mathematical Physics, Paris (1994), Rio (2006) - plenary 1 European Mathematical Congress, Paris (1992), Amsterdam (2008) - plenary Lecture Series: A. Zygmund Lectures, Univ. -
Asian Nobel Prize' for Mapping the Universe 27 May 2010
Scientists win 'Asian Nobel Prize' for mapping the universe 27 May 2010 Three US scientists whose work helped map the category. universe are among the recipients of the one- million-US-dollar Shaw Prize, known as the "Asian (c) 2010 AFP Nobel," the competition's organisers said Thursday. Princeton University professors Lyman Page and David Spergel and Charles Bennett of Johns Hopkins University, won the award for an experiment that helped to determine the "geometry, age and composition of the universe to unprecedented precision." The trio will share the Shaw Prize's award for astronomy, with one-million-US-dollar prizes also awarded in the categories for mathematical sciences and life sciences and medicine. The University of California's David Julius won the award for life sciences and medicine for his "seminal discoveries" of how the skin senses pain and temperature, the organisers' statement said. "(Julius's) work has provided insights into fundamental mechanisms underlying the sense of touch as well as knowledge that opens the door to rational drug design for the treatment of chronic pain," the statement said. Princeton's Jean Bourgain won an award for his "profound work" in mathematical sciences, it said. The Shaw Prize, funded by Hong Kong film producer and philanthropist Run Run Shaw and first awarded in 2004, honours exceptional contributions "to the advancement of civilization and the well-being of humankind." The awards will be presented at a ceremony in Hong Kong on September 28. Last year, two scientists whose work challenged the assumption that obesity is caused by a lack of will power won the life sciences and medicine 1 / 2 APA citation: Scientists win 'Asian Nobel Prize' for mapping the universe (2010, May 27) retrieved 27 September 2021 from https://phys.org/news/2010-05-scientists-asian-nobel-prize-universe.html This document is subject to copyright. -
Spring 2014 Fine Letters
Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544 Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize. -
On Measures of Entropy and Information
On Measures of Entropy and Information Tech. Note 009 v0.7 http://threeplusone.com/info Gavin E. Crooks 2018-09-22 Contents 5 Csiszar´ f-divergences 12 Csiszar´ f-divergence ................ 12 0 Notes on notation and nomenclature 2 Dual f-divergence .................. 12 Symmetric f-divergences .............. 12 1 Entropy 3 K-divergence ..................... 12 Entropy ........................ 3 Fidelity ........................ 12 Joint entropy ..................... 3 Marginal entropy .................. 3 Hellinger discrimination .............. 12 Conditional entropy ................. 3 Pearson divergence ................. 14 Neyman divergence ................. 14 2 Mutual information 3 LeCam discrimination ............... 14 Mutual information ................. 3 Skewed K-divergence ................ 14 Multivariate mutual information ......... 4 Alpha-Jensen-Shannon-entropy .......... 14 Interaction information ............... 5 Conditional mutual information ......... 5 6 Chernoff divergence 14 Binding information ................ 6 Chernoff divergence ................. 14 Residual entropy .................. 6 Chernoff coefficient ................. 14 Total correlation ................... 6 Renyi´ divergence .................. 15 Lautum information ................ 6 Alpha-divergence .................. 15 Uncertainty coefficient ............... 7 Cressie-Read divergence .............. 15 Tsallis divergence .................. 15 3 Relative entropy 7 Sharma-Mittal divergence ............. 15 Relative entropy ................... 7 Cross entropy -
Tailoring Differentially Private Bayesian Inference to Distance
Tailoring Differentially Private Bayesian Inference to Distance Between Distributions Jiawen Liu*, Mark Bun**, Gian Pietro Farina*, and Marco Gaboardi* *University at Buffalo, SUNY. fjliu223,gianpiet,gaboardig@buffalo.edu **Princeton University. [email protected] Contents 1 Introduction 3 2 Preliminaries 5 3 Technical Problem Statement and Motivations6 4 Mechanism Proposition8 4.1 Laplace Mechanism Family.............................8 4.1.1 using `1 norm metric.............................8 4.1.2 using improved `1 norm metric.......................8 4.2 Exponential Mechanism Family...........................9 4.2.1 Standard Exponential Mechanism.....................9 4.2.2 Exponential Mechanism with Hellinger Metric and Local Sensitivity.. 10 4.2.3 Exponential Mechanism with Hellinger Metric and Smoothed Sensitivity 10 5 Privacy Analysis 12 5.1 Privacy of Laplace Mechanism Family....................... 12 5.2 Privacy of Exponential Mechanism Family..................... 12 5.2.1 expMech(;; ) −Differential Privacy..................... 12 5.2.2 expMechlocal(;; ) non-Differential Privacy................. 12 5.2.3 expMechsmoo −Differential Privacy Proof................. 12 6 Accuracy Analysis 14 6.1 Accuracy Bound for Baseline Mechanisms..................... 14 6.1.1 Accuracy Bound for Laplace Mechanism.................. 14 6.1.2 Accuracy Bound for Improved Laplace Mechanism............ 16 6.2 Accuracy Bound for expMechsmoo ......................... 16 6.3 Accuracy Comparison between expMechsmoo, lapMech and ilapMech ...... 16 7 Experimental Evaluations 18 7.1 Efficiency Evaluation................................. 18 7.2 Accuracy Evaluation................................. 18 7.2.1 Theoretical Results.............................. 18 7.2.2 Experimental Results............................ 20 1 7.3 Privacy Evaluation.................................. 22 8 Conclusion and Future Work 22 2 Abstract Bayesian inference is a statistical method which allows one to derive a posterior distribution, starting from a prior distribution and observed data. -
An Information-Geometric Approach to Feature Extraction and Moment
An information-geometric approach to feature extraction and moment reconstruction in dynamical systems Suddhasattwa Dasa, Dimitrios Giannakisa, Enik˝oSz´ekelyb,∗ aCourant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA bSwiss Data Science Center, ETH Z¨urich and EPFL, 1015 Lausanne, Switzerland Abstract We propose a dimension reduction framework for feature extraction and moment reconstruction in dy- namical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data space of the observables themselves as in more conventional methods. Our approach is based on the fact that orbits of a dynamical system induce probability measures over the measur- able space defined by (partial) observations of the system. We equip the space of these probability measures with a divergence, i.e., a distance between probability distributions, and use this divergence to define a kernel integral operator. The eigenfunctions of this operator create an orthonormal basis of functions that capture different timescales of the dynamical system. One of our main results shows that the evolution of the moments of the dynamics-dependent probability measures can be related to a time-averaging operator on the original dynamical system. Using this result, we show that the moments can be expanded in the eigenfunction basis, thus opening up the avenue for nonparametric forecasting of the moments. If the col- lection of probability measures is itself a manifold, we can in addition equip the statistical manifold with the Riemannian metric and use techniques from information geometry. We present applications to ergodic dynamical systems on the 2-torus and the Lorenz 63 system, and show on a real-world example that a small number of eigenvectors is sufficient to reconstruct the moments (here the first four moments) of an atmospheric time series, i.e., the realtime multivariate Madden-Julian oscillation index. -
Statistics As Both a Purely Mathematical Activity and an Applied Science NAW 5/18 Nr
Piet Groeneboom, Jan van Mill, Aad van der Vaart Statistics as both a purely mathematical activity and an applied science NAW 5/18 nr. 1 maart 2017 55 Piet Groeneboom Jan van Mill Aad van der Vaart Delft Institute of Applied Mathematics KdV Institute for Mathematics Mathematical Institute Delft University of Technology University of Amsterdam Leiden University [email protected] [email protected] [email protected] In Memoriam Kobus Oosterhoff (1933–2015) Statistics as both a purely mathematical activity and an applied science On 27 May 2015 Kobus Oosterhoff passed away at the age of 82. Kobus was employed at contact with Hemelrijk and the encourage- the Mathematisch Centrum in Amsterdam from 1961 to 1969, at the Roman Catholic Univer- ment received from him, but he did his the- ity of Nijmegen from 1970 to 1974, and then as professor in Mathematical Statistics at the sis under the direction of Willem van Zwet Vrije Universiteit Amsterdam from 1975 until his retirement in 1996. In this obituary Piet who, one year younger than Kobus, had Groeneboom, Jan van Mill and Aad van der Vaart look back on his life and work. been a professor at Leiden University since 1965. Kobus became Willem’s first PhD stu- Kobus (officially: Jacobus) Oosterhoff was diploma’ (comparable to a masters) in dent, defending his dissertation Combina- born on 7 May 1933 in Leeuwarden, the 1963. His favorite lecturer was the topolo- tion of One-sided Test Statistics on 26 June capital of the province of Friesland in the gist J. de Groot, who seems to have deeply 1969 at Leiden University. -
On Some Properties of Goodness of Fit Measures Based on Statistical Entropy
IJRRAS 13 (1) ● October 2012 www.arpapress.com/Volumes/Vol13Issue1/IJRRAS_13_1_22.pdf ON SOME PROPERTIES OF GOODNESS OF FIT MEASURES BASED ON STATISTICAL ENTROPY Atif Evren1 & Elif Tuna2 1,2 Yildiz Technical University Faculty of Sciences and Literature , Department of Statistics Davutpasa, Esenler, 34210, Istanbul Turkey ABSTRACT Goodness of fit tests can be categorized under several ways. One categorization may be due to the differences between observed and expected frequencies. The other categorization may be based upon the differences between some values of distribution functions. Still the other one may be based upon the divergence of one distribution from the other. Some widely used and well known divergences like Kullback-Leibler divergence or Jeffreys divergence are based on entropy concepts. In this study, we compare some basic goodness of fit tests in terms of their statistical properties with some applications. Keywords: Measures for goodness of fit, likelihood ratio, power divergence statistic, Kullback-Leibler divergence, Jeffreys’ divergence, Hellinger distance, Bhattacharya divergence. 1. INTRODUCTION Boltzmann may be the first scientist who emphasized the probabilistic meaning of thermodynamical entropy. For him, the entropy of a physical system is a measure of disorder related to it [35]. For probability distributions, on the other hand, the general idea is that observing a random variable whose value is known is uninformative. Entropy is zero if there is unit probability at a single point, whereas if the distribution is widely dispersed over a large number of individually small probabilities, the entropy is high [10]. Statistical entropy has some conflicting explanations so that sometimes it measures two complementary conceptions like information and lack of information.