Machine Learning Overview

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Machine Learning Overview"

Transcription

1 Machine Learning Overview Sargur N. Srihari University at Buffalo, State University of New York USA 1

2 Outline 1. What is Machine Learning (ML)? 1. As a scientific Discipline 2. As an area of Computer Science/AI 2. Core learning methods 1. Supervised (Regression/Classification/Deep) 2. Unsupervised (PCA, Clustering, Topic Models) 3. Reinforcement 3. Main drivers 1. Mobile systems (big data) 2. Personalization 2

3 Machine Learning as a Discipline Focused on two inter-related fundamental scientific/engineering questions 1. How can one construct computer systems that automatically improve through experience? 2. What are the statistical-computational-informationtheoretic laws that govern all learning systems Including computers, humans and organizations? Machine learning is also important for highly practical computer software fielded across many applications 3

4 Machine Learning as Software Area Programming computers to: Perform tasks that humans perform well but difficult to specify algorithmically Principled way of building high performance information processing systems Probabilistic responses to queries IR Adaptive user interfaces, personalized assistants (information systems) Scientific/engineering applications 4

5 ML within AI ML has emerged as method of choice for practical software for: Computer vision Speech recognition Natural language processing Robot control Other applications Far easier to train by showing examples of input-output behavior Than manually anticipate response for every input 5

6 Example Problem: Handwritten Digit Recognition Wide variability of same numeral Handcrafted rules will result in large no of rules and exceptions Better to have a machine that learns from a large training set Handwriting recognition cannot be done without machine learning! 6

7 Most Successful Application of ML Learning to recognize spoken words Speaker-specific strategies for recognizing primitive sounds (phonemes) and words from speech signal Neural networks and methods for learning HMMs for customizing to individual speakers, vocabularies and microphone characteristics Recently Google increased accuracy for Table 1.1 Android by 25% 7

8 ML Example: Self-Driving Vehicle ALVINN: Drive at 70mph for 90 miles on public highways Google Prototype Tesla Autopilot Learning to drive an autonomous vehicle Train computer-controlled vehicles to steer correctly Associate steering commands with image sequences Deployment: Taxi Courier Service 8

9 Drivers of ML Progress Mobile systems gather/transport vast amounts of data: Big data Turn to ML solutions to obtain insights, predictions, decisions Granularized personalized data Personalization: relevance of posts shown Advertising copywriting Historical medical records: Determine treatment Historical traffic data: Control congestion 9

10 Learning Problem Definition Improving some measure of performance P when executing some task T through some type of training experience E Example: Learning to detect credit card fraud Task T Assign label of fraud or not fraud to credit card transaction Performance measure P Accuracy of fraud classifier With higher penalty when fraud is labeled as not fraud Training experience E Historical credit card transactions labeled as fraud or not 10

11 The ML Approach Data Collection Samples Model Selection Probability distribution to model process Parameter Estimation Values/distributions Generalization (Training) Inference Find responses to queries Decision (Inference OR Testing) 11

12 ML History within AI ML/PR Methods around for over 50 years 12

13 Core Methods 1. Supervised Learning Training data consists of (x,y) pairs Goal is prediction y* for input x* 2. Unsupervised Learning Analysis of unlabeled data 3. Reinforcement Learning Training data inbetween supervised/unsupervised Indication of whether action is correct or not Rewad signal may refer to an entire input sequence 13

14 Supervised Learning Most widely used methods of ML, e.g., Spam classification of Face recognizers over images Medical diagnosis systems Inputs x are vectors or more complex objects documents, DNA sequences or graphs Outputs are binary, multiclass(k), Multi-label (more than one class), ranking, Structured: y is a graph satisfying constraints, e.g., POS tagging 14 Real-valued or mixture of discrete and real-valued

15 Supervised Classification Example Off-shore oil transfer pipelines Non-invasive measurement of proportion of oil,water, gas Called Three-phase Oil/Water/Gas Flow Input data: Dual-energy gamma densitometry Beam of gamma rays passed through pipe Attenuation in intensity indicates density of material Single beam insufficient Two degrees of freedom: fraction of oil, fraction of water One beam of Gamma rays of two energies (frequencies) Detector Six Beams 12 measurements attenuation

16 Prediction Problems 1. Predict Volume Fractions of oil/water/gas 2. Predict configuration (one of three) Twelve Features Three classes Two variables, 100 points shown Naïve cell based voting fails exponential growth of cells with dimensionality 12 dimensions discretized into 6 gives 3 million cells Hardly any points in each cell Which class should x belong to? 16

17 Probability Theory Sum Rule for Marginalization L p(x = x i ) = p(x = x i,y = y j ) j=1 Product Rule: for combining p(x,y ) = n ij N = p(y X)p(X) Bayes Rule p( X Y) p( Y) p ( Y X ) = where p ( X ) = p( X Y) p( Y) Y p( X ) Viewed as Posterior α likelihood x prior Fully Bayesian approach Conjugate distributions Feasible with increased computational power Intractable posterior handled using either Variational Bayes or Stochastic sampling e.g., Markov Chain Monte Carlo, Gibbs 17

18 Probability Distributions Discrete- Binary Binomial N samples of Bernoulli N=1 Bernoulli Single binary variable Conjugate Prior Beta Continuous variable between {0,1] Discrete- Multi-valued Large N Multinomial One of K values = K-dimensional binary vector Conjugate Prior K=2 Dirichlet K random variables between [0.1] Continuous Gaussian Student s-t Generalization of Gaussian robust to Outliers Infinite mixture of Gaussians Gamma ConjugatePrior of univariate Gaussian precision Gaussian-Gamma Conjugate prior of univariate Gaussian Unknown mean and precision Wishart Conjugate Prior of multivariate Gaussian precision matrix Gaussian-Wishart Conjugate prior of multi-variate Gaussian Unknown mean and precision matrix Exponential Special case of Gamma Angular Von Mises Uniform 18

19 Statistical Models Generative Naïve Bayes Mixtures of multinomials Mixtures of Gaussians Hidden Markov Models (HMM) Bayesian networks Markov random fields Discriminative Logistic regression SVMs Traditional neural networks Nearest neighbor Conditional Random Fields (CRF) 19

20 HMMs for Speech Recognition Three distinct layers 1. Language Model: generates sentences as sequences of words 2. Word Model: described as a sequence of phonemes /p//u//sh/ 3. Acoustic model: shows progression of the acoustic signal through a phoneme 20

21 DBN for monitoring a vehicle Represents system dynamics X 5 : Observation depends on car s location (and map not modeled) and error status of sensor (failure) (X 4 ) Weather Weather' Weather 0 X 1 : Bad weather makes sensor likely to fail (X 4 ) Velocity Location Velocity' Location' Velocity 0 Location 0 X 3 : Location depends on previous position and velocity (X 2 ) Failure Failure' Obs' Failure 0 Ob Time slice t Time slice t +1 Time slice 0 (a) 21 (b)

22 Regression Problem data set Corresponding inverse problem by reversing x and t Red curve is result of fitting a two-layer neural network by minimizing squared error Very poor fit to data: GMMs used here 22

23 Regression: Learning to Rank Input (x i ): (d Features of Query-URL pair) (d >200) In LETOR 4.0 dataset 46 query-document features Maximum of 124 URLs/query Log frequency of query in anchor text Query word in color on page # of images on page # of (out) links on page PageRank of page URL length URL contains ~ Page length Traditional IR uses TF/IDF Output (y): Relevance Value Target Variable - Point-wise (0,1,2,3) - Regression returns continuous value - Allows fine-grained ranking of URLs

24 Deep Learning Multilayer stack of simple modules subject to: Learning, Non-linear map (ReLU) 5 to 20 layers Sensitive to minute details (Samoyeds from white wolves) Invariant (Background, pose, lighting, other objects) Convolutional Nets alternate convolutional layer and pooling layer Stunning success ConvNet +Recurrent Net 1. Representation by CNN RNN trained to translate

25 Unsupervised Learning Labeled data under assumption of underlying structure of data, e.g., 1. Clustering is to find partition of data 2. Identify a low-dimensional manifold PCA, manifold learning, factor analysis, random projections, auto-encoders Topic modeling, Recommendation systems A criterion function is used e.g., max likelihood Computational complexity is key to exploit large unlabeled data sets 25

26 Clustering Finding a partition for observed data And a rule for predicting future data Old Faithful Geyser in Yellowstone Simple Gaussian unable to capture structure Linear superposition of two Gaussians is better Gaussian cannot model such data sets Gaussian Mixture Models give very complex densities K p( x) = π N( x µ, Σ ) k = 1 k k k 272 observations Duration (mins, horiz axis) vs Time to next eruption (vertical) p k are mixing coefficients that sum to one Log-likelihood function is N K ln p ( X π, µ, Σ) = ln π k ( n k Σk ) = N x µ, = n 1 k 1 There is no closed-form solution Use either iterative numerical optimization techniques or Expectation Maximization One dimension Three Gaussians in blue Sum in red 26

27 Topic Models Unsupervised methods to analyze documents Topics are distributions over words A document is a distribution across topics Methods: SVD, Collaborative Filtering Topics Topic 1 training 0.08 network 0.05 neural 0.03 Topic 2 noise uncertain reliability positive Topic 3 data estimate estimation An Example of Topic Modeling The ability to learn from data with uncertain and missing information is a fundamental requirement for learning systems. In the "real world", features are missing due to unrecorded information or due to occlusion in vision, and measurements are affected by noise. In some cases the experimenter might want to assign varying degrees of reliability to the data. In regression, uncertainty is typically attributed to the dependent variable which is assumed to be disturbed by additive noise. But there is no reason to assume that input features might not be uncertain as well or even missing completely. In some cases, we can ignore the problem: instead of trying to model the relationship between the true input and the output we are satisfied with modeling the relationship between the uncertain input and the output. But there are at least two reasons why we might want to explicitly deal with uncertain inputs. First, we might be interested in the underlying relationship between the true input and the output (e.g. the relationship has some physical meaning). Second, the problem might be non-stationary in the sense that for different samples different inputs are uncertain or missing or the levels of uncertainty vary. The naive strategy of training networks for all possible input combinations explodes in complexity and would require sufficient data for all relevant cases. It makes more sense to define one underlying true model and relate all data to this one model. Ahmad and Tresp (1993) have shown how to include uncertainty during recall under the assumption that the network approximates the "true" underlying function. In this paper, we first show how input uncertainty can be taken into account in the training of a feedforward neural network. Then we show that for networks of Gaussian basis functions it is possible to obtain closed-form solutions. We validate the solutions on two applications. Topic Distribution Topic 1 Topic 2 Topic 3 27

28 Recommendation Systems Data indicates links between users and items Suggest other items to a user based on data across all users Solution: SVD, Collaborative Filtering 28

29 Reinforcement Learning Dog is given a reward/punishment for an action Policies: what actions to take in a particular situation Utility estimation: how good is state (à used by policy) No supervised output but delayed reward Credit assignment what was responsible for outcome Applications: Game playing Robot in a maze Multiple agents, partial observability, 29

30 Causal Learning A Causal Bayesian Network Example of Inference: Cancer is independent of Age and Gender given exposure to Toxics and Smoking Computationally feasible inference 30

31 Summary Machine Learning Discipline Study how systems improve with experience Study statistical-computational-information-theoretic laws governing learning systems Used with success in all AI applications Core methods: Supervised Classification, Regression, Ranking Fully Bayesian approach together with Variational methods and Monte Carlo sampling Deep Learning Unsupervised (PCA, Topic Models, Clustering) Reinforcement Drivers are mobile systems (big data), personalization 31

Statistical Models in Data Mining

Statistical Models in Data Mining Statistical Models in Data Mining Sargur N. Srihari University at Buffalo The State University of New York Department of Computer Science and Engineering Department of Biostatistics 1 Srihari Flood of

More information

Class Overview and General Introduction to Machine Learning

Class Overview and General Introduction to Machine Learning Class Overview and General Introduction to Machine Learning Piyush Rai www.cs.utah.edu/~piyush CS5350/6350: Machine Learning August 23, 2011 (CS5350/6350) Intro to ML August 23, 2011 1 / 25 Course Logistics

More information

STA 4273H: Statistical Machine Learning

STA 4273H: Statistical Machine Learning STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 6 Three Approaches to Classification Construct

More information

INTRODUCTION TO NEURAL NETWORKS

INTRODUCTION TO NEURAL NETWORKS INTRODUCTION TO NEURAL NETWORKS Pictures are taken from http://www.cs.cmu.edu/~tom/mlbook-chapter-slides.html http://research.microsoft.com/~cmbishop/prml/index.htm By Nobel Khandaker Neural Networks An

More information

A crash course in probability and Naïve Bayes classification

A crash course in probability and Naïve Bayes classification Probability theory A crash course in probability and Naïve Bayes classification Chapter 9 Random variable: a variable whose possible values are numerical outcomes of a random phenomenon. s: A person s

More information

Introduction to Machine Learning Lecture 1. Mehryar Mohri Courant Institute and Google Research mohri@cims.nyu.edu

Introduction to Machine Learning Lecture 1. Mehryar Mohri Courant Institute and Google Research mohri@cims.nyu.edu Introduction to Machine Learning Lecture 1 Mehryar Mohri Courant Institute and Google Research mohri@cims.nyu.edu Introduction Logistics Prerequisites: basics concepts needed in probability and statistics

More information

Linear Classification. Volker Tresp Summer 2015

Linear Classification. Volker Tresp Summer 2015 Linear Classification Volker Tresp Summer 2015 1 Classification Classification is the central task of pattern recognition Sensors supply information about an object: to which class do the object belong

More information

Statistical Machine Learning

Statistical Machine Learning Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes

More information

Data Mining Chapter 6: Models and Patterns Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University

Data Mining Chapter 6: Models and Patterns Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University Data Mining Chapter 6: Models and Patterns Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University Models vs. Patterns Models A model is a high level, global description of a

More information

CS 2750 Machine Learning. Lecture 1. Machine Learning. http://www.cs.pitt.edu/~milos/courses/cs2750/ CS 2750 Machine Learning.

CS 2750 Machine Learning. Lecture 1. Machine Learning. http://www.cs.pitt.edu/~milos/courses/cs2750/ CS 2750 Machine Learning. Lecture Machine Learning Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square, x5 http://www.cs.pitt.edu/~milos/courses/cs75/ Administration Instructor: Milos Hauskrecht milos@cs.pitt.edu 539 Sennott

More information

C19 Machine Learning

C19 Machine Learning C9 Machine Learning 8 Lectures Hilary Term 25 2 Tutorial Sheets A. Zisserman Overview: Supervised classification perceptron, support vector machine, loss functions, kernels, random forests, neural networks

More information

10-601. Machine Learning. http://www.cs.cmu.edu/afs/cs/academic/class/10601-f10/index.html

10-601. Machine Learning. http://www.cs.cmu.edu/afs/cs/academic/class/10601-f10/index.html 10-601 Machine Learning http://www.cs.cmu.edu/afs/cs/academic/class/10601-f10/index.html Course data All up-to-date info is on the course web page: http://www.cs.cmu.edu/afs/cs/academic/class/10601-f10/index.html

More information

Parametric Models Part I: Maximum Likelihood and Bayesian Density Estimation

Parametric Models Part I: Maximum Likelihood and Bayesian Density Estimation Parametric Models Part I: Maximum Likelihood and Bayesian Density Estimation Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Fall 2015 CS 551, Fall 2015

More information

Neural Networks. CAP5610 Machine Learning Instructor: Guo-Jun Qi

Neural Networks. CAP5610 Machine Learning Instructor: Guo-Jun Qi Neural Networks CAP5610 Machine Learning Instructor: Guo-Jun Qi Recap: linear classifier Logistic regression Maximizing the posterior distribution of class Y conditional on the input vector X Support vector

More information

Introduction to Machine Learning. Speaker: Harry Chao Advisor: J.J. Ding Date: 1/27/2011

Introduction to Machine Learning. Speaker: Harry Chao Advisor: J.J. Ding Date: 1/27/2011 Introduction to Machine Learning Speaker: Harry Chao Advisor: J.J. Ding Date: 1/27/2011 1 Outline 1. What is machine learning? 2. The basic of machine learning 3. Principles and effects of machine learning

More information

Machine Learning CS 6830. Lecture 01. Razvan C. Bunescu School of Electrical Engineering and Computer Science bunescu@ohio.edu

Machine Learning CS 6830. Lecture 01. Razvan C. Bunescu School of Electrical Engineering and Computer Science bunescu@ohio.edu Machine Learning CS 6830 Razvan C. Bunescu School of Electrical Engineering and Computer Science bunescu@ohio.edu What is Learning? Merriam-Webster: learn = to acquire knowledge, understanding, or skill

More information

203.4770: Introduction to Machine Learning Dr. Rita Osadchy

203.4770: Introduction to Machine Learning Dr. Rita Osadchy 203.4770: Introduction to Machine Learning Dr. Rita Osadchy 1 Outline 1. About the Course 2. What is Machine Learning? 3. Types of problems and Situations 4. ML Example 2 About the course Course Homepage:

More information

Data, Measurements, Features

Data, Measurements, Features Data, Measurements, Features Middle East Technical University Dep. of Computer Engineering 2009 compiled by V. Atalay What do you think of when someone says Data? We might abstract the idea that data are

More information

Classification Problems

Classification Problems Classification Read Chapter 4 in the text by Bishop, except omit Sections 4.1.6, 4.1.7, 4.2.4, 4.3.3, 4.3.5, 4.3.6, 4.4, and 4.5. Also, review sections 1.5.1, 1.5.2, 1.5.3, and 1.5.4. Classification Problems

More information

Machine Learning I Week 14: Sequence Learning Introduction

Machine Learning I Week 14: Sequence Learning Introduction Machine Learning I Week 14: Sequence Learning Introduction Alex Graves Technische Universität München 29. January 2009 Literature Pattern Recognition and Machine Learning Chapter 13: Sequential Data Christopher

More information

Sense Making in an IOT World: Sensor Data Analysis with Deep Learning

Sense Making in an IOT World: Sensor Data Analysis with Deep Learning Sense Making in an IOT World: Sensor Data Analysis with Deep Learning Natalia Vassilieva, PhD Senior Research Manager GTC 2016 Deep learning proof points as of today Vision Speech Text Other Search & information

More information

Basics of Statistical Machine Learning

Basics of Statistical Machine Learning CS761 Spring 2013 Advanced Machine Learning Basics of Statistical Machine Learning Lecturer: Xiaojin Zhu jerryzhu@cs.wisc.edu Modern machine learning is rooted in statistics. You will find many familiar

More information

MACHINE LEARNING IN HIGH ENERGY PHYSICS

MACHINE LEARNING IN HIGH ENERGY PHYSICS MACHINE LEARNING IN HIGH ENERGY PHYSICS LECTURE #1 Alex Rogozhnikov, 2015 INTRO NOTES 4 days two lectures, two practice seminars every day this is introductory track to machine learning kaggle competition!

More information

CSC321 Introduction to Neural Networks and Machine Learning. Lecture 21 Using Boltzmann machines to initialize backpropagation.

CSC321 Introduction to Neural Networks and Machine Learning. Lecture 21 Using Boltzmann machines to initialize backpropagation. CSC321 Introduction to Neural Networks and Machine Learning Lecture 21 Using Boltzmann machines to initialize backpropagation Geoffrey Hinton Some problems with backpropagation The amount of information

More information

Logistic Regression. Jia Li. Department of Statistics The Pennsylvania State University. Logistic Regression

Logistic Regression. Jia Li. Department of Statistics The Pennsylvania State University. Logistic Regression Logistic Regression Department of Statistics The Pennsylvania State University Email: jiali@stat.psu.edu Logistic Regression Preserve linear classification boundaries. By the Bayes rule: Ĝ(x) = arg max

More information

Supervised Learning (Big Data Analytics)

Supervised Learning (Big Data Analytics) Supervised Learning (Big Data Analytics) Vibhav Gogate Department of Computer Science The University of Texas at Dallas Practical advice Goal of Big Data Analytics Uncover patterns in Data. Can be used

More information

Learning is a very general term denoting the way in which agents:

Learning is a very general term denoting the way in which agents: What is learning? Learning is a very general term denoting the way in which agents: Acquire and organize knowledge (by building, modifying and organizing internal representations of some external reality);

More information

Linear Threshold Units

Linear Threshold Units Linear Threshold Units w x hx (... w n x n w We assume that each feature x j and each weight w j is a real number (we will relax this later) We will study three different algorithms for learning linear

More information

CCNY. BME I5100: Biomedical Signal Processing. Linear Discrimination. Lucas C. Parra Biomedical Engineering Department City College of New York

CCNY. BME I5100: Biomedical Signal Processing. Linear Discrimination. Lucas C. Parra Biomedical Engineering Department City College of New York BME I5100: Biomedical Signal Processing Linear Discrimination Lucas C. Parra Biomedical Engineering Department CCNY 1 Schedule Week 1: Introduction Linear, stationary, normal - the stuff biology is not

More information

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not. Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C

More information

Search Taxonomy. Web Search. Search Engine Optimization. Information Retrieval

Search Taxonomy. Web Search. Search Engine Optimization. Information Retrieval Information Retrieval INFO 4300 / CS 4300! Retrieval models Older models» Boolean retrieval» Vector Space model Probabilistic Models» BM25» Language models Web search» Learning to Rank Search Taxonomy!

More information

HT2015: SC4 Statistical Data Mining and Machine Learning

HT2015: SC4 Statistical Data Mining and Machine Learning HT2015: SC4 Statistical Data Mining and Machine Learning Dino Sejdinovic Department of Statistics Oxford http://www.stats.ox.ac.uk/~sejdinov/sdmml.html Bayesian Nonparametrics Parametric vs Nonparametric

More information

Bayes and Naïve Bayes. cs534-machine Learning

Bayes and Naïve Bayes. cs534-machine Learning Bayes and aïve Bayes cs534-machine Learning Bayes Classifier Generative model learns Prediction is made by and where This is often referred to as the Bayes Classifier, because of the use of the Bayes rule

More information

Statistical Machine Learning from Data

Statistical Machine Learning from Data Samy Bengio Statistical Machine Learning from Data 1 Statistical Machine Learning from Data Gaussian Mixture Models Samy Bengio IDIAP Research Institute, Martigny, Switzerland, and Ecole Polytechnique

More information

Neural Networks for Machine Learning. Lecture 13a The ups and downs of backpropagation

Neural Networks for Machine Learning. Lecture 13a The ups and downs of backpropagation Neural Networks for Machine Learning Lecture 13a The ups and downs of backpropagation Geoffrey Hinton Nitish Srivastava, Kevin Swersky Tijmen Tieleman Abdel-rahman Mohamed A brief history of backpropagation

More information

Statistics Graduate Courses

Statistics Graduate Courses Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.

More information

Predict Influencers in the Social Network

Predict Influencers in the Social Network Predict Influencers in the Social Network Ruishan Liu, Yang Zhao and Liuyu Zhou Email: rliu2, yzhao2, lyzhou@stanford.edu Department of Electrical Engineering, Stanford University Abstract Given two persons

More information

Feature engineering. Léon Bottou COS 424 4/22/2010

Feature engineering. Léon Bottou COS 424 4/22/2010 Feature engineering Léon Bottou COS 424 4/22/2010 Summary Summary I. The importance of features II. Feature relevance III. Selecting features IV. Learning features Léon Bottou 2/29 COS 424 4/22/2010 I.

More information

CHAPTER 2 Estimating Probabilities

CHAPTER 2 Estimating Probabilities CHAPTER 2 Estimating Probabilities Machine Learning Copyright c 2016. Tom M. Mitchell. All rights reserved. *DRAFT OF January 24, 2016* *PLEASE DO NOT DISTRIBUTE WITHOUT AUTHOR S PERMISSION* This is a

More information

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION Introduction In the previous chapter, we explored a class of regression models having particularly simple analytical

More information

Introduction to Machine Learning Using Python. Vikram Kamath

Introduction to Machine Learning Using Python. Vikram Kamath Introduction to Machine Learning Using Python Vikram Kamath Contents: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Introduction/Definition Where and Why ML is used Types of Learning Supervised Learning Linear Regression

More information

MA2823: Foundations of Machine Learning

MA2823: Foundations of Machine Learning MA2823: Foundations of Machine Learning École Centrale Paris Fall 2015 Chloé-Agathe Azencot Centre for Computational Biology, Mines ParisTech chloe agathe.azencott@mines paristech.fr TAs: Jiaqian Yu jiaqian.yu@centralesupelec.fr

More information

Introduction to Machine Learning

Introduction to Machine Learning Introduction to Machine Learning Brown University CSCI 1950-F, Spring 2012 Instructor: Erik Sudderth Graduate TAs: Dae Il Kim & Ben Swanson Head Undergraduate TA: William Allen Undergraduate TAs: Soravit

More information

Is a Data Scientist the New Quant? Stuart Kozola MathWorks

Is a Data Scientist the New Quant? Stuart Kozola MathWorks Is a Data Scientist the New Quant? Stuart Kozola MathWorks 2015 The MathWorks, Inc. 1 Facts or information used usually to calculate, analyze, or plan something Information that is produced or stored by

More information

Christfried Webers. Canberra February June 2015

Christfried Webers. Canberra February June 2015 c Statistical Group and College of Engineering and Computer Science Canberra February June (Many figures from C. M. Bishop, "Pattern Recognition and ") 1of 829 c Part VIII Linear Classification 2 Logistic

More information

PS 271B: Quantitative Methods II. Lecture Notes

PS 271B: Quantitative Methods II. Lecture Notes PS 271B: Quantitative Methods II Lecture Notes Langche Zeng zeng@ucsd.edu The Empirical Research Process; Fundamental Methodological Issues 2 Theory; Data; Models/model selection; Estimation; Inference.

More information

Network Machine Learning Research Group. Intended status: Informational October 19, 2015 Expires: April 21, 2016

Network Machine Learning Research Group. Intended status: Informational October 19, 2015 Expires: April 21, 2016 Network Machine Learning Research Group S. Jiang Internet-Draft Huawei Technologies Co., Ltd Intended status: Informational October 19, 2015 Expires: April 21, 2016 Abstract Network Machine Learning draft-jiang-nmlrg-network-machine-learning-00

More information

INTRODUCTION TO MACHINE LEARNING 3RD EDITION

INTRODUCTION TO MACHINE LEARNING 3RD EDITION ETHEM ALPAYDIN The MIT Press, 2014 Lecture Slides for INTRODUCTION TO MACHINE LEARNING 3RD EDITION alpaydin@boun.edu.tr http://www.cmpe.boun.edu.tr/~ethem/i2ml3e CHAPTER 1: INTRODUCTION Big Data 3 Widespread

More information

Bayesian Machine Learning (ML): Modeling And Inference in Big Data. Zhuhua Cai Google, Rice University caizhua@gmail.com

Bayesian Machine Learning (ML): Modeling And Inference in Big Data. Zhuhua Cai Google, Rice University caizhua@gmail.com Bayesian Machine Learning (ML): Modeling And Inference in Big Data Zhuhua Cai Google Rice University caizhua@gmail.com 1 Syllabus Bayesian ML Concepts (Today) Bayesian ML on MapReduce (Next morning) Bayesian

More information

Introduction to Data Mining

Introduction to Data Mining Introduction to Data Mining 1 Why Data Mining? Explosive Growth of Data Data collection and data availability Automated data collection tools, Internet, smartphones, Major sources of abundant data Business:

More information

Azure Machine Learning, SQL Data Mining and R

Azure Machine Learning, SQL Data Mining and R Azure Machine Learning, SQL Data Mining and R Day-by-day Agenda Prerequisites No formal prerequisites. Basic knowledge of SQL Server Data Tools, Excel and any analytical experience helps. Best of all:

More information

Cell Phone based Activity Detection using Markov Logic Network

Cell Phone based Activity Detection using Markov Logic Network Cell Phone based Activity Detection using Markov Logic Network Somdeb Sarkhel sxs104721@utdallas.edu 1 Introduction Mobile devices are becoming increasingly sophisticated and the latest generation of smart

More information

Final Exam, Spring 2007

Final Exam, Spring 2007 10-701 Final Exam, Spring 2007 1. Personal info: Name: Andrew account: E-mail address: 2. There should be 16 numbered pages in this exam (including this cover sheet). 3. You can use any material you brought:

More information

Bayesian networks - Time-series models - Apache Spark & Scala

Bayesian networks - Time-series models - Apache Spark & Scala Bayesian networks - Time-series models - Apache Spark & Scala Dr John Sandiford, CTO Bayes Server Data Science London Meetup - November 2014 1 Contents Introduction Bayesian networks Latent variables Anomaly

More information

Question 2 Naïve Bayes (16 points)

Question 2 Naïve Bayes (16 points) Question 2 Naïve Bayes (16 points) About 2/3 of your email is spam so you downloaded an open source spam filter based on word occurrences that uses the Naive Bayes classifier. Assume you collected the

More information

Lecture 9: Introduction to Pattern Analysis

Lecture 9: Introduction to Pattern Analysis Lecture 9: Introduction to Pattern Analysis g Features, patterns and classifiers g Components of a PR system g An example g Probability definitions g Bayes Theorem g Gaussian densities Features, patterns

More information

Machine Learning. Chapter 18, 21. Some material adopted from notes by Chuck Dyer

Machine Learning. Chapter 18, 21. Some material adopted from notes by Chuck Dyer Machine Learning Chapter 18, 21 Some material adopted from notes by Chuck Dyer What is learning? Learning denotes changes in a system that... enable a system to do the same task more efficiently the next

More information

The Exponential Family

The Exponential Family The Exponential Family David M. Blei Columbia University November 3, 2015 Definition A probability density in the exponential family has this form where p.x j / D h.x/ expf > t.x/ a./g; (1) is the natural

More information

Semi-Supervised Support Vector Machines and Application to Spam Filtering

Semi-Supervised Support Vector Machines and Application to Spam Filtering Semi-Supervised Support Vector Machines and Application to Spam Filtering Alexander Zien Empirical Inference Department, Bernhard Schölkopf Max Planck Institute for Biological Cybernetics ECML 2006 Discovery

More information

Machine learning for algo trading

Machine learning for algo trading Machine learning for algo trading An introduction for nonmathematicians Dr. Aly Kassam Overview High level introduction to machine learning A machine learning bestiary What has all this got to do with

More information

CS 2750 Machine Learning. Lecture 1. Machine Learning. CS 2750 Machine Learning.

CS 2750 Machine Learning. Lecture 1. Machine Learning.  CS 2750 Machine Learning. Lecture 1 Machine Learning Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square, x-5 http://www.cs.pitt.edu/~milos/courses/cs75/ Administration Instructor: Milos Hauskrecht milos@cs.pitt.edu 539 Sennott

More information

DATA ANALYTICS USING R

DATA ANALYTICS USING R DATA ANALYTICS USING R Duration: 90 Hours Intended audience and scope: The course is targeted at fresh engineers, practicing engineers and scientists who are interested in learning and understanding data

More information

Machine Learning and Statistics: What s the Connection?

Machine Learning and Statistics: What s the Connection? Machine Learning and Statistics: What s the Connection? Institute for Adaptive and Neural Computation School of Informatics, University of Edinburgh, UK August 2006 Outline The roots of machine learning

More information

Lecture 10: Sequential Data Models

Lecture 10: Sequential Data Models CSC2515 Fall 2007 Introduction to Machine Learning Lecture 10: Sequential Data Models 1 Example: sequential data Until now, considered data to be i.i.d. Turn attention to sequential data Time-series: stock

More information

Big Data Analytics CSCI 4030

Big Data Analytics CSCI 4030 High dim. data Graph data Infinite data Machine learning Apps Locality sensitive hashing PageRank, SimRank Filtering data streams SVM Recommen der systems Clustering Community Detection Web advertising

More information

Hidden Markov Models. and. Sequential Data

Hidden Markov Models. and. Sequential Data Hidden Markov Models and Sequential Data Sequential Data Often arise through measurement of time series Snowfall measurements on successive days in Buffalo Rainfall measurements in Chirrapunji Daily values

More information

Introduction to machine learning and pattern recognition Lecture 1 Coryn Bailer-Jones

Introduction to machine learning and pattern recognition Lecture 1 Coryn Bailer-Jones Introduction to machine learning and pattern recognition Lecture 1 Coryn Bailer-Jones http://www.mpia.de/homes/calj/mlpr_mpia2008.html 1 1 What is machine learning? Data description and interpretation

More information

Tracking Algorithms. Lecture17: Stochastic Tracking. Joint Probability and Graphical Model. Probabilistic Tracking

Tracking Algorithms. Lecture17: Stochastic Tracking. Joint Probability and Graphical Model. Probabilistic Tracking Tracking Algorithms (2015S) Lecture17: Stochastic Tracking Bohyung Han CSE, POSTECH bhhan@postech.ac.kr Deterministic methods Given input video and current state, tracking result is always same. Local

More information

Bayesian Statistics: Indian Buffet Process

Bayesian Statistics: Indian Buffet Process Bayesian Statistics: Indian Buffet Process Ilker Yildirim Department of Brain and Cognitive Sciences University of Rochester Rochester, NY 14627 August 2012 Reference: Most of the material in this note

More information

Data Mining - Evaluation of Classifiers

Data Mining - Evaluation of Classifiers Data Mining - Evaluation of Classifiers Lecturer: JERZY STEFANOWSKI Institute of Computing Sciences Poznan University of Technology Poznan, Poland Lecture 4 SE Master Course 2008/2009 revised for 2010

More information

Class #6: Non-linear classification. ML4Bio 2012 February 17 th, 2012 Quaid Morris

Class #6: Non-linear classification. ML4Bio 2012 February 17 th, 2012 Quaid Morris Class #6: Non-linear classification ML4Bio 2012 February 17 th, 2012 Quaid Morris 1 Module #: Title of Module 2 Review Overview Linear separability Non-linear classification Linear Support Vector Machines

More information

Course: Model, Learning, and Inference: Lecture 5

Course: Model, Learning, and Inference: Lecture 5 Course: Model, Learning, and Inference: Lecture 5 Alan Yuille Department of Statistics, UCLA Los Angeles, CA 90095 yuille@stat.ucla.edu Abstract Probability distributions on structured representation.

More information

Applying Deep Learning to Car Data Logging (CDL) and Driver Assessor (DA) October 22-Oct-15

Applying Deep Learning to Car Data Logging (CDL) and Driver Assessor (DA) October 22-Oct-15 Applying Deep Learning to Car Data Logging (CDL) and Driver Assessor (DA) October 22-Oct-15 GENIVI is a registered trademark of the GENIVI Alliance in the USA and other countries Copyright GENIVI Alliance

More information

Data Mining Algorithms Part 1. Dejan Sarka

Data Mining Algorithms Part 1. Dejan Sarka Data Mining Algorithms Part 1 Dejan Sarka Join the conversation on Twitter: @DevWeek #DW2015 Instructor Bio Dejan Sarka (dsarka@solidq.com) 30 years of experience SQL Server MVP, MCT, 13 books 7+ courses

More information

Literature: (6) Pattern Recognition and Machine Learning Christopher M. Bishop MIT Press

Literature: (6) Pattern Recognition and Machine Learning Christopher M. Bishop MIT Press Literature: (6) Pattern Recognition and Machine Learning Christopher M. Bishop MIT Press -! Generative statistical models try to learn how to generate data from latent variables (for example class labels).

More information

These slides follow closely the (English) course textbook Pattern Recognition and Machine Learning by Christopher Bishop

These slides follow closely the (English) course textbook Pattern Recognition and Machine Learning by Christopher Bishop Music and Machine Learning (IFT6080 Winter 08) Prof. Douglas Eck, Université de Montréal These slides follow closely the (English) course textbook Pattern Recognition and Machine Learning by Christopher

More information

Supporting Online Material for

Supporting Online Material for www.sciencemag.org/cgi/content/full/313/5786/504/dc1 Supporting Online Material for Reducing the Dimensionality of Data with Neural Networks G. E. Hinton* and R. R. Salakhutdinov *To whom correspondence

More information

A Supervised Approach To Musical Chord Recognition

A Supervised Approach To Musical Chord Recognition Pranav Rajpurkar Brad Girardeau Takatoki Migimatsu Stanford University, Stanford, CA 94305 USA pranavsr@stanford.edu bgirarde@stanford.edu takatoki@stanford.edu Abstract In this paper, we present a prototype

More information

Monotonicity Hints. Abstract

Monotonicity Hints. Abstract Monotonicity Hints Joseph Sill Computation and Neural Systems program California Institute of Technology email: joe@cs.caltech.edu Yaser S. Abu-Mostafa EE and CS Deptartments California Institute of Technology

More information

Bayesian Learning. CSL465/603 - Fall 2016 Narayanan C Krishnan

Bayesian Learning. CSL465/603 - Fall 2016 Narayanan C Krishnan Bayesian Learning CSL465/603 - Fall 2016 Narayanan C Krishnan ckn@iitrpr.ac.in Outline Bayes Theorem MAP Learners Bayes optimal classifier Naïve Bayes classifier Example text classification Bayesian networks

More information

Tensor Methods for Machine Learning, Computer Vision, and Computer Graphics

Tensor Methods for Machine Learning, Computer Vision, and Computer Graphics Tensor Methods for Machine Learning, Computer Vision, and Computer Graphics Part I: Factorizations and Statistical Modeling/Inference Amnon Shashua School of Computer Science & Eng. The Hebrew University

More information

8/29/2015. Data Mining and Machine Learning. Erich Seamon University of Idaho

8/29/2015. Data Mining and Machine Learning. Erich Seamon University of Idaho Data Mining and Machine Learning Erich Seamon University of Idaho www.webpages.uidaho.edu/erichs erichs@uidaho.edu 1 I am NOMAD 2 1 Data Mining and Machine Learning Outline Outlining the data mining and

More information

Machine Learning. CUNY Graduate Center, Spring 2013. Professor Liang Huang. huang@cs.qc.cuny.edu

Machine Learning. CUNY Graduate Center, Spring 2013. Professor Liang Huang. huang@cs.qc.cuny.edu Machine Learning CUNY Graduate Center, Spring 2013 Professor Liang Huang huang@cs.qc.cuny.edu http://acl.cs.qc.edu/~lhuang/teaching/machine-learning Logistics Lectures M 9:30-11:30 am Room 4419 Personnel

More information

An Introduction to Data Mining. Big Data World. Related Fields and Disciplines. What is Data Mining? 2/12/2015

An Introduction to Data Mining. Big Data World. Related Fields and Disciplines. What is Data Mining? 2/12/2015 An Introduction to Data Mining for Wind Power Management Spring 2015 Big Data World Every minute: Google receives over 4 million search queries Facebook users share almost 2.5 million pieces of content

More information

Machine Learning. 01 - Introduction

Machine Learning. 01 - Introduction Machine Learning 01 - Introduction Machine learning course One lecture (Wednesday, 9:30, 346) and one exercise (Monday, 17:15, 203). Oral exam, 20 minutes, 5 credit points. Some basic mathematical knowledge

More information

Probability Theory. Elementary rules of probability Sum rule. Product rule. p. 23

Probability Theory. Elementary rules of probability Sum rule. Product rule. p. 23 Probability Theory Uncertainty is key concept in machine learning. Probability provides consistent framework for the quantification and manipulation of uncertainty. Probability of an event is the fraction

More information

Machine Learning for Data Science (CS4786) Lecture 1

Machine Learning for Data Science (CS4786) Lecture 1 Machine Learning for Data Science (CS4786) Lecture 1 Tu-Th 10:10 to 11:25 AM Hollister B14 Instructors : Lillian Lee and Karthik Sridharan ROUGH DETAILS ABOUT THE COURSE Diagnostic assignment 0 is out:

More information

Steven C.H. Hoi School of Information Systems Singapore Management University Email: chhoi@smu.edu.sg

Steven C.H. Hoi School of Information Systems Singapore Management University Email: chhoi@smu.edu.sg Steven C.H. Hoi School of Information Systems Singapore Management University Email: chhoi@smu.edu.sg Introduction http://stevenhoi.org/ Finance Recommender Systems Cyber Security Machine Learning Visual

More information

Lecture 3: Linear methods for classification

Lecture 3: Linear methods for classification Lecture 3: Linear methods for classification Rafael A. Irizarry and Hector Corrada Bravo February, 2010 Today we describe four specific algorithms useful for classification problems: linear regression,

More information

An Introduction to Machine Learning

An Introduction to Machine Learning An Introduction to Machine Learning L5: Novelty Detection and Regression Alexander J. Smola Statistical Machine Learning Program Canberra, ACT 0200 Australia Alex.Smola@nicta.com.au Tata Institute, Pune,

More information

Machine Learning and Data Analysis overview. Department of Cybernetics, Czech Technical University in Prague. http://ida.felk.cvut.

Machine Learning and Data Analysis overview. Department of Cybernetics, Czech Technical University in Prague. http://ida.felk.cvut. Machine Learning and Data Analysis overview Jiří Kléma Department of Cybernetics, Czech Technical University in Prague http://ida.felk.cvut.cz psyllabus Lecture Lecturer Content 1. J. Kléma Introduction,

More information

November 28 th, Carlos Guestrin. Lower dimensional projections

November 28 th, Carlos Guestrin. Lower dimensional projections PCA Machine Learning 070/578 Carlos Guestrin Carnegie Mellon University November 28 th, 2007 Lower dimensional projections Rather than picking a subset of the features, we can new features that are combinations

More information

Social Media Mining. Data Mining Essentials

Social Media Mining. Data Mining Essentials Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers

More information

Markov chains and Markov Random Fields (MRFs)

Markov chains and Markov Random Fields (MRFs) Markov chains and Markov Random Fields (MRFs) 1 Why Markov Models We discuss Markov models now. This is the simplest statistical model in which we don t assume that all variables are independent; we assume

More information

Lecture 6: The Bayesian Approach

Lecture 6: The Bayesian Approach Lecture 6: The Bayesian Approach What Did We Do Up to Now? We are given a model Log-linear model, Markov network, Bayesian network, etc. This model induces a distribution P(X) Learning: estimate a set

More information

Lecture 20: Clustering

Lecture 20: Clustering Lecture 20: Clustering Wrap-up of neural nets (from last lecture Introduction to unsupervised learning K-means clustering COMP-424, Lecture 20 - April 3, 2013 1 Unsupervised learning In supervised learning,

More information

Simple and efficient online algorithms for real world applications

Simple and efficient online algorithms for real world applications Simple and efficient online algorithms for real world applications Università degli Studi di Milano Milano, Italy Talk @ Centro de Visión por Computador Something about me PhD in Robotics at LIRA-Lab,

More information

Novelty Detection in image recognition using IRF Neural Networks properties

Novelty Detection in image recognition using IRF Neural Networks properties Novelty Detection in image recognition using IRF Neural Networks properties Philippe Smagghe, Jean-Luc Buessler, Jean-Philippe Urban Université de Haute-Alsace MIPS 4, rue des Frères Lumière, 68093 Mulhouse,

More information

Bayesian probability theory

Bayesian probability theory Bayesian probability theory Bruno A. Olshausen arch 1, 2004 Abstract Bayesian probability theory provides a mathematical framework for peforming inference, or reasoning, using probability. The foundations

More information

Practical Data Science with Azure Machine Learning, SQL Data Mining, and R

Practical Data Science with Azure Machine Learning, SQL Data Mining, and R Practical Data Science with Azure Machine Learning, SQL Data Mining, and R Overview This 4-day class is the first of the two data science courses taught by Rafal Lukawiecki. Some of the topics will be

More information