Introduction to Machine Learning

Size: px
Start display at page:

Download "Introduction to Machine Learning"

Transcription

1 Introduction to Machine Learning Prof. Alexander Ihler Prof. Max Welling icamp Tutorial July 22

2 What is machine learning? The ability of a machine to improve its performance based on previous results: learn from experience Observe the world (data) Change our behavior accordingly Typical examples Predicting outcomes Explaining observations Finding interesting or unusual data Why? Automate very large or very fast predictions These days: web-scale data problems

3 Classification Discriminating between two (or more) types of data Example: Spam filtering Bad Cures fast and effective! - Canadian *** Pharmacy # Internet Inline Drugstore Viagra Our price $.5 Cialis Our price $.99 Good Interested in your research on graphical models - Dear Prof. Ihler, I have read some of your papers on probabilistic graphical models. Because I

4 Classification Example: face detection

5 Regression Based on past history, predict future outcomes Wall Street Netflix

6 Data Mining & Understanding Massive volumes of data available Webpages, Google books, Too large to hand-curate or organize How does Google decide the most relevant documents? How can we look for text documents about law, medicine, etc? What makes a document similar? Gets even harder for images, video,

7 How does machine learning work? Meta-programming Predict apply rules to examples Score get feedback on performance Learn change predictor to do better Program / Predictor Learning algorithm Change µ Improve performance Training data (examples) Features Feedback / Target values Characterized by some parameters µ Procedure (using µ) that outputs a prediction Compare / score performance

8 How does machine learning work? Meta-programming Predict apply rules to examples Score get feedback on performance Learn change predictor to do better Program / Predictor Learning algorithm Change µ Improve performance Training data (examples) Features Feedback / Target values Characterized by some parameters µ Procedure (using µ) that outputs a prediction Compare / score performance

9 Nearest neighbor classifier X 2!? X!

10 Nearest neighbor classifier Predictor : Given new features: Find nearest example Return its value X 2!? X!

11 Nearest neighbor classifier All points where we decide Decision Boundary X 2!? All points where we decide X!

12 Nearest neighbor classifier Predictor : Evaluate line: If r >, return else return X 2!? X!

13 Contrast: linear classifier Predictor : Evaluate line: If r >, return else return X 2! Linear decision boundary (r = ) X!

14 More Data Points? Linear decision boundary always linear X 2! Complexity of a classifier Parametric: describe form explicitly in terms of some parameters X! Non-parametric: number of parameters required increases with the amount of data

15 Questions to consider How would we select a good linear classifier? (How to measure error?) How are these two methods related? How do we pick between them? X 2! X!

16 Regression; Scatter plots 4 Target y 2 2 Feature x Suggests a relationship between x and y Prediction: new x, what is y?

17 Predicting new examples 4 Target y y (m+) =? 2 x (m+) 2 Feature x Regression: given the observed data, estimate y (m+) given new x (m+)

18 Nearest neighbor regression 4 Target y y (m+) =? 2 x (m+) 2 Feature x Find training datum x (i) closest to x (m+) Predict y (i)

19 Nearest neighbor regression Target y 4 Predictor : Given new features: Find nearest example Return its value 2 2 Feature x Defines a function f(x) implicitly Form is piecewise constant

20 Linear regression 4 Predictor : Evaluate line: Target y return r 2 2 Feature x Define form of function f(x) explicitly Find a good f(x) within that family

21 Regression vs. Classification Regression Classification y y flatten x x Features x Real-valued target t Predict continuous function ŷ(x) Features x Discrete class c (usually / or +/- ) Predict discrete function ŷ(x) x

22 How does machine learning work? Meta-programming Predict apply rules to examples Score get feedback on performance Learn change predictor to do better Program / Predictor Learning algorithm Change µ Improve performance Training data (examples) Features Feedback / Target values Characterized by some parameters µ Procedure (using µ) that outputs a prediction Compare / score performance

23 Measuring error X 2! X!

24 Measuring error X 2! X!

25 Measuring error Misclassification rate: fraction of training data whose prediction is wrong (Might also care about type of mistake ) X 2! X!

26 Measuring error What makes a good predictor?

27 Measuring error What makes a good predictor?

28 Measuring error What makes a good predictor?

29 Measuring error Observation Error or residual Prediction 2

30 Sum of squared error How can we quantify the error? Could choose something else, of course Computationally convenient (more later) Measures the variance of the residuals Corresponds to Gaussian model of noise

31 How does machine learning work? Meta-programming Predict apply rules to examples Score get feedback on performance Learn change predictor to do better Program / Predictor Learning algorithm Change µ Improve performance Training data (examples) Features Feedback / Target values Characterized by some parameters µ Procedure (using µ) that outputs a prediction Compare / score performance

32 Visualizing the cost function

33 Finding good parameters Want to find parameters which minimize our error Think of a cost surface : error residual for that µ

34 Gradient descent? How to change µ to improve J(µ)? Choose a direction in which J(µ) is decreasing

35 Gradient descent How to change µ to improve J(µ)? Choose a direction in which J(µ) is decreasing Gradient Positive => increasing Negative => decreasing

36 Gradient descent in more dimensions Gradient vector Indicates direction of steepest ascent (negative = steepest descent)

37 Gradient descent Initialization Step size Can change as a function of iteration Gradient direction Stopping condition Initialize µ Do { µ Ã µ - r µ J(µ) } while ( rj > ² )

38 Gradient for the SSE SSE r J =?

39 Gradient descent Initialization Step size Can change as a function of iteration Gradient direction Stopping condition Initialize µ Do { µ Ã µ - r µ J(µ) } while ( rj > ² ) { Error magnitude & direction for datum j { Sensitivity to each µ i

40 Derivative of SSE { Error magnitude & direction for datum j { Sensitivity to each µ i Rewrite using matrix form (Matlab) >> e = y th*x ; DJ = e*x; th=th al*dj;

41 Gradient descent on cost function

42 Comments on gradient descent Very general algorithm we ll see it many times Local minima Sensitive to starting point

43 Comments on gradient descent Very general algorithm Can use in almost any problem! Local minima Sensitive to starting point Step size Too large? Too small? Automatic ways to choose? May want step size to decrease with iteration Common choices: Fixed Linear: C/(iteration) More advance methods (e.g., Newton s method)

44 How does machine learning work? Meta-programming Predict apply rules to examples Score get feedback on performance Learn change predictor to do better Program / Predictor Learning algorithm Change µ Improve performance Training data (examples) Features Feedback / Target values Characterized by some parameters µ Procedure (using µ) that outputs a prediction Compare / score performance

45 Adding features Linear classifier can t learn some functions D example: Not linearly separable Add quadratic features Linearly separable in new features

46 Higher-order polynomials Are more features better? Nested hypotheses 2 nd order more general than st, 3 rd order than 2 nd, Fits the observed data better

47 Test data After training the model Go out and get more data from the world New observations (x,y) How well does our model perform?

48 How Overfitting affects Prediction Predictive Error Error on Test Data Error on Training Data Ideal Range for Model Complexity Model Complexity Underfitting Overfitting

Machine Learning and Data Mining. Regression Problem. (adapted from) Prof. Alexander Ihler

Machine Learning and Data Mining. Regression Problem. (adapted from) Prof. Alexander Ihler Machine Learning and Data Mining Regression Problem (adapted from) Prof. Alexander Ihler Overview Regression Problem Definition and define parameters ϴ. Prediction using ϴ as parameters Measure the error

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

CS 688 Pattern Recognition Lecture 4. Linear Models for Classification

CS 688 Pattern Recognition Lecture 4. Linear Models for Classification CS 688 Pattern Recognition Lecture 4 Linear Models for Classification Probabilistic generative models Probabilistic discriminative models 1 Generative Approach ( x ) p C k p( C k ) Ck p ( ) ( x Ck ) p(

More information

Lecture 2: The SVM classifier

Lecture 2: The SVM classifier Lecture 2: The SVM classifier C19 Machine Learning Hilary 2015 A. Zisserman Review of linear classifiers Linear separability Perceptron Support Vector Machine (SVM) classifier Wide margin Cost function

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

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

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

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

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

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

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

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

Data Mining and Data Warehousing. Henryk Maciejewski. Data Mining Predictive modelling: regression

Data Mining and Data Warehousing. Henryk Maciejewski. Data Mining Predictive modelling: regression Data Mining and Data Warehousing Henryk Maciejewski Data Mining Predictive modelling: regression Algorithms for Predictive Modelling Contents Regression Classification Auxiliary topics: Estimation of prediction

More information

Probabilistic Linear Classification: Logistic Regression. Piyush Rai IIT Kanpur

Probabilistic Linear Classification: Logistic Regression. Piyush Rai IIT Kanpur Probabilistic Linear Classification: Logistic Regression Piyush Rai IIT Kanpur Probabilistic Machine Learning (CS772A) Jan 18, 2016 Probabilistic Machine Learning (CS772A) Probabilistic Linear Classification:

More information

Numerical Methods Lecture 5 - Curve Fitting Techniques

Numerical Methods Lecture 5 - Curve Fitting Techniques Numerical Methods Lecture 5 - Curve Fitting Techniques Topics motivation interpolation linear regression higher order polynomial form exponential form Curve fitting - motivation For root finding, we used

More information

Decision Trees from large Databases: SLIQ

Decision Trees from large Databases: SLIQ Decision Trees from large Databases: SLIQ C4.5 often iterates over the training set How often? If the training set does not fit into main memory, swapping makes C4.5 unpractical! SLIQ: Sort the values

More information

Cross-validation for detecting and preventing overfitting

Cross-validation for detecting and preventing overfitting Cross-validation for detecting and preventing overfitting Note to other teachers and users of these slides. Andrew would be delighted if ou found this source material useful in giving our own lectures.

More information

Lecture 8 February 4

Lecture 8 February 4 ICS273A: Machine Learning Winter 2008 Lecture 8 February 4 Scribe: Carlos Agell (Student) Lecturer: Deva Ramanan 8.1 Neural Nets 8.1.1 Logistic Regression Recall the logistic function: g(x) = 1 1 + e θt

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

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

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

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

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

Logistic Regression. Vibhav Gogate The University of Texas at Dallas. Some Slides from Carlos Guestrin, Luke Zettlemoyer and Dan Weld.

Logistic Regression. Vibhav Gogate The University of Texas at Dallas. Some Slides from Carlos Guestrin, Luke Zettlemoyer and Dan Weld. Logistic Regression Vibhav Gogate The University of Texas at Dallas Some Slides from Carlos Guestrin, Luke Zettlemoyer and Dan Weld. Generative vs. Discriminative Classifiers Want to Learn: h:x Y X features

More information

CSCI567 Machine Learning (Fall 2014)

CSCI567 Machine Learning (Fall 2014) CSCI567 Machine Learning (Fall 2014) Drs. Sha & Liu {feisha,yanliu.cs}@usc.edu September 22, 2014 Drs. Sha & Liu ({feisha,yanliu.cs}@usc.edu) CSCI567 Machine Learning (Fall 2014) September 22, 2014 1 /

More information

Introduction to nonparametric regression: Least squares vs. Nearest neighbors

Introduction to nonparametric regression: Least squares vs. Nearest neighbors Introduction to nonparametric regression: Least squares vs. Nearest neighbors Patrick Breheny October 30 Patrick Breheny STA 621: Nonparametric Statistics 1/16 Introduction For the remainder of the course,

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

Artificial Neural Networks and Support Vector Machines. CS 486/686: Introduction to Artificial Intelligence

Artificial Neural Networks and Support Vector Machines. CS 486/686: Introduction to Artificial Intelligence Artificial Neural Networks and Support Vector Machines CS 486/686: Introduction to Artificial Intelligence 1 Outline What is a Neural Network? - Perceptron learners - Multi-layer networks What is a Support

More information

Content-Based Recommendation

Content-Based Recommendation Content-Based Recommendation Content-based? Item descriptions to identify items that are of particular interest to the user Example Example Comparing with Noncontent based Items User-based CF Searches

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

Response variables assume only two values, say Y j = 1 or = 0, called success and failure (spam detection, credit scoring, contracting.

Response variables assume only two values, say Y j = 1 or = 0, called success and failure (spam detection, credit scoring, contracting. Prof. Dr. J. Franke All of Statistics 1.52 Binary response variables - logistic regression Response variables assume only two values, say Y j = 1 or = 0, called success and failure (spam detection, credit

More information

An Introduction to Data Mining

An Introduction to Data Mining An Introduction to Intel Beijing wei.heng@intel.com January 17, 2014 Outline 1 DW Overview What is Notable Application of Conference, Software and Applications Major Process in 2 Major Tasks in Detail

More information

Local classification and local likelihoods

Local classification and local likelihoods Local classification and local likelihoods November 18 k-nearest neighbors The idea of local regression can be extended to classification as well The simplest way of doing so is called nearest neighbor

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. Artificial Intelligence. Learning. Types of Learning. Inductive Learning Method. Inductive Learning. Learning.

Learning. Artificial Intelligence. Learning. Types of Learning. Inductive Learning Method. Inductive Learning. Learning. Learning Learning is essential for unknown environments, i.e., when designer lacks omniscience Artificial Intelligence Learning Chapter 8 Learning is useful as a system construction method, i.e., expose

More information

CSC 321 H1S Study Guide (Last update: April 3, 2016) Winter 2016

CSC 321 H1S Study Guide (Last update: April 3, 2016) Winter 2016 1. Suppose our training set and test set are the same. Why would this be a problem? 2. Why is it necessary to have both a test set and a validation set? 3. Images are generally represented as n m 3 arrays,

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

Support Vector Machine (SVM)

Support Vector Machine (SVM) Support Vector Machine (SVM) CE-725: Statistical Pattern Recognition Sharif University of Technology Spring 2013 Soleymani Outline Margin concept Hard-Margin SVM Soft-Margin SVM Dual Problems of Hard-Margin

More information

New Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Introduction

New Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Introduction Introduction New Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Predictive analytics encompasses the body of statistical knowledge supporting the analysis of massive data sets.

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

COMP 551 Applied Machine Learning Lecture 6: Performance evaluation. Model assessment and selection.

COMP 551 Applied Machine Learning Lecture 6: Performance evaluation. Model assessment and selection. COMP 551 Applied Machine Learning Lecture 6: Performance evaluation. Model assessment and selection. Instructor: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/comp551 Unless otherwise

More information

Regression analysis. MTAT Data Mining Anna Leontjeva

Regression analysis. MTAT Data Mining Anna Leontjeva Regression analysis MTAT.03.183 Data Mining 2016 Anna Leontjeva Previous lecture Supervised vs. Unsupervised Learning? Previous lecture Supervised vs. Unsupervised Learning? Iris setosa Iris versicolor

More information

CLASSIFICATION AND CLUSTERING. Anveshi Charuvaka

CLASSIFICATION AND CLUSTERING. Anveshi Charuvaka CLASSIFICATION AND CLUSTERING Anveshi Charuvaka Learning from Data Classification Regression Clustering Anomaly Detection Contrast Set Mining Classification: Definition Given a collection of records (training

More information

Collaborative Filtering. Radek Pelánek

Collaborative Filtering. Radek Pelánek Collaborative Filtering Radek Pelánek 2015 Collaborative Filtering assumption: users with similar taste in past will have similar taste in future requires only matrix of ratings applicable in many domains

More information

Linear Models for Classification

Linear Models for Classification Linear Models for Classification Sumeet Agarwal, EEL709 (Most figures from Bishop, PRML) Approaches to classification Discriminant function: Directly assigns each data point x to a particular class Ci

More information

Introduction to Learning & Decision Trees

Introduction to Learning & Decision Trees Artificial Intelligence: Representation and Problem Solving 5-38 April 0, 2007 Introduction to Learning & Decision Trees Learning and Decision Trees to learning What is learning? - more than just memorizing

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

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

Principles of Dat Da a t Mining Pham Tho Hoan hoanpt@hnue.edu.v hoanpt@hnue.edu. n

Principles of Dat Da a t Mining Pham Tho Hoan hoanpt@hnue.edu.v hoanpt@hnue.edu. n Principles of Data Mining Pham Tho Hoan hoanpt@hnue.edu.vn References [1] David Hand, Heikki Mannila and Padhraic Smyth, Principles of Data Mining, MIT press, 2002 [2] Jiawei Han and Micheline Kamber,

More information

Introduction to Convex Optimization for Machine Learning

Introduction to Convex Optimization for Machine Learning Introduction to Convex Optimization for Machine Learning John Duchi University of California, Berkeley Practical Machine Learning, Fall 2009 Duchi (UC Berkeley) Convex Optimization for Machine Learning

More information

Machine Learning Logistic Regression

Machine Learning Logistic Regression Machine Learning Logistic Regression Jeff Howbert Introduction to Machine Learning Winter 2012 1 Logistic regression Name is somewhat misleading. Really a technique for classification, not regression.

More information

Data Mining Cluster Analysis: Advanced Concepts and Algorithms. ref. Chapter 9. Introduction to Data Mining

Data Mining Cluster Analysis: Advanced Concepts and Algorithms. ref. Chapter 9. Introduction to Data Mining Data Mining Cluster Analysis: Advanced Concepts and Algorithms ref. Chapter 9 Introduction to Data Mining by Tan, Steinbach, Kumar 1 Outline Prototype-based Fuzzy c-means Mixture Model Clustering Density-based

More information

Data Mining: An Overview. David Madigan http://www.stat.columbia.edu/~madigan

Data Mining: An Overview. David Madigan http://www.stat.columbia.edu/~madigan Data Mining: An Overview David Madigan http://www.stat.columbia.edu/~madigan Overview Brief Introduction to Data Mining Data Mining Algorithms Specific Eamples Algorithms: Disease Clusters Algorithms:

More information

Learning. CS461 Artificial Intelligence Pinar Duygulu. Bilkent University, Spring 2007. Slides are mostly adapted from AIMA and MIT Open Courseware

Learning. CS461 Artificial Intelligence Pinar Duygulu. Bilkent University, Spring 2007. Slides are mostly adapted from AIMA and MIT Open Courseware 1 Learning CS 461 Artificial Intelligence Pinar Duygulu Bilkent University, Slides are mostly adapted from AIMA and MIT Open Courseware 2 Learning What is learning? 3 Induction David Hume Bertrand Russell

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

Data Mining Part 5. Prediction

Data Mining Part 5. Prediction Data Mining Part 5. Prediction 5.7 Spring 2010 Instructor: Dr. Masoud Yaghini Outline Introduction Linear Regression Other Regression Models References Introduction Introduction Numerical prediction is

More information

A Simple Introduction to Support Vector Machines

A Simple Introduction to Support Vector Machines A Simple Introduction to Support Vector Machines Martin Law Lecture for CSE 802 Department of Computer Science and Engineering Michigan State University Outline A brief history of SVM Large-margin linear

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

Actuarial. Modeling Seminar Part 2. Matthew Morton FSA, MAAA Ben Williams

Actuarial. Modeling Seminar Part 2. Matthew Morton FSA, MAAA Ben Williams Actuarial Data Analytics / Predictive Modeling Seminar Part 2 Matthew Morton FSA, MAAA Ben Williams Agenda Introduction Overview of Seminar Traditional Experience Study Traditional vs. Predictive Modeling

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

Environmental Remote Sensing GEOG 2021

Environmental Remote Sensing GEOG 2021 Environmental Remote Sensing GEOG 2021 Lecture 4 Image classification 2 Purpose categorising data data abstraction / simplification data interpretation mapping for land cover mapping use land cover class

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

Gaussian Processes in Machine Learning

Gaussian Processes in Machine Learning Gaussian Processes in Machine Learning Carl Edward Rasmussen Max Planck Institute for Biological Cybernetics, 72076 Tübingen, Germany carl@tuebingen.mpg.de WWW home page: http://www.tuebingen.mpg.de/ carl

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

Introduction to Pattern Recognition

Introduction to Pattern Recognition Introduction to Pattern Recognition Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2009 CS 551, Spring 2009 c 2009, Selim Aksoy (Bilkent University)

More information

Data Mining for Model Creation. Presentation by Paul Below, EDS 2500 NE Plunkett Lane Poulsbo, WA USA 98370 paul.below@eds.

Data Mining for Model Creation. Presentation by Paul Below, EDS 2500 NE Plunkett Lane Poulsbo, WA USA 98370 paul.below@eds. Sept 03-23-05 22 2005 Data Mining for Model Creation Presentation by Paul Below, EDS 2500 NE Plunkett Lane Poulsbo, WA USA 98370 paul.below@eds.com page 1 Agenda Data Mining and Estimating Model Creation

More information

Empirical Model-Building and Response Surfaces

Empirical Model-Building and Response Surfaces Empirical Model-Building and Response Surfaces GEORGE E. P. BOX NORMAN R. DRAPER Technische Universitat Darmstadt FACHBEREICH INFORMATIK BIBLIOTHEK Invortar-Nf.-. Sachgsbiete: Standort: New York John Wiley

More information

MVA ENS Cachan. Lecture 2: Logistic regression & intro to MIL Iasonas Kokkinos Iasonas.kokkinos@ecp.fr

MVA ENS Cachan. Lecture 2: Logistic regression & intro to MIL Iasonas Kokkinos Iasonas.kokkinos@ecp.fr Machine Learning for Computer Vision 1 MVA ENS Cachan Lecture 2: Logistic regression & intro to MIL Iasonas Kokkinos Iasonas.kokkinos@ecp.fr Department of Applied Mathematics Ecole Centrale Paris Galen

More information

Data Mining Practical Machine Learning Tools and Techniques

Data Mining Practical Machine Learning Tools and Techniques Ensemble learning Data Mining Practical Machine Learning Tools and Techniques Slides for Chapter 8 of Data Mining by I. H. Witten, E. Frank and M. A. Hall Combining multiple models Bagging The basic idea

More information

Simple Linear Regression Chapter 11

Simple Linear Regression Chapter 11 Simple Linear Regression Chapter 11 Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related

More information

Quiz 1 for Name: Good luck! 20% 20% 20% 20% Quiz page 1 of 16

Quiz 1 for Name: Good luck! 20% 20% 20% 20% Quiz page 1 of 16 Quiz 1 for 6.034 Name: 20% 20% 20% 20% Good luck! 6.034 Quiz page 1 of 16 Question #1 30 points 1. Figure 1 illustrates decision boundaries for two nearest-neighbour classifiers. Determine which one of

More information

Machine Learning in Spam Filtering

Machine Learning in Spam Filtering Machine Learning in Spam Filtering A Crash Course in ML Konstantin Tretyakov kt@ut.ee Institute of Computer Science, University of Tartu Overview Spam is Evil ML for Spam Filtering: General Idea, Problems.

More information

Model-based boosting in R

Model-based boosting in R Model-based boosting in R Introduction to Gradient Boosting Matthias Schmid Institut für Medizininformatik, Biometrie und Epidemiologie (IMBE) Friedrich-Alexander-Universität Erlangen-Nürnberg Statistical

More information

Review of some concepts in predictive modeling

Review of some concepts in predictive modeling Review of some concepts in predictive modeling Brigham and Women s Hospital Harvard-MIT Division of Health Sciences and Technology HST.951J: Medical Decision Support A disjoint list of topics? Naïve Bayes

More information

Evaluating Machine Learning Algorithms. Machine DIT

Evaluating Machine Learning Algorithms. Machine DIT Evaluating Machine Learning Algorithms Machine Learning @ DIT 2 Evaluating Classification Accuracy During development, and in testing before deploying a classifier in the wild, we need to be able to quantify

More information

Lecture 5: Correlation and Linear Regression

Lecture 5: Correlation and Linear Regression Lecture 5: Correlation and Linear Regression 3.5. (Pearson) correlation coefficient The correlation coefficient measures the strength of the linear relationship between two variables. The correlation is

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

Data Clustering. Dec 2nd, 2013 Kyrylo Bessonov

Data Clustering. Dec 2nd, 2013 Kyrylo Bessonov Data Clustering Dec 2nd, 2013 Kyrylo Bessonov Talk outline Introduction to clustering Types of clustering Supervised Unsupervised Similarity measures Main clustering algorithms k-means Hierarchical Main

More information

Support Vector Machines Explained

Support Vector Machines Explained March 1, 2009 Support Vector Machines Explained Tristan Fletcher www.cs.ucl.ac.uk/staff/t.fletcher/ Introduction This document has been written in an attempt to make the Support Vector Machines (SVM),

More information

Machine Learning and Data Mining. Clustering. (adapted from) Prof. Alexander Ihler

Machine Learning and Data Mining. Clustering. (adapted from) Prof. Alexander Ihler Machine Learning and Data Mining Clustering (adapted from) Prof. Alexander Ihler Unsupervised learning Supervised learning Predict target value ( y ) given features ( x ) Unsupervised learning Understand

More information

BINARY PRINCIPAL COMPONENT ANALYSIS IN THE NETFLIX COLLABORATIVE FILTERING TASK

BINARY PRINCIPAL COMPONENT ANALYSIS IN THE NETFLIX COLLABORATIVE FILTERING TASK BINARY PRINCIPAL COMPONENT ANALYSIS IN THE NETFLIX COLLABORATIVE FILTERING TASK László Kozma, Alexander Ilin, Tapani Raiko Helsinki University of Technology Adaptive Informatics Research Center P.O. Box

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

K-nearest-neighbor: an introduction to machine learning

K-nearest-neighbor: an introduction to machine learning K-nearest-neighbor: an introduction to machine learning Xiaojin Zhu jerryzhu@cs.wisc.edu Computer Sciences Department University of Wisconsin, Madison slide 1 Outline Types of learning Classification:

More information

Linear smoother. ŷ = S y. where s ij = s ij (x) e.g. s ij = diag(l i (x)) To go the other way, you need to diagonalize S

Linear smoother. ŷ = S y. where s ij = s ij (x) e.g. s ij = diag(l i (x)) To go the other way, you need to diagonalize S Linear smoother ŷ = S y where s ij = s ij (x) e.g. s ij = diag(l i (x)) To go the other way, you need to diagonalize S 2 Online Learning: LMS and Perceptrons Partially adapted from slides by Ryan Gabbard

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

Introduction to Neural Networks : Revision Lectures

Introduction to Neural Networks : Revision Lectures Introduction to Neural Networks : Revision Lectures John A. Bullinaria, 2004 1. Module Aims and Learning Outcomes 2. Biological and Artificial Neural Networks 3. Training Methods for Multi Layer Perceptrons

More information

LABEL PROPAGATION ON GRAPHS. SEMI-SUPERVISED LEARNING. ----Changsheng Liu 10-30-2014

LABEL PROPAGATION ON GRAPHS. SEMI-SUPERVISED LEARNING. ----Changsheng Liu 10-30-2014 LABEL PROPAGATION ON GRAPHS. SEMI-SUPERVISED LEARNING ----Changsheng Liu 10-30-2014 Agenda Semi Supervised Learning Topics in Semi Supervised Learning Label Propagation Local and global consistency Graph

More information

Neural Networks & Boosting

Neural Networks & Boosting Neural Networks & Boosting Bob Stine Dept of Statistics, School University of Pennsylvania Questions How is logistic regression different from OLS? Logistic mean function for probabilities Larger weight

More information

Drug Store Sales Prediction

Drug Store Sales Prediction Drug Store Sales Prediction Chenghao Wang, Yang Li Abstract - In this paper we tried to apply machine learning algorithm into a real world problem drug store sales forecasting. Given store information,

More information

Introduction to Logistic Regression

Introduction to Logistic Regression OpenStax-CNX module: m42090 1 Introduction to Logistic Regression Dan Calderon This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract Gives introduction

More information

Machine Learning - Spring 2012 Problem Set 3

Machine Learning - Spring 2012 Problem Set 3 10-701 Machine Learning - Spring 2012 Problem Set 3 Out: February 29th, 1:30pm In: March 19h, 1:30pm TA: Hai-Son Le (hple@cs.cmu.edu) School Of Computer Science, Carnegie Mellon University Homework will

More information

Several Views of Support Vector Machines

Several Views of Support Vector Machines Several Views of Support Vector Machines Ryan M. Rifkin Honda Research Institute USA, Inc. Human Intention Understanding Group 2007 Tikhonov Regularization We are considering algorithms of the form min

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

Boosting. riedmiller@informatik.uni-freiburg.de

Boosting. riedmiller@informatik.uni-freiburg.de . Machine Learning Boosting Prof. Dr. Martin Riedmiller AG Maschinelles Lernen und Natürlichsprachliche Systeme Institut für Informatik Technische Fakultät Albert-Ludwigs-Universität Freiburg riedmiller@informatik.uni-freiburg.de

More information

Principles of Data Mining by Hand&Mannila&Smyth

Principles of Data Mining by Hand&Mannila&Smyth Principles of Data Mining by Hand&Mannila&Smyth Slides for Textbook Ari Visa,, Institute of Signal Processing Tampere University of Technology October 4, 2010 Data Mining: Concepts and Techniques 1 Differences

More information

Big Data Analytics. Lucas Rego Drumond

Big Data Analytics. Lucas Rego Drumond Big Data Analytics Lucas Rego Drumond Information Systems and Machine Learning Lab (ISMLL) Institute of Computer Science University of Hildesheim, Germany Going For Large Scale Going For Large Scale 1

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

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

L15: statistical clustering

L15: statistical clustering Similarity measures Criterion functions Cluster validity Flat clustering algorithms k-means ISODATA L15: statistical clustering Hierarchical clustering algorithms Divisive Agglomerative CSCE 666 Pattern

More information

Sibyl: a system for large scale machine learning

Sibyl: a system for large scale machine learning Sibyl: a system for large scale machine learning Tushar Chandra, Eugene Ie, Kenneth Goldman, Tomas Lloret Llinares, Jim McFadden, Fernando Pereira, Joshua Redstone, Tal Shaked, Yoram Singer Machine Learning

More information