Uncertainty in Deep Learning
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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. -
Improved Policy Networks for Computer Go
Improved Policy Networks for Computer Go Tristan Cazenave Universite´ Paris-Dauphine, PSL Research University, CNRS, LAMSADE, PARIS, FRANCE Abstract. Golois uses residual policy networks to play Go. Two improvements to these residual policy networks are proposed and tested. The first one is to use three output planes. The second one is to add Spatial Batch Normalization. 1 Introduction Deep Learning for the game of Go with convolutional neural networks has been ad- dressed by [2]. It has been further improved using larger networks [7, 10]. AlphaGo [9] combines Monte Carlo Tree Search with a policy and a value network. Residual Networks improve the training of very deep networks [4]. These networks can gain accuracy from considerably increased depth. On the ImageNet dataset a 152 layers networks achieves 3.57% error. It won the 1st place on the ILSVRC 2015 classifi- cation task. The principle of residual nets is to add the input of the layer to the output of each layer. With this simple modification training is faster and enables deeper networks. Residual networks were recently successfully adapted to computer Go [1]. As a follow up to this paper, we propose improvements to residual networks for computer Go. The second section details different proposed improvements to policy networks for computer Go, the third section gives experimental results, and the last section con- cludes. 2 Proposed Improvements We propose two improvements for policy networks. The first improvement is to use multiple output planes as in DarkForest. The second improvement is to use Spatial Batch Normalization. 2.1 Multiple Output Planes In DarkForest [10] training with multiple output planes containing the next three moves to play has been shown to improve the level of play of a usual policy network with 13 layers. -
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. -
Radford M. Neal Curriculum Vitae, 25 April 2021
Radford M. Neal Curriculum Vitae, 25 April 2021 Biographical Information Personal Data Date of Birth: 12 Sept 1956 Citizenship: Canadian Home address: University address: 21 Shaftesbury Avenue, #106 Department of Statistical Sciences Toronto, Ontario M4T 3B4 University of Toronto M5S 3G3 U of T web page: http://www.cs.utoronto.ca/∼radford/ Blog (not affiliated with U of T): https://radfordneal.wordpress.com E-mail addresses: [email protected], [email protected] Degrees Awarded BSc (Honours) in Computer Science, University of Calgary, 1977 MSc in Computer Science, University of Calgary, 1980 Thesis title: An Editor for Trees Supervisor: David Hill Ph.D in Computer Science, University of Toronto, 1995 Thesis title: Bayesian Learning for Neural Networks Supervisor: Geoffrey Hinton Employment and Other Relevant Experience Present position: Professor Emeritus, Department of Statistical Sciences and Department of Computer Science, University of Toronto, Appointed as Lecturer 1 July 1994. Appointed as Associate Member (Limited Term) of the graduate faculty 13 January 1995. Promoted to Assistant Professor 1 July 1995. Promoted to Associate Professor and full member of the graduate faculty 1 July 1999. Promoted fo Full Professor 1 July 2001. Awarded a Canada Research Chair in Statistics and Machine Learning 1 July 2003 (held to 31 December 2016). Cross-appointed to the Dalla Lana School of Public Health 14 February 2006. Retired as of 1 January 2017. Earlier teaching experience: Sessional instructor in computer science at the University of Calgary for the following courses: 1 Summers 1979-1981 Taught half of the core second-year course on machine archi- tecture and programming. -
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. -
Lecture Notes Geoffrey Hinton
Lecture Notes Geoffrey Hinton Overjoyed Luce crops vectorially. Tailor write-ups his glasshouse divulgating unmanly or constructively after Marcellus barb and outdriven squeakingly, diminishable and cespitose. Phlegmatical Laurance contort thereupon while Bruce always dimidiating his melancholiac depresses what, he shores so finitely. For health care about working memory networks are the class and geoffrey hinton and modify or are A practical guide to training restricted boltzmann machines Lecture Notes in. Trajectory automatically learn about different domains, geoffrey explained what a lecture notes geoffrey hinton notes was central bottleneck form of data should take much like a single example, geoffrey hinton with mctsnets. Gregor sieber and password you may need to this course that models decisions. Jimmy Ba Geoffrey Hinton Volodymyr Mnih Joel Z Leibo and Catalin Ionescu. YouTube lectures by Geoffrey Hinton3 1 Introduction In this topic of boosting we combined several simple classifiers into very complex classifier. Separating Figure from stand with a Parallel Network Paul. But additionally has efficient. But everett also look up. You already know how the course that is just to my assignment in the page and writer recognition and trends in the effect of the motivating this. These perplex the or free liquid Intelligence educational. Citation to lose sight of language. Sparse autoencoder CS294A Lecture notes Andrew Ng Stanford University. Geoffrey Hinton on what's nothing with CNNs Daniel C Elton. Toronto Geoffrey Hinton Advanced Machine Learning CSC2535 2011 Spring. Cross validated is sparse, a proof of how to list of possible configurations have to see. Cnns that just download a computational power nor the squared error in permanent electrode array with respect to the. -
CSC321 Lecture 23: Go
CSC321 Lecture 23: Go Roger Grosse Roger Grosse CSC321 Lecture 23: Go 1 / 22 Final Exam Monday, April 24, 7-10pm A-O: NR 25 P-Z: ZZ VLAD Covers all lectures, tutorials, homeworks, and programming assignments 1/3 from the first half, 2/3 from the second half If there's a question on this lecture, it will be easy Emphasis on concepts covered in multiple of the above Similar in format and difficulty to the midterm, but about 3x longer Practice exams will be posted Roger Grosse CSC321 Lecture 23: Go 2 / 22 Overview Most of the problem domains we've discussed so far were natural application areas for deep learning (e.g. vision, language) We know they can be done on a neural architecture (i.e. the human brain) The predictions are inherently ambiguous, so we need to find statistical structure Board games are a classic AI domain which relied heavily on sophisticated search techniques with a little bit of machine learning Full observations, deterministic environment | why would we need uncertainty? This lecture is about AlphaGo, DeepMind's Go playing system which took the world by storm in 2016 by defeating the human Go champion Lee Sedol Roger Grosse CSC321 Lecture 23: Go 3 / 22 Overview Some milestones in computer game playing: 1949 | Claude Shannon proposes the idea of game tree search, explaining how games could be solved algorithmically in principle 1951 | Alan Turing writes a chess program that he executes by hand 1956 | Arthur Samuel writes a program that plays checkers better than he does 1968 | An algorithm defeats human novices at Go 1992 -
An Empirical Study on Evaluation Metrics of Generativeadversarialnetworks
Under review as a conference paper at ICLR 2018 AN EMPIRICAL STUDY ON EVALUATION METRICS OF GENERATIVE ADVERSARIAL NETWORKS Anonymous authors Paper under double-blind review ABSTRACT Despite the widespread interest in generative adversarial networks (GANs), few works have studied the metrics that quantitatively evaluate GANs’ performance. In this paper, we revisit several representative sample-based evaluation metrics for GANs, and address the important problem of how to evaluate the evaluation metrics. We start with a few necessary conditions for metrics to produce meaningful scores, such as distinguishing real from generated samples, identifying mode dropping and mode collapsing, and detecting overfitting. Then with a series of carefully designed experiments, we are able to comprehensively investigate existing sample-based metrics and identify their strengths and limitations in practical settings. Based on these results, we observe that kernel Maximum Mean Discrepancy (MMD) and the 1-Nearest-Neighbour (1-NN) two-sample test seem to satisfy most of the desirable properties, provided that the distances between samples are computed in a suitable feature space. Our experiments also unveil interesting properties about the behavior of several popular GAN models, such as whether they are memorizing training samples, and how far these state-of-the-art GANs are from perfect. 1 INTRODUCTION Generative adversarial networks (GANs) (Goodfellow et al., 2014) have been studied extensively in recent years. Besides producing surprisingly plausible images of faces (Radford et al., 2015; Larsen et al., 2015) and bedrooms (Radford et al., 2015; Arjovsky et al., 2017; Gulrajani et al., 2017), they have also been innovatively applied in, for example, semi-supervised learning (Odena, 2016; Makhzani et al., 2015), image-to-image translation (Isola et al., 2016; Zhu et al., 2017), and simulated image refinement (Shrivastava et al., 2016). -
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,