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Risk Bounds for Classification and Regression Rules That Interpolate
Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate Mikhail Belkin Daniel Hsu Partha P. Mitra The Ohio State University Columbia University Cold Spring Harbor Laboratory Abstract Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phe- nomenon of strong generalization performance for “overfitted” / interpolated clas- sifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise. Very little theory is available to explain these observations. The vast majority of theoretical analyses of generalization allows for interpolation only when there is little or no label noise. This paper takes a step toward a theoretical foundation for interpolated classifiers by analyzing local interpolating schemes, including geometric simplicial interpolation algorithm and singularly weighted k-nearest neighbor schemes. Consistency or near-consistency is proved for these schemes in classification and regression problems. Moreover, the nearest neighbor schemes exhibit optimal rates under some standard statistical assumptions. Finally, this paper suggests a way to explain the phenomenon of adversarial ex- amples, which are seemingly ubiquitous in modern machine learning, and also discusses some connections to kernel machines and random forests in the interpo- lated regime. 1 Introduction The central problem of supervised inference is to predict labels of unseen data points from a set of labeled training data. The literature on this subject is vast, ranging from classical parametric and non-parametric statistics [48, 49] to more recent machine learning methods, such as kernel machines [39], boosting [36], random forests [15], and deep neural networks [25]. -
Probabilistic Circuits: Representations, Inference, Learning and Theory
Inference Probabilistic Representations Learning Circuits Theory Antonio Vergari YooJung Choi University of California, Los Angeles University of California, Los Angeles Robert Peharz Guy Van den Broeck TU Eindhoven University of California, Los Angeles January 7th, 2021 - IJCAI-PRICAI 2020 Fully factorized NaiveBayes AndOrGraphs PDGs Trees PSDDs CNets LTMs SPNs NADEs Thin Junction Trees ACs MADEs MAFs VAEs DPPs FVSBNs TACs IAFs NAFs RAEs Mixtures BNs NICE FGs GANs RealNVP MNs The Alphabet Soup of probabilistic models 2/153 Fully factorized NaiveBayes AndOrGraphs PDGs Trees PSDDs CNets LTMs SPNs NADEs Thin Junction Trees ACs MADEs MAFs VAEs DPPs FVSBNs TACs IAFs NAFs RAEs Mixtures BNs NICE FGs GANs RealNVP MNs Intractable and tractable models 3/153 Fully factorized NaiveBayes AndOrGraphs PDGs Trees PSDDs CNets LTMs SPNs NADEs Thin Junction Trees ACs MADEs MAFs VAEs DPPs FVSBNs TACs IAFs NAFs RAEs Mixtures BNs NICE FGs GANs RealNVP MNs tractability is a spectrum 4/153 Fully factorized NaiveBayes AndOrGraphs PDGs Trees PSDDs CNets LTMs SPNs NADEs Thin Junction Trees ACs MADEs MAFs VAEs DPPs FVSBNs TACs IAFs NAFs RAEs Mixtures BNs NICE FGs GANs RealNVP MNs Expressive models without compromises 5/153 Fully factorized NaiveBayes AndOrGraphs PDGs Trees PSDDs CNets LTMs SPNs NADEs Thin Junction Trees ACs MADEs MAFs VAEs DPPs FVSBNs TACs IAFs NAFs RAEs Mixtures BNs NICE FGs GANs RealNVP MNs a unifying framework for tractable models 6/153 Why tractable inference? or expressiveness vs tractability 7/153 Why tractable inference? or expressiveness -
Risk Bounds for Classification and Regression Rules That Interpolate
Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate Mikhail Belkin1, Daniel Hsu2, and Partha P. Mitra3 1The Ohio State University, Columbus, OH 2Columbia University, New York, NY 3Cold Spring Harbor Laboratory, Cold Spring Harbor, NY October 29, 2018 Abstract Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for “overfitted” / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise. Very little theory is available to explain these observations. The vast majority of theoretical analyses of generalization allows for interpolation only when there is little or no label noise. This paper takes a step toward a theoretical foundation for interpolated classifiers by analyzing local interpolating schemes, including geometric simplicial interpolation algorithm and singularly weighted k-nearest neighbor schemes. Consistency or near-consistency is proved for these schemes in classification and regression problems. Moreover, the nearest neighbor schemes exhibit optimal rates under some standard statistical assumptions. Finally, this paper suggests a way to explain the phenomenon of adversarial examples, which are seemingly ubiquitous in modern machine learning, and also discusses some connections to kernel machines and random forests in the interpolated regime. 1 Introduction arXiv:1806.05161v3 [stat.ML] 26 Oct 2018 The central problem of supervised inference is to predict labels of unseen data points from a set of labeled training data. -
The Case for Quantum Key Distribution
The Case for Quantum Key Distribution Douglas Stebila1, Michele Mosca2,3,4, and Norbert Lütkenhaus2,4,5 1 Information Security Institute, Queensland University of Technology, Brisbane, Australia 2 Institute for Quantum Computing, University of Waterloo 3 Dept. of Combinatorics & Optimization, University of Waterloo 4 Perimeter Institute for Theoretical Physics 5 Dept. of Physics & Astronomy, University of Waterloo Waterloo, Ontario, Canada Email: [email protected], [email protected], [email protected] December 2, 2009 Abstract Quantum key distribution (QKD) promises secure key agreement by using quantum mechanical systems. We argue that QKD will be an important part of future cryptographic infrastructures. It can provide long-term confidentiality for encrypted information without reliance on computational assumptions. Although QKD still requires authentication to prevent man-in-the-middle attacks, it can make use of either information-theoretically secure symmetric key authentication or computationally secure public key authentication: even when using public key authentication, we argue that QKD still offers stronger security than classical key agreement. 1 Introduction Since its discovery, the field of quantum cryptography — and in particular, quantum key distribution (QKD) — has garnered widespread technical and popular interest. The promise of “unconditional security” has brought public interest, but the often unbridled optimism expressed for this field has also spawned criticism and analysis [Sch03, PPS04, Sch07, Sch08]. QKD is a new tool in the cryptographer’s toolbox: it allows for secure key agreement over an untrusted channel where the output key is entirely independent from any input value, a task that is impossible using classical1 cryptography. QKD does not eliminate the need for other cryptographic primitives, such as authentication, but it can be used to build systems with new security properties. -
TRINITY COLLEGE Cambridge Trinity College Cambridge College Trinity Annual Record Annual
2016 TRINITY COLLEGE cambridge trinity college cambridge annual record annual record 2016 Trinity College Cambridge Annual Record 2015–2016 Trinity College Cambridge CB2 1TQ Telephone: 01223 338400 e-mail: [email protected] website: www.trin.cam.ac.uk Contents 5 Editorial 11 Commemoration 12 Chapel Address 15 The Health of the College 18 The Master’s Response on Behalf of the College 25 Alumni Relations & Development 26 Alumni Relations and Associations 37 Dining Privileges 38 Annual Gatherings 39 Alumni Achievements CONTENTS 44 Donations to the College Library 47 College Activities 48 First & Third Trinity Boat Club 53 Field Clubs 71 Students’ Union and Societies 80 College Choir 83 Features 84 Hermes 86 Inside a Pirate’s Cookbook 93 “… Through a Glass Darkly…” 102 Robert Smith, John Harrison, and a College Clock 109 ‘We need to talk about Erskine’ 117 My time as advisor to the BBC’s War and Peace TRINITY ANNUAL RECORD 2016 | 3 123 Fellows, Staff, and Students 124 The Master and Fellows 139 Appointments and Distinctions 141 In Memoriam 155 A Ninetieth Birthday Speech 158 An Eightieth Birthday Speech 167 College Notes 181 The Register 182 In Memoriam 186 Addresses wanted CONTENTS TRINITY ANNUAL RECORD 2016 | 4 Editorial It is with some trepidation that I step into Boyd Hilton’s shoes and take on the editorship of this journal. He managed the transition to ‘glossy’ with flair and panache. As historian of the College and sometime holder of many of its working offices, he also brought a knowledge of its past and an understanding of its mysteries that I am unable to match. -
2013 Industry Canada Report
Industry Canada Report 2012/13 Reporting Period Institute for Quantum Computing University of Waterloo June 15, 2013 Industry Canada Report | 2 Note from the Executive Director Harnessing the quantum world will lead to new technologies and applications that will change the world. The quantum properties of nature allow the accomplishment of tasks which seem intractable with today’s technologies, offer new means of securing private information and foster the development of new sensors with precision yet unseen. In a short 10 years, the Institute for Quantum Computing (IQC) at the University of Waterloo has become a world-renowned institute for research in the quantum world. With more than 160 researchers, we are well on our way to reaching our goal of 33 faculty, 60 post doctoral fellows and 165 students. The research has been world class and many results have received international attention. We have recruited some of the world’s leading researchers and rising stars in the field. 2012 has been a landmark year. Not only did we celebrate our 10th anniversary, but we also expanded into our new headquarters in the Mike and Ophelia Lazaridis Quantum-Nano Centre in the heart of the University of Waterloo campus. This 285,000 square foot facility provides the perfect environment to continue our research, grow our faculty complement and attract the brightest students from around the globe. In this report, you will see many examples of the wonderful achievements we’ve celebrated this year. IQC researcher Andrew Childs and his team proposed a new computational model that has the potential to become an architecture for a scalable quantum computer. -
Part I Officers in Institutions Placed Under the Supervision of the General Board
2 OFFICERS NUMBER–MICHAELMAS TERM 2009 [SPECIAL NO.7 PART I Chancellor: H.R.H. The Prince PHILIP, Duke of Edinburgh, T Vice-Chancellor: 2003, Prof. ALISON FETTES RICHARD, N, 2010 Deputy Vice-Chancellors for 2009–2010: Dame SANDRA DAWSON, SID,ATHENE DONALD, R,GORDON JOHNSON, W,STUART LAING, CC,DAVID DUNCAN ROBINSON, M,JEREMY KEITH MORRIS SANDERS, SE, SARAH LAETITIA SQUIRE, HH, the Pro-Vice-Chancellors Pro-Vice-Chancellors: 2004, ANDREW DAVID CLIFF, CHR, 31 Dec. 2009 2004, IAN MALCOLM LESLIE, CHR, 31 Dec. 2009 2008, JOHN MARTIN RALLISON, T, 30 Sept. 2011 2004, KATHARINE BRIDGET PRETTY, HO, 31 Dec. 2009 2009, STEPHEN JOHN YOUNG, EM, 31 July 2012 High Steward: 2001, Dame BRIDGET OGILVIE, G Deputy High Steward: 2009, ANNE MARY LONSDALE, NH Commissary: 2002, The Rt Hon. Lord MACKAY OF CLASHFERN, T Proctors for 2009–2010: JEREMY LLOYD CADDICK, EM LINDSAY ANNE YATES, JN Deputy Proctors for MARGARET ANN GUITE, G 2009–2010: PAUL DUNCAN BEATTIE, CC Orator: 2008, RUPERT THOMPSON, SE Registrary: 2007, JONATHAN WILLIAM NICHOLLS, EM Librarian: 2009, ANNE JARVIS, W Acting Deputy Librarian: 2009, SUSANNE MEHRER Director of the Fitzwilliam Museum and Marlay Curator: 2008, TIMOTHY FAULKNER POTTS, CL Director of Development and Alumni Relations: 2002, PETER LAWSON AGAR, SE Esquire Bedells: 2003, NICOLA HARDY, JE 2009, ROGER DERRICK GREEVES, CL University Advocate: 2004, PHILIPPA JANE ROGERSON, CAI, 2010 Deputy University Advocates: 2007, ROSAMUND ELLEN THORNTON, EM, 2010 2006, CHRISTOPHER FORBES FORSYTH, R, 2010 OFFICERS IN INSTITUTIONS PLACED UNDER THE SUPERVISION OF THE GENERAL BOARD PROFESSORS Accounting 2003 GEOFFREY MEEKS, DAR Active Tectonics 2002 JAMES ANTHONY JACKSON, Q Aeronautical Engineering, Francis Mond 1996 WILLIAM NICHOLAS DAWES, CHU Aerothermal Technology 2000 HOWARD PETER HODSON, G Algebra 2003 JAN SAXL, CAI Algebraic Geometry (2000) 2000 NICHOLAS IAN SHEPHERD-BARRON, T Algebraic Geometry (2001) 2001 PELHAM MARK HEDLEY WILSON, T American History, Paul Mellon 1992 ANTHONY JOHN BADGER, CL American History and Institutions, Pitt 2009 NANCY A. -
Machine Learning Conference Report
Part of the conference series Breakthrough science and technologies Transforming our future Machine learning Conference report Machine learning report – Conference report 1 Introduction On 22 May 2015, the Royal Society hosted a unique, high level conference on the subject of machine learning. The conference brought together scientists, technologists and experts from across academia, industry and government to learn about the state-of-the-art in machine learning from world and UK experts. The presentations covered four main areas of machine learning: cutting-edge developments in software, the underpinning hardware, current applications and future social and economic impacts. This conference is the first in a new series organised This report is not a verbatim record, but summarises by the Royal Society, entitled Breakthrough Science the discussions that took place during the day and the and Technologies: Transforming our Future, which will key points raised. Comments and recommendations address the major scientific and technical challenges reflect the views and opinions of the speakers and of the next decade. Each conference will focus on one not necessarily that of the Royal Society. Full versions technology and cover key issues including the current of the presentations can be found on our website at: state of the UK industry sector, future direction of royalsociety.org/events/2015/05/breakthrough-science- research and the wider social and economic implications. technologies-machine-learning The conference series is being organised through the Royal Society’s Science and Industry programme, which demonstrates our commitment to reintegrate science and industry at the Society and to promote science and its value, build relationships and foster translation. -
AAAI News AAAI News
AAAI News AAAI News Winter News from the Association for the Advancement of Artificial Intelligence AAAI-18 Registration Student Activities looking for internships or jobs to meet with representatives from over 30 com - As part of its outreach to students, Is Open! panies and academia in an informal AAAI-18 will continue several special "meet-and-greet" atmosphere. If you AAAI-18 registration information is programs specifically for students, are representing a company, research now available at aaai.org/aaai18, and including the Doctoral Consortium, organization or university and would online registration can be completed at the Student Abstract Program, Lunch like to participate in the job fair, please regonline.com/aaai18. The deadline with a Fellow, and the Volunteer Pro - send an email with your contact infor - for late registration rates is January 5, gram, in addition to the following: 2018. Complete tutorial and workshop mation to [email protected] no later than January 5. The organizers of information, as well as other special Student Reception the AAAI/ACM SIGAI Job Fair are John program information is available at AAAI will welcome all students to Dickerson (University of Maryland, these sites. AAAI-18 by hosting an evening stu - USA) and Nicholas Mattei (IBM, USA). dent reception on Friday, February 2. Make Your Hotel Reservation Although the reception is especially The Winograd Now! beneficial to new students at the con - Schema Challenge AAAI has reserved a block of rooms at ference, all are welcome! Please join us and make all the newcomers welcome! Nuance Communications, Inc. is spon - the Hilton New Orleans Riverside at soring a competition to encourage reduced conference rates. -
Projector Quantum Monte Carlo Methods for Linear and Non-Linear Wavefunction Ansatzes
Projector Quantum Monte Carlo Methods for Linear and Non-linear Wavefunction Ansatzes Lauretta Rebecca Schwarz Trinity Hall University of Cambridge This dissertation is submitted for the degree of Doctor of Philosophy at the University of Cambridge October 2017 Projector Quantum Monte Carlo Methods for Linear and Non-linear Wavefunction Ansatzes Lauretta Rebecca Schwarz Abstract This thesis is concerned with the development of a Projector Quantum Monte Carlo method for non-linear wavefunction ansatzes and its application to strongly correlated materials. This new approach is partially inspired by a prior application of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method to the three- band (p − d) Hubbard model. Through repeated stochastic application of a projector FCIQMC projects out a stochastic description of the Full Configuration Interaction (FCI) ground state wavefunction, a linear combination of Slater determinants spanning the full Hilbert space. The study of the p − d Hubbard model demonstrates that the nature of this FCI expansion is profoundly affected by the choice of single-particle basis. In a counterintuitive manner, the effectiveness of a one-particle basis to produce a sparse, compact and rapidly converging FCI expansion is not necessarily paralleled by its ability to describe the physics of the system within a single determinant. The results suggest that with an appropriate basis, single-reference quantum chemical approaches may be able to describe many-body wavefunctions of strongly correlated materials. Furthermore, this thesis presents a reformulation of the projected imaginary time evolution of FCIQMC as a Lagrangian minimisation. This naturally allows for the optimisation of polynomial complex wavefunction ansatzes with a polynomial rather than exponential scaling with system size. -
Probabilistic Machine Learning: Foundations and Frontiers
Probabilistic Machine Learning: Foundations and Frontiers Zoubin Ghahramani1,2,3,4 1 University of Cambridge 2 Alan Turing Institute 3 Leverhulme Centre for the Future of Intelligence 4 Uber AI Labs [email protected] http://mlg.eng.cam.ac.uk/zoubin/ Sackler Forum, National Academy of Sciences Washington DC, 2017 Machine Learning Zoubin Ghahramani 2 / 53 Many Related Terms Statistical Modelling Artificial Intelligence Neural Networks Machine Learning Data Mining Data Analytics Deep Learning Pattern Recognition Data Science Zoubin Ghahramani 3 / 53 Many Related Fields Engineering Computer Science Statistics Machine Learning Computational Applied Mathematics Neuroscience Economics Cognitive Science Physics Zoubin Ghahramani 4 / 53 Many Many Applications Bioinformatics Computer Vision Robotics Scientific Data Analysis Natural Language Processing Machine Learning Information Retrieval Speech Recognition Recommender Systems Signal Processing Machine Translation Medical Informatics Targeted Advertising Finance Data Compression Zoubin Ghahramani 5 / 53 Machine Learning • Machine learning is an interdisciplinary field that develops both the mathematical foundations and practical applications of systems that learn from data. Main conferences and journals: NIPS, ICML, AISTATS, UAI, KDD, JMLR, IEEE TPAMI Zoubin Ghahramani 6 / 53 Canonical problems in machine learning Zoubin Ghahramani 7 / 53 Classification x x x o x xxx o x o o o x x o o x o • Task: predict discrete class label from input data • Applications: face recognition, image recognition, -
Quantum Communications Hub Annual Report
Contents Foreword 3 Introduction 4 Quantum Communications Hub – Vision 5 Quantum Key Distribution 6 Technology Themes 7 The Partnership 9 Strategy, Advice, Leadership 10 The Project Team 14 Governance 15 Project Website 16 The Quantum Communications Hub – The First 12 Months 17 Commercialisation Routes and Partners 22 User Engagement 23 Formal Launch of the Hub 23 Highlight on the Adastral Park Cluster 25 Highlight on The National Quantum Technologies Showcase 26 Highlight on KETS 27 Highlight on Standards 28 Impact on Policy 29 Future Research Directions 33 Appendices 40 1 2 Introduction The UK National Quantum Technologies Programme (UKNQTP) is a UK Government initiative designed to support translation of quantum science into commercial Foreword technological applications. The aim is to turn world-leading science into new technologies and services, creating catalysts for new markets, thus boosting the UK economy and resulting in demonstrable effects across all spheres of verydaye The UK National Quantum Technologies Programme life. Unlike previous investments in what are perceived as emerging and promising has been established to turn the results of world-leading new areas for growth, the focus of this particular programme is on technological scientific research into actual technologies. In the Quantum development and commercialisation, rather than generation of new science. This Communications Hub, it is our job to do this in the secure approach is based on the strength of the UK’s academic leadership in quantum science, communications sector. In this sector some technologies coupled with the acknowledgment of the timeliness of technological advances in and demonstrators already exist, so the goal of the Hub is this area.