Machine Learning Theory (CS 6783)
|
|
|
- Gwendoline Richardson
- 5 years ago
- Views:
Transcription
1 Machine Learning Theory (CS 6783) Tu-Th 1:25 to 2:40 PM Kimball, B-11 Instructor : Karthik Sridharan
2 ABOUT THE COURSE No exams! 5 assignments that count towards your grades (55%) One term project (40%) 5% for class participation
3 PRE-REQUISITES Basic probability theory Basics of algorithms and analysis Introductory level machine learning course Mathematical maturity, comfortable reading/writing formal mathematical proofs.
4 TERM PROJECT One of the following three options : 1 Pick your research problem, get it approved by me, write a report on your work 2 Pick two papers on learning theory, get it approved by me, write a report with your own views/opinions 3 I will provide a list of problems, workout problems worth a total of 10 stars out of this list Oct 16th submit proposal/get your project approved by me Finals week projects are due
5 Lets get started...
6 WHAT IS MACHINE LEARNING Use past observations to automatically learn to make better predictions/decisions in the future.
7 W HERE IS IT USED? Recommendation Systems
8 WHERE IS IT USED? Pedestrian Detection
9 WHERE IS IT USED? Market Predictions
10 W HERE IS IT USED? Spam Classification
11 WHERE IS IT USED? Online advertising (improving click through rates) Climate/weather prediction Text categorization Unsupervised clustering (of articles... )...
12 WHAT IS LEARNING THEORY
13 WHAT IS LEARNING THEORY Oops...
14 WHAT IS MACHINE LEARNING THEORY How do formalize machine learning problems Right framework for right problems (Eg. online, statistical) What does it mean for a problem to be learnable How many instances do we need to see to learn to given accuracy How do we build sound learning algorithms based on theory Computational learning theory : which problems are efficiently learnable
15 OUTLINE OF TOPICS Learning problem and frameworks, settings, minimax rates Statistical learning theory Probably Approximately Correct (PAC) and Agnostic PAC frameworks Empirical Risk Minimization, Uniform convergence, Empirical process theory Finite model classes, MDL bounds, PAC Bayes theorem Infinite model classes, Rademacher complexity Binary Classification : growth function, VC dimension Real-valued function classes, covering numbers, chaining, fat-shattering dimension Supervised learning : necessary and sufficient conditions for learnability Online learning theory Sequential minimax and value of online learning game Martingale Uniform convergence, sequential empirical process theory Sequential Rademacher complexity Binary Classification : Littlestone dimension Real valued function classes, sequential covering numbers, chaining bounds, sequential fat-shattering dimension Online supervised learning : necessary & sufficient conditions for learnability Designing learning algorithms : relaxations, random play-outs Computational Learning theory and more if time permits...
16 LEARNING PROBLEM : BASIC NOTATION Input space/ feature space : X (Eg. bag-of-words, n-grams, vector of grey-scale values, user-movie pair to rate) Feature extraction is an art,... an art we won t cover in this course Output space/ label space Y (Eg. {±1}, [K], R-valued output, structured output) Loss function : l Y Y R (Eg. 0 1 loss l(y, y) = 1 {y y}, sq-loss l(y, y) = (y y ) 2 ), absolute loss l(y, y) = y y Measures performance/cost per instance (inaccuracy of prediction/ cost of decision). Model class/hypothesis class F Y X (Eg. F = {x f x f 2 1}, F = {x sign(f x)})
17 FORMALIZING LEARNING PROBLEMS How is data generated? How do we measure performance or success? Where do we place our prior assumption or model assumptions?
18 FORMALIZING LEARNING PROBLEMS How is data generated? How do we measure performance or success? Where do we place our prior assumption or model assumptions? What we observe?
19 PROBABLY APPROXIMATELY CORRECT LEARNING Y = {±1}, l(y, y) = 1 {y y}, F Y X Learner only observes training sample S = {(x 1, y 1 ),..., (x n, y n )} x 1,..., x n D X t [n], y t = f (x t ) where f F Goal : find ŷ Y X to minimize P x DX (ŷ(x) f (x)) (Either in expectation or with high probability)
20 PROBABLY APPROXIMATELY CORRECT LEARNING Definition Given δ > 0, ɛ > 0, sample complexity n(ɛ, δ) is the smallest n such that we can always find forecaster ŷ s.t. with probability at least 1 δ, P x DX (ŷ(x) f (x)) ɛ (efficiently PAC learnable if we can learn efficiently in 1/δ and 1/ɛ) Eg. : learning output for deterministic systems
21 NON-PARAMETRIC REGRESSION Y R, l(y, y) = (y y ) 2, F Y X Learner only observes training sample S = {(x 1, y 1 ),..., (x n, y n )} x 1,..., x n D X t [n], y t = f (x t ) + ε t where f F and ε t N(0, σ) Goal : find ŷ R X to minimize ŷ f 2 L 2 (D X ) = E x D X [(ŷ(x) f (x)) 2 ] (Either in expectation or in high probability) = E x DX [(ŷ(x) y) 2 ] inf f F E x D X [(f (x) y) 2 ] Eg. : clinical trials (inference problems) model class known.
22 NON-PARAMETRIC REGRESSION Y R, l(ŷ, y) = (y ŷ) 2, F Y X Learner only observes training sample S = {(x 1, y 1 ),..., (x n, y n )} x 1,..., x n D X t [n], y t = f (x t ) + ε t where f F and ε t N(0, σ) Goal : find ŷ R X to minimize ŷ f 2 L 2 (D X ) = E x D X [(ŷ(x) f (x)) 2 ] (Either in expectation or in high probability) = E x DX [(ŷ(x) y) 2 ] inf f F E x D X [(f (x) y) 2 ] Eg. : clinical trials (inference problems) model class known.
23 STATISTICAL LEARNING (AGNOSTIC PAC) Learner only observes training sample S = {(x 1, y 1 ),..., (x n, y n )} drawn iid from joint distribution D on X Y Goal : find ŷ R X to minimize expected loss over future instances E (x,y) D [l(ŷ(x), y)] inf f F E (x,y) D [l(f (x), y)] ɛ L D (ŷ) inf f F L D(f ) ɛ
24 STATISTICAL LEARNING (AGNOSTIC PAC) Definition Given δ > 0, ɛ > 0, sample complexity n(ɛ, δ) is the smallest n such that we can always find forecaster ŷ s.t. with probability at least 1 δ, L D (ŷ) inf f F L D(f ) ɛ
25 L EARNING P ROBLEMS Pedestrian Detection Spam Classification
26 L EARNING P ROBLEMS Pedestrian Detection Spam Classification (Batch/Statistical setting) (Online/adversarial setting)
27 ONLINE LEARNING (SEQUENTIAL PREDICTION) For t = 1 to n Learner receives x t X Learner predicts output ŷ t Y True output y t Y is revealed End for Goal : minimize regret Reg n (F) = 1 n 1 l(ŷ t, y t ) inf t=1 f F n l(f (x t ), y t ) t=1
28 OTHER PROBLEMS/FRAMEWORKS Unsupervised learning, clustering Semi-supervised learning Active learning and selective sampling Online convex optimization Bandit problems, partial monitoring,...
29 SNEEK PEEK No Free Lunch Theorems Statistical learning theory Empirical risk minimization Uniform convergence and learning Finite model classes, MDL, PAC Bayes theorem,...
30 HOMEWORK 0 : WARMUP Brush up Markov inequality, Chebychev inequality, central limit theorem Read up or brush up, concentration inequalities (specifically Hoeffding bound, Bernstein bound, Hoeffding-Azuma inequality, McDiarmid s inequality also referred to as bounded difference inequality) Brush up union bound Watch out for homework 0, no need to submit, just a warmup
Machine Learning Theory (CS 6783)
Machine Learning Theory (CS 6783) Tu-Th 1:25 to 2:40 PM Hollister, 306 Instructor : Karthik Sridharan ABOUT THE COURSE No exams! 5 assignments that count towards your grades (55%) One term project (40%)
COMS 4771 Introduction to Machine Learning. Nakul Verma
COMS 4771 Introduction to Machine Learning Nakul Verma Announcements HW2 due now! Project proposal due on tomorrow Midterm next lecture! HW3 posted Last time Linear Regression Parametric vs Nonparametric
12. Structural Risk Minimization. ECE 830 & CS 761, Spring 2016
12. Structural Risk Minimization ECE 830 & CS 761, Spring 2016 1 / 23 General setup for statistical learning theory We observe training examples {x i, y i } n i=1 x i = features X y i = labels / responses
CS 6375 Machine Learning
CS 6375 Machine Learning Nicholas Ruozzi University of Texas at Dallas Slides adapted from David Sontag and Vibhav Gogate Course Info. Instructor: Nicholas Ruozzi Office: ECSS 3.409 Office hours: Tues.
Lecture Learning infinite hypothesis class via VC-dimension and Rademacher complexity;
CSCI699: Topics in Learning and Game Theory Lecture 2 Lecturer: Ilias Diakonikolas Scribes: Li Han Today we will cover the following 2 topics: 1. Learning infinite hypothesis class via VC-dimension and
Foundations of Machine Learning
Introduction to ML Mehryar Mohri Courant Institute and Google Research mohri@cims.nyu.edu page 1 Logistics Prerequisites: basics in linear algebra, probability, and analysis of algorithms. Workload: about
Empirical Risk Minimization
Empirical Risk Minimization Fabrice Rossi SAMM Université Paris 1 Panthéon Sorbonne 2018 Outline Introduction PAC learning ERM in practice 2 General setting Data X the input space and Y the output space
An Introduction to Statistical Theory of Learning. Nakul Verma Janelia, HHMI
An Introduction to Statistical Theory of Learning Nakul Verma Janelia, HHMI Towards formalizing learning What does it mean to learn a concept? Gain knowledge or experience of the concept. The basic process
IFT Lecture 7 Elements of statistical learning theory
IFT 6085 - Lecture 7 Elements of statistical learning theory This version of the notes has not yet been thoroughly checked. Please report any bugs to the scribes or instructor. Scribe(s): Brady Neal and
Introduction to Machine Learning (67577) Lecture 3
Introduction to Machine Learning (67577) Lecture 3 Shai Shalev-Shwartz School of CS and Engineering, The Hebrew University of Jerusalem General Learning Model and Bias-Complexity tradeoff Shai Shalev-Shwartz
Understanding Generalization Error: Bounds and Decompositions
CIS 520: Machine Learning Spring 2018: Lecture 11 Understanding Generalization Error: Bounds and Decompositions Lecturer: Shivani Agarwal Disclaimer: These notes are designed to be a supplement to the
Generalization bounds
Advanced Course in Machine Learning pring 200 Generalization bounds Handouts are jointly prepared by hie Mannor and hai halev-hwartz he problem of characterizing learnability is the most basic question
Generalization, Overfitting, and Model Selection
Generalization, Overfitting, and Model Selection Sample Complexity Results for Supervised Classification Maria-Florina (Nina) Balcan 10/03/2016 Two Core Aspects of Machine Learning Algorithm Design. How
PAC Learning Introduction to Machine Learning. Matt Gormley Lecture 14 March 5, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University PAC Learning Matt Gormley Lecture 14 March 5, 2018 1 ML Big Picture Learning Paradigms:
Advanced Introduction to Machine Learning CMU-10715
Advanced Introduction to Machine Learning CMU-10715 Risk Minimization Barnabás Póczos What have we seen so far? Several classification & regression algorithms seem to work fine on training datasets: Linear
The No-Regret Framework for Online Learning
The No-Regret Framework for Online Learning A Tutorial Introduction Nahum Shimkin Technion Israel Institute of Technology Haifa, Israel Stochastic Processes in Engineering IIT Mumbai, March 2013 N. Shimkin,
Introduction to Machine Learning CMU-10701
Introduction to Machine Learning CMU10701 11. Learning Theory Barnabás Póczos Learning Theory We have explored many ways of learning from data But How good is our classifier, really? How much data do we
Introduction to Machine Learning
Introduction to Machine Learning Vapnik Chervonenkis Theory Barnabás Póczos Empirical Risk and True Risk 2 Empirical Risk Shorthand: True risk of f (deterministic): Bayes risk: Let us use the empirical
Machine Learning. Lecture 9: Learning Theory. Feng Li.
Machine Learning Lecture 9: Learning Theory Feng Li fli@sdu.edu.cn https://funglee.github.io School of Computer Science and Technology Shandong University Fall 2018 Why Learning Theory How can we tell
The PAC Learning Framework -II
The PAC Learning Framework -II Prof. Dan A. Simovici UMB 1 / 1 Outline 1 Finite Hypothesis Space - The Inconsistent Case 2 Deterministic versus stochastic scenario 3 Bayes Error and Noise 2 / 1 Outline
Generalization, Overfitting, and Model Selection
Generalization, Overfitting, and Model Selection Sample Complexity Results for Supervised Classification MariaFlorina (Nina) Balcan 10/05/2016 Reminders Midterm Exam Mon, Oct. 10th Midterm Review Session
Naïve Bayes Introduction to Machine Learning. Matt Gormley Lecture 18 Oct. 31, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Naïve Bayes Matt Gormley Lecture 18 Oct. 31, 2018 1 Reminders Homework 6: PAC Learning
Active Learning and Optimized Information Gathering
Active Learning and Optimized Information Gathering Lecture 7 Learning Theory CS 101.2 Andreas Krause Announcements Project proposal: Due tomorrow 1/27 Homework 1: Due Thursday 1/29 Any time is ok. Office
Generalization Bounds and Stability
Generalization Bounds and Stability Lorenzo Rosasco Tomaso Poggio 9.520 Class 9 2009 About this class Goal To recall the notion of generalization bounds and show how they can be derived from a stability
Online Learning and Sequential Decision Making
Online Learning and Sequential Decision Making Emilie Kaufmann CNRS & CRIStAL, Inria SequeL, emilie.kaufmann@univ-lille.fr Research School, ENS Lyon, Novembre 12-13th 2018 Emilie Kaufmann Online Learning
Computational Learning Theory: Probably Approximately Correct (PAC) Learning. Machine Learning. Spring The slides are mainly from Vivek Srikumar
Computational Learning Theory: Probably Approximately Correct (PAC) Learning Machine Learning Spring 2018 The slides are mainly from Vivek Srikumar 1 This lecture: Computational Learning Theory The Theory
Topics in Natural Language Processing
Topics in Natural Language Processing Shay Cohen Institute for Language, Cognition and Computation University of Edinburgh Lecture 9 Administrativia Next class will be a summary Please email me questions
Statistical Learning Learning From Examples
Statistical Learning Learning From Examples We want to estimate the working temperature range of an iphone. We could study the physics and chemistry that affect the performance of the phone too hard We
Computational and Statistical Learning Theory
Computational and Statistical Learning Theory Problem set 1 Due: Monday, October 10th Please send your solutions to learning-submissions@ttic.edu Notation: Input space: X Label space: Y = {±1} Sample:
Learnability, Stability, Regularization and Strong Convexity
Learnability, Stability, Regularization and Strong Convexity Nati Srebro Shai Shalev-Shwartz HUJI Ohad Shamir Weizmann Karthik Sridharan Cornell Ambuj Tewari Michigan Toyota Technological Institute Chicago
Machine Learning 2007: Slides 1. Instructor: Tim van Erven Website: erven/teaching/0708/ml/
Machine 2007: Slides 1 Instructor: Tim van Erven (Tim.van.Erven@cwi.nl) Website: www.cwi.nl/ erven/teaching/0708/ml/ September 6, 2007, updated: September 13, 2007 1 / 37 Overview The Most Important Supervised
Introduction to Machine Learning. Introduction to ML - TAU 2016/7 1
Introduction to Machine Learning Introduction to ML - TAU 2016/7 1 Course Administration Lecturers: Amir Globerson (gamir@post.tau.ac.il) Yishay Mansour (Mansour@tau.ac.il) Teaching Assistance: Regev Schweiger
Machine Learning (CS 567) Lecture 2
Machine Learning (CS 567) Lecture 2 Time: T-Th 5:00pm - 6:20pm Location: GFS118 Instructor: Sofus A. Macskassy (macskass@usc.edu) Office: SAL 216 Office hours: by appointment Teaching assistant: Cheol
PAC-learning, VC Dimension and Margin-based Bounds
More details: General: http://www.learning-with-kernels.org/ Example of more complex bounds: http://www.research.ibm.com/people/t/tzhang/papers/jmlr02_cover.ps.gz PAC-learning, VC Dimension and Margin-based
Does Unlabeled Data Help?
Does Unlabeled Data Help? Worst-case Analysis of the Sample Complexity of Semi-supervised Learning. Ben-David, Lu and Pal; COLT, 2008. Presentation by Ashish Rastogi Courant Machine Learning Seminar. Outline
Agnostic Online learnability
Technical Report TTIC-TR-2008-2 October 2008 Agnostic Online learnability Shai Shalev-Shwartz Toyota Technological Institute Chicago shai@tti-c.org ABSTRACT We study a fundamental question. What classes
Least Squares Regression
E0 70 Machine Learning Lecture 4 Jan 7, 03) Least Squares Regression Lecturer: Shivani Agarwal Disclaimer: These notes are a brief summary of the topics covered in the lecture. They are not a substitute
Generalization theory
Generalization theory Daniel Hsu Columbia TRIPODS Bootcamp 1 Motivation 2 Support vector machines X = R d, Y = { 1, +1}. Return solution ŵ R d to following optimization problem: λ min w R d 2 w 2 2 + 1
Understanding Machine Learning A theory Perspective
Understanding Machine Learning A theory Perspective Shai Ben-David University of Waterloo MLSS at MPI Tubingen, 2017 Disclaimer Warning. This talk is NOT about how cool machine learning is. I am sure you
CS155: Probability and Computing: Randomized Algorithms and Probabilistic Analysis
CS155: Probability and Computing: Randomized Algorithms and Probabilistic Analysis Eli Upfal Eli Upfal@brown.edu Office: 319 TA s: Lorenzo De Stefani and Sorin Vatasoiu cs155tas@cs.brown.edu It is remarkable
Machine Learning. Instructor: Pranjal Awasthi
Machine Learning Instructor: Pranjal Awasthi Course Info Requested an SPN and emailed me Wait for Carol Difrancesco to give them out. Not registered and need SPN Email me after class No promises It s a
COS 402 Machine Learning and Artificial Intelligence Fall Lecture 3: Learning Theory
COS 402 Machine Learning and Artificial Intelligence Fall 2016 Lecture 3: Learning Theory Sanjeev Arora Elad Hazan Admin Exercise 1 due next Tue, in class Enrolment Recap We have seen: AI by introspection
PATTERN RECOGNITION AND MACHINE LEARNING
PATTERN RECOGNITION AND MACHINE LEARNING Chapter 1. Introduction Shuai Huang April 21, 2014 Outline 1 What is Machine Learning? 2 Curve Fitting 3 Probability Theory 4 Model Selection 5 The curse of dimensionality
Generalization and Overfitting
Generalization and Overfitting Model Selection Maria-Florina (Nina) Balcan February 24th, 2016 PAC/SLT models for Supervised Learning Data Source Distribution D on X Learning Algorithm Expert / Oracle
Online Learning: Random Averages, Combinatorial Parameters, and Learnability
Online Learning: Random Averages, Combinatorial Parameters, and Learnability Alexander Rakhlin Department of Statistics University of Pennsylvania Karthik Sridharan Toyota Technological Institute at Chicago
PAC-learning, VC Dimension and Margin-based Bounds
More details: General: http://www.learning-with-kernels.org/ Example of more complex bounds: http://www.research.ibm.com/people/t/tzhang/papers/jmlr02_cover.ps.gz PAC-learning, VC Dimension and Margin-based
Class 2 & 3 Overfitting & Regularization
Class 2 & 3 Overfitting & Regularization Carlo Ciliberto Department of Computer Science, UCL October 18, 2017 Last Class The goal of Statistical Learning Theory is to find a good estimator f n : X Y, approximating
Stat 406: Algorithms for classification and prediction. Lecture 1: Introduction. Kevin Murphy. Mon 7 January,
1 Stat 406: Algorithms for classification and prediction Lecture 1: Introduction Kevin Murphy Mon 7 January, 2008 1 1 Slides last updated on January 7, 2008 Outline 2 Administrivia Some basic definitions.
ECE521 week 3: 23/26 January 2017
ECE521 week 3: 23/26 January 2017 Outline Probabilistic interpretation of linear regression - Maximum likelihood estimation (MLE) - Maximum a posteriori (MAP) estimation Bias-variance trade-off Linear
Statistical Approaches to Learning and Discovery. Week 4: Decision Theory and Risk Minimization. February 3, 2003
Statistical Approaches to Learning and Discovery Week 4: Decision Theory and Risk Minimization February 3, 2003 Recall From Last Time Bayesian expected loss is ρ(π, a) = E π [L(θ, a)] = L(θ, a) df π (θ)
ORIE 4741: Learning with Big Messy Data. Generalization
ORIE 4741: Learning with Big Messy Data Generalization Professor Udell Operations Research and Information Engineering Cornell September 23, 2017 1 / 21 Announcements midterm 10/5 makeup exam 10/2, by
Generalization Bounds in Machine Learning. Presented by: Afshin Rostamizadeh
Generalization Bounds in Machine Learning Presented by: Afshin Rostamizadeh Outline Introduction to generalization bounds. Examples: VC-bounds Covering Number bounds Rademacher bounds Stability bounds
Models, Data, Learning Problems
Universität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen Models, Data, Learning Problems Tobias Scheffer Overview Types of learning problems: Supervised Learning (Classification, Regression,
On the tradeoff between computational complexity and sample complexity in learning
On the tradeoff between computational complexity and sample complexity in learning Shai Shalev-Shwartz School of Computer Science and Engineering The Hebrew University of Jerusalem Joint work with Sham
Online Learning. Jordan Boyd-Graber. University of Colorado Boulder LECTURE 21. Slides adapted from Mohri
Online Learning Jordan Boyd-Graber University of Colorado Boulder LECTURE 21 Slides adapted from Mohri Jordan Boyd-Graber Boulder Online Learning 1 of 31 Motivation PAC learning: distribution fixed over
CS281B/Stat241B. Statistical Learning Theory. Lecture 1.
CS281B/Stat241B. Statistical Learning Theory. Lecture 1. Peter Bartlett 1. Organizational issues. 2. Overview. 3. Probabilistic formulation of prediction problems. 4. Game theoretic formulation of prediction
Computational and Statistical Learning theory
Computational and Statistical Learning theory Problem set 2 Due: January 31st Email solutions to : karthik at ttic dot edu Notation : Input space : X Label space : Y = {±1} Sample : (x 1, y 1,..., (x n,
Learning Theory. Machine Learning CSE546 Carlos Guestrin University of Washington. November 25, Carlos Guestrin
Learning Theory Machine Learning CSE546 Carlos Guestrin University of Washington November 25, 2013 Carlos Guestrin 2005-2013 1 What now n We have explored many ways of learning from data n But How good
Least Squares Regression
CIS 50: Machine Learning Spring 08: Lecture 4 Least Squares Regression Lecturer: Shivani Agarwal Disclaimer: These notes are designed to be a supplement to the lecture. They may or may not cover all the
Tutorial: PART 1. Online Convex Optimization, A Game- Theoretic Approach to Learning.
Tutorial: PART 1 Online Convex Optimization, A Game- Theoretic Approach to Learning http://www.cs.princeton.edu/~ehazan/tutorial/tutorial.htm Elad Hazan Princeton University Satyen Kale Yahoo Research
Computational Learning Theory
Computational Learning Theory Pardis Noorzad Department of Computer Engineering and IT Amirkabir University of Technology Ordibehesht 1390 Introduction For the analysis of data structures and algorithms
http://imgs.xkcd.com/comics/electoral_precedent.png Statistical Learning Theory CS4780/5780 Machine Learning Fall 2012 Thorsten Joachims Cornell University Reading: Mitchell Chapter 7 (not 7.4.4 and 7.5)
CS 598 Statistical Reinforcement Learning. Nan Jiang
CS 598 Statistical Reinforcement Learning Nan Jiang Overview What s this course about? A grad-level seminar course on theory of RL 3 What s this course about? A grad-level seminar course on theory of RL
Computational Learning Theory. CS 486/686: Introduction to Artificial Intelligence Fall 2013
Computational Learning Theory CS 486/686: Introduction to Artificial Intelligence Fall 2013 1 Overview Introduction to Computational Learning Theory PAC Learning Theory Thanks to T Mitchell 2 Introduction
Online Learning, Mistake Bounds, Perceptron Algorithm
Online Learning, Mistake Bounds, Perceptron Algorithm 1 Online Learning So far the focus of the course has been on batch learning, where algorithms are presented with a sample of training data, from which
FORMULATION OF THE LEARNING PROBLEM
FORMULTION OF THE LERNING PROBLEM MIM RGINSKY Now that we have seen an informal statement of the learning problem, as well as acquired some technical tools in the form of concentration inequalities, we
Be able to define the following terms and answer basic questions about them:
CS440/ECE448 Section Q Fall 2017 Final Review Be able to define the following terms and answer basic questions about them: Probability o Random variables, axioms of probability o Joint, marginal, conditional
Multi-armed bandit models: a tutorial
Multi-armed bandit models: a tutorial CERMICS seminar, March 30th, 2016 Multi-Armed Bandit model: general setting K arms: for a {1,..., K}, (X a,t ) t N is a stochastic process. (unknown distributions)
Online Learning and Sequential Decision Making
Online Learning and Sequential Decision Making Emilie Kaufmann CNRS & CRIStAL, Inria SequeL, emilie.kaufmann@univ-lille.fr Research School, ENS Lyon, Novembre 12-13th 2018 Emilie Kaufmann Sequential Decision
Lecture 5 Neural models for NLP
CS546: Machine Learning in NLP (Spring 2018) http://courses.engr.illinois.edu/cs546/ Lecture 5 Neural models for NLP Julia Hockenmaier juliahmr@illinois.edu 3324 Siebel Center Office hours: Tue/Thu 2pm-3pm
1 A Lower Bound on Sample Complexity
COS 511: Theoretical Machine Learning Lecturer: Rob Schapire Lecture #7 Scribe: Chee Wei Tan February 25, 2008 1 A Lower Bound on Sample Complexity In the last lecture, we stopped at the lower bound on
E0 370 Statistical Learning Theory Lecture 5 (Aug 25, 2011)
E0 370 Statistical Learning Theory Lecture 5 Aug 5, 0 Covering Nubers, Pseudo-Diension, and Fat-Shattering Diension Lecturer: Shivani Agarwal Scribe: Shivani Agarwal Introduction So far we have seen how
Models of Language Acquisition: Part II
Models of Language Acquisition: Part II Matilde Marcolli CS101: Mathematical and Computational Linguistics Winter 2015 Probably Approximately Correct Model of Language Learning General setting of Statistical
Littlestone s Dimension and Online Learnability
Littlestone s Dimension and Online Learnability Shai Shalev-Shwartz Toyota Technological Institute at Chicago The Hebrew University Talk at UCSD workshop, February, 2009 Joint work with Shai Ben-David
Computational Learning Theory: Shattering and VC Dimensions. Machine Learning. Spring The slides are mainly from Vivek Srikumar
Computational Learning Theory: Shattering and VC Dimensions Machine Learning Spring 2018 The slides are mainly from Vivek Srikumar 1 This lecture: Computational Learning Theory The Theory of Generalization
CS340 Machine learning Lecture 5 Learning theory cont'd. Some slides are borrowed from Stuart Russell and Thorsten Joachims
CS340 Machine learning Lecture 5 Learning theory cont'd Some slides are borrowed from Stuart Russell and Thorsten Joachims Inductive learning Simplest form: learn a function from examples f is the target
Advanced Introduction to Machine Learning
10-715 Advanced Introduction to Machine Learning Homework Due Oct 15, 10.30 am Rules Please follow these guidelines. Failure to do so, will result in loss of credit. 1. Homework is due on the due date
9/12/17. Types of learning. Modeling data. Supervised learning: Classification. Supervised learning: Regression. Unsupervised learning: Clustering
Types of learning Modeling data Supervised: we know input and targets Goal is to learn a model that, given input data, accurately predicts target data Unsupervised: we know the input only and want to make
Computational and Statistical Learning Theory
Computational and Statistical Learning Theory TTIC 31120 Prof. Nati Srebro Lecture 17: Stochastic Optimization Part II: Realizable vs Agnostic Rates Part III: Nearest Neighbor Classification Stochastic
Computational Learning Theory. CS534 - Machine Learning
Computational Learning Theory CS534 Machine Learning Introduction Computational learning theory Provides a theoretical analysis of learning Shows when a learning algorithm can be expected to succeed Shows
From Complexity to Intelligence
From Complexity to Intelligence Machine Learning and Complexity PAGE 1 / 72 Table of contents Reminder Introduction to Machine Learning What is Machine Learning? Types of Learning Unsupervised Learning
Introduction to Machine Learning Midterm Exam
10-701 Introduction to Machine Learning Midterm Exam Instructors: Eric Xing, Ziv Bar-Joseph 17 November, 2015 There are 11 questions, for a total of 100 points. This exam is open book, open notes, but
Consistency of Nearest Neighbor Methods
E0 370 Statistical Learning Theory Lecture 16 Oct 25, 2011 Consistency of Nearest Neighbor Methods Lecturer: Shivani Agarwal Scribe: Arun Rajkumar 1 Introduction In this lecture we return to the study
Bandit models: a tutorial
Gdt COS, December 3rd, 2015 Multi-Armed Bandit model: general setting K arms: for a {1,..., K}, (X a,t ) t N is a stochastic process. (unknown distributions) Bandit game: a each round t, an agent chooses
Computational Learning Theory
1 Computational Learning Theory 2 Computational learning theory Introduction Is it possible to identify classes of learning problems that are inherently easy or difficult? Can we characterize the number
Introduction and Models
CSE522, Winter 2011, Learning Theory Lecture 1 and 2-01/04/2011, 01/06/2011 Lecturer: Ofer Dekel Introduction and Models Scribe: Jessica Chang Machine learning algorithms have emerged as the dominant and
Machine Learning. Computational Learning Theory. Le Song. CSE6740/CS7641/ISYE6740, Fall 2012
Machine Learning CSE6740/CS7641/ISYE6740, Fall 2012 Computational Learning Theory Le Song Lecture 11, September 20, 2012 Based on Slides from Eric Xing, CMU Reading: Chap. 7 T.M book 1 Complexity of Learning
VC Dimension Review. The purpose of this document is to review VC dimension and PAC learning for infinite hypothesis spaces.
VC Dimension Review The purpose of this document is to review VC dimension and PAC learning for infinite hypothesis spaces. Previously, in discussing PAC learning, we were trying to answer questions about
Learning Theory Continued
Learning Theory Continued Machine Learning CSE446 Carlos Guestrin University of Washington May 13, 2013 1 A simple setting n Classification N data points Finite number of possible hypothesis (e.g., dec.
Learning with multiple models. Boosting.
CS 2750 Machine Learning Lecture 21 Learning with multiple models. Boosting. Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Learning with multiple models: Approach 2 Approach 2: use multiple models
The sample complexity of agnostic learning with deterministic labels
The sample complexity of agnostic learning with deterministic labels Shai Ben-David Cheriton School of Computer Science University of Waterloo Waterloo, ON, N2L 3G CANADA shai@uwaterloo.ca Ruth Urner College
Learning Theory. Ingo Steinwart University of Stuttgart. September 4, 2013
Learning Theory Ingo Steinwart University of Stuttgart September 4, 2013 Ingo Steinwart University of Stuttgart () Learning Theory September 4, 2013 1 / 62 Basics Informal Introduction Informal Description
Statistical Machine Learning Theory. From Multi-class Classification to Structured Output Prediction. Hisashi Kashima.
http://goo.gl/jv7vj9 Course website KYOTO UNIVERSITY Statistical Machine Learning Theory From Multi-class Classification to Structured Output Prediction Hisashi Kashima kashima@i.kyoto-u.ac.jp DEPARTMENT
Computational Learning Theory
CS 446 Machine Learning Fall 2016 OCT 11, 2016 Computational Learning Theory Professor: Dan Roth Scribe: Ben Zhou, C. Cervantes 1 PAC Learning We want to develop a theory to relate the probability of successful
Logic and machine learning review. CS 540 Yingyu Liang
Logic and machine learning review CS 540 Yingyu Liang Propositional logic Logic If the rules of the world are presented formally, then a decision maker can use logical reasoning to make rational decisions.
Decision trees COMS 4771
Decision trees COMS 4771 1. Prediction functions (again) Learning prediction functions IID model for supervised learning: (X 1, Y 1),..., (X n, Y n), (X, Y ) are iid random pairs (i.e., labeled examples).
Lecture 3: Introduction to Complexity Regularization
ECE90 Spring 2007 Statistical Learning Theory Instructor: R. Nowak Lecture 3: Introduction to Complexity Regularization We ended the previous lecture with a brief discussion of overfitting. Recall that,
Machine Learning for NLP
Machine Learning for NLP Linear Models Joakim Nivre Uppsala University Department of Linguistics and Philology Slides adapted from Ryan McDonald, Google Research Machine Learning for NLP 1(26) Outline
Machine Learning: Homework 5
0-60 Machine Learning: Homework 5 Due 5:0 p.m. Thursday, March, 06 TAs: Travis Dick and Han Zhao Instructions Late homework policy: Homework is worth full credit if submitted before the due date, half
Introduction to Machine Learning (67577) Lecture 5
Introduction to Machine Learning (67577) Lecture 5 Shai Shalev-Shwartz School of CS and Engineering, The Hebrew University of Jerusalem Nonuniform learning, MDL, SRM, Decision Trees, Nearest Neighbor Shai