} It is non-zero, and maximized given a uniform distribution } Thus, for any distribution possible, we have:

Size: px
Start display at page:

Download "} It is non-zero, and maximized given a uniform distribution } Thus, for any distribution possible, we have:"

Transcription

1 Review: Entropy and Information H(P) = X i p i log p i Class #04: Mutual Information & Decision rees Machine Learning (CS 419/519): M. Allen, 1 Sept. 18 } Entropy is the information gained on average when observing events that occur according to a probability distribution } It is non-zero, and maximized given a uniform distribution } hus, for any distribution possible, we have: P = {p 1,p,...,p k } 0 apple H(P) apple log k Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) Review: Joint Probability & Independence } If we have two events e 1 and e, the probability that both events occur, called the oint probability, is written: P (e 1 ^ e )=P (e 1,e ) } We say that two events are independent if and only if: P (e 1,e )=P (e 1 ) P (e ) } Independent events tell us nothing about each other Review: Conditional Probability } Given two events e 1 and e, the probability that e 1 occurs, given that e also occurs, called the conditional probability of e 1 given e, is written: P (e 1 e ) } In general, the conditional probability of an event can be quite different from the basic probability that it occurs } hus, for our weather example, we might have: W = {R, R} P W = {0.5, 0.5} U = {U, U} P U = {0., 0.8} P (U R) =0.8 P (U R) =0.1 P ( U R) =0. P ( U R) =0.9 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 3 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 4 1

2 Properties of Conditional Probability } Conditional probability can be defined using oint probability: P (e 1 e )= P (e 1,e ) P (e ) P (e 1,e )=P (e 1 e )P (e ) } hus, if the events are actually independent, we get: P (e 1 e )= P (e 1,e ) P (e ) P (e 1 e )= P (e 1)P (e ) P (e ) P (e 1 e )=P (e 1 ) By definition of independence Calculating Joint Probabilities } We have the simple and conditional probabilities of rain and my umbrellacarrying behavior: W = {R, R} P W = {0.5, 0.5} U = {U, U} P U = {0., 0.8} P (U R) =0.8 P (U R) =0.1 P ( U R) =0. P ( U R) =0.9 } his allows us to calculate various oint probabilities: P (U, R) =P (U R)P (R) = =0.4 P (U, R) =P (U R)P ( R) = =0.05 P ( U, R) =P ( U R)P (R) = =0.1 P ( U, R) =P ( U R)P ( R) = =0.45 otal set of probabilities sums to 1.0 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 5 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 6 Mutual Information } Suppose we have two sets of possible events, each with its own probability distributions: E = {e 1,e,...,e m } P E = {p 1,p,...,p m } E 0 = {e 0 1,e 0,...,e 0 n} P E 0 = {p 0 1,p 0,...,p 0 n} } We can define mutual information, the amount that one event tells us about the other: I(E; E 0 )= X e i,e 0 } Effectively, this measures how much knowing that E 0 has happened reduces the entropy of P (e i,e 0 ) log P (e i,e 0 ) P (e i )P (e 0 ) Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 7 E Mutual Information } his allows us to quantify exactly how much knowing whether or not it is raining tells us about whether or not I will be carrying an umbrella: P (U, R) I(U; W) =P (U, R) log P (U)P (R) + P (U, R) log P (U, R) P (U)P ( R) + P ( U, R) P ( U, R) log P ( U)P (R) + P ( U, R) log P ( U, R) P ( U)P ( R) 0.4 =0.4log log log log =0.4 log log log log = te: the final value doesn t matter so much (e.g., it would change if we used a different base for our logarithms). It does allow us to compare different combinations of variables, however, to see which tells us the most about another. Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 8

3 Properties of Mutual Information I(E; E 0 )= X P (e i,e 0 P (e i,e 0 ) log ) P (e i )P (e 0 e i,e 0 ) } As defined, mutual information is: 1. Symmetric: I(E; E 0 )=I(E 0 ; E) Because: P (e i,e 0 )=P (e 0,e i ). n-negative: I(E; E 0 ) 0 Because: it s complicated, but trust me 3. Zero when events are independent (i.e., when independent, one event tells us nothing about the other that we didn t already know): I(E; E 0 )= X e i,e 0 = X e i,e 0 P (e i,e 0 P (e i,e 0 ) log ) P (e i )P (e 0 ) = X P (e i )P (e 0 P (e i )P (e 0 ) log ) P (e i )P (e 0 e i,e 0 ) P (e i )P (e 0 ) log 1= X e i,e 0 P (e i )P (e 0 ) 0=0 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 9 Review: Inductive Learning } In its simplest form, induction is the task of learning a function on some inputs from examples of its outputs } or a target function, f, each training example is a pair (x, f (x )) } We assume that we do not yet know the actual form of the function f (if we did, we don t need to learn) } Learning problem: find a hypothesis function, h, such that h (x ) = f (x ) most of the time, based on a training set of example input-output pairs Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 10 Decision rees } A decision tree leads us from a set of attributes (features of the input) to some output } or example, we have a database of customer records for restaraunts } hese customers have made a number of decisions about whether to wait for a table, based on a number of attributes: 1. Alternate: is there an alternative restaurant nearby?. Bar: is there a comfortable bar area to wait in? 3. ri/sat: is today riday or Saturday? 4. Hungry: are we hungry? 5. Patrons: number of people in the restaurant (ne, Some, ull) 6. Price: price range ($, $$, $$$) 7. Raining: is it raining outside? 8. Reservation: have we made a reservation? 9. ype: kind of restaurant (rench, Italian, hai, Burger) 10. WaitEstimate: estimated wait time in minutes (0-10, 10-30, 30-60, >60) } he function we want to learn is whether or not a (future) customer will decide to wait, given some particular set of attributes Decisions Based on Attributes } raining set: cases where patrons have decided to wait or not, along with the associated attributes for each case } We now want to learn a tree that agrees with the decisions already made, in hopes that it will allow us to predict future decisions Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 11 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 1 3

4 Decision ree unctions } or the examples given, here is a true tree (one that will lead from the inputs to the same outputs) ne Some ull Patrons? > Bar? Reservation? WaitEstimate? Alternate? ri/sat? Hungry? Alternate? Raining? Decision rees are Expressive A B A &&!B } Such trees can express any deterministic function we: } or example, in boolean functions, each row of a truth-table will correspond to a path in a tree } or any such function, there is always a tree: ust make each example a different path to a correct leaf output } A Problem: such trees most often do not generalize to new examples } Another Problem: we want compact trees to simplify inference B A B Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 13 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 14 Why t Search for rees? } One thing we might consider would be to search through possible trees to find ones that are most compact and consistent with our inputs } Exhaustive search is too expensive, however, due to the large number of possible functions (trees) that exist } or n binary-valued attributes, and boolean decision outputs, there are n possibilities } or 5 such attributes, we have 4,94,967,96 trees! } Even restricting our search to conunctions over attributes, it is easy to get 3 n possible trees Building rees op-down } Rather than search for all trees, we build our trees by: 1. Choosing an attribute A from our set. Dividing our examples according to the values of A 3. Placing each subset of examples into a sub-tree below the node for attribute A } his can be implemented in a number of ways, but is perhaps most easily understood recursively } he main question becomes: how do we choose the attribute A that we use to split our examples? Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 15 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 16 4

5 Decision ree Learning Algorithm function DECISION-REE-LEARNING(examples, attributes, parent examples) returns tree if examples is empty then return PLURALIY-VALUE(parent examples) else if all examples have the same classification then return the classification else if attributes is empty then return PLURALIY-VALUE(examples) else A argmax a attributes IMPORANCE(a, examples) tree anewdecisiontreewithroottesta for each value v k of A do exs {e : e examples and e.a = v k} subtree DECISION-REE-LEARNING(exs, attributes A, examples) add a branch to tree with label (A = v k) and subtree subtree return tree his Week } Information heory & Decision rees } Readings: } Blog post on Information heory (linked from class schedule) } Section 18.3 from Russell & rvig } Office Hours: Wing 10 } Monday/Wednesday/riday, 1:00 PM 1:00 PM } uesday/hursday, 1:30 PM 3:00 PM PLURALIY-VALUE(): returns output decision-value for maority of examples IMPORANCE(): rates attributes for their importance in making decisions for the given set of examples (the only actually complex part) Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 17 Wednesday, 1 Sep. 018 Machine Learning (CS 419/519) 18 5

Machine Learning (CS 419/519): M. Allen, 14 Sept. 18 made, in hopes that it will allow us to predict future decisions

Machine Learning (CS 419/519): M. Allen, 14 Sept. 18 made, in hopes that it will allow us to predict future decisions Review: Decisions Based on Attributes } raining set: cases where patrons have decided to wait or not, along with the associated attributes for each case Class #05: Mutual Information & Decision rees Machine

More information

Learning Decision Trees

Learning Decision Trees Learning Decision Trees CS194-10 Fall 2011 Lecture 8 CS194-10 Fall 2011 Lecture 8 1 Outline Decision tree models Tree construction Tree pruning Continuous input features CS194-10 Fall 2011 Lecture 8 2

More information

Decision Trees. None Some Full > No Yes. No Yes. No Yes. No Yes. No Yes. No Yes. No Yes. Patrons? WaitEstimate? Hungry? Alternate?

Decision Trees. None Some Full > No Yes. No Yes. No Yes. No Yes. No Yes. No Yes. No Yes. Patrons? WaitEstimate? Hungry? Alternate? Decision rees Decision trees is one of the simplest methods for supervised learning. It can be applied to both regression & classification. Example: A decision tree for deciding whether to wait for a place

More information

CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING. Santiago Ontañón

CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING. Santiago Ontañón CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING Santiago Ontañón so367@drexel.edu Summary so far: Rational Agents Problem Solving Systematic Search: Uninformed Informed Local Search Adversarial Search

More information

CS 380: ARTIFICIAL INTELLIGENCE

CS 380: ARTIFICIAL INTELLIGENCE CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING 11/11/2013 Santiago Ontañón santi@cs.drexel.edu https://www.cs.drexel.edu/~santi/teaching/2013/cs380/intro.html Summary so far: Rational Agents Problem

More information

Learning from Observations. Chapter 18, Sections 1 3 1

Learning from Observations. Chapter 18, Sections 1 3 1 Learning from Observations Chapter 18, Sections 1 3 Chapter 18, Sections 1 3 1 Outline Learning agents Inductive learning Decision tree learning Measuring learning performance Chapter 18, Sections 1 3

More information

Decision Trees. CS 341 Lectures 8/9 Dan Sheldon

Decision Trees. CS 341 Lectures 8/9 Dan Sheldon Decision rees CS 341 Lectures 8/9 Dan Sheldon Review: Linear Methods Y! So far, we ve looked at linear methods! Linear regression! Fit a line/plane/hyperplane X 2 X 1! Logistic regression! Decision boundary

More information

Introduction to Artificial Intelligence. Learning from Oberservations

Introduction to Artificial Intelligence. Learning from Oberservations Introduction to Artificial Intelligence Learning from Oberservations Bernhard Beckert UNIVERSITÄT KOBLENZ-LANDAU Winter Term 2004/2005 B. Beckert: KI für IM p.1 Outline Learning agents Inductive learning

More information

1. Courses are either tough or boring. 2. Not all courses are boring. 3. Therefore there are tough courses. (Cx, Tx, Bx, )

1. Courses are either tough or boring. 2. Not all courses are boring. 3. Therefore there are tough courses. (Cx, Tx, Bx, ) Logic FOL Syntax FOL Rules (Copi) 1. Courses are either tough or boring. 2. Not all courses are boring. 3. Therefore there are tough courses. (Cx, Tx, Bx, ) Dealing with Time Translate into first-order

More information

From inductive inference to machine learning

From inductive inference to machine learning From inductive inference to machine learning ADAPTED FROM AIMA SLIDES Russel&Norvig:Artificial Intelligence: a modern approach AIMA: Inductive inference AIMA: Inductive inference 1 Outline Bayesian inferences

More information

Learning and Neural Networks

Learning and Neural Networks Artificial Intelligence Learning and Neural Networks Readings: Chapter 19 & 20.5 of Russell & Norvig Example: A Feed-forward Network w 13 I 1 H 3 w 35 w 14 O 5 I 2 w 23 w 24 H 4 w 45 a 5 = g 5 (W 3,5 a

More information

Bayesian learning Probably Approximately Correct Learning

Bayesian learning Probably Approximately Correct Learning Bayesian learning Probably Approximately Correct Learning Peter Antal antal@mit.bme.hu A.I. December 1, 2017 1 Learning paradigms Bayesian learning Falsification hypothesis testing approach Probably Approximately

More information

Statistical Learning. Philipp Koehn. 10 November 2015

Statistical Learning. Philipp Koehn. 10 November 2015 Statistical Learning Philipp Koehn 10 November 2015 Outline 1 Learning agents Inductive learning Decision tree learning Measuring learning performance Bayesian learning Maximum a posteriori and maximum

More information

Chapter 18. Decision Trees and Ensemble Learning. Recall: Learning Decision Trees

Chapter 18. Decision Trees and Ensemble Learning. Recall: Learning Decision Trees CSE 473 Chapter 18 Decision Trees and Ensemble Learning Recall: Learning Decision Trees Example: When should I wait for a table at a restaurant? Attributes (features) relevant to Wait? decision: 1. Alternate:

More information

EECS 349:Machine Learning Bryan Pardo

EECS 349:Machine Learning Bryan Pardo EECS 349:Machine Learning Bryan Pardo Topic 2: Decision Trees (Includes content provided by: Russel & Norvig, D. Downie, P. Domingos) 1 General Learning Task There is a set of possible examples Each example

More information

Decision Trees. Ruy Luiz Milidiú

Decision Trees. Ruy Luiz Milidiú Decision Trees Ruy Luiz Milidiú Resumo Objetivo Examinar o conceito de Árvores de Decisão e suas aplicações Sumário Surpresa e Informação Entropia Informação Mútua Divergência e Entropia Cruzada Ganho

More information

Introduction to Machine Learning

Introduction to Machine Learning Introduction to Machine Learning Reading for today: R&N 18.1-18.4 Next lecture: R&N 18.6-18.12, 20.1-20.3.2 Outline The importance of a good representation Different types of learning problems Different

More information

Learning Decision Trees

Learning Decision Trees Learning Decision Trees Machine Learning Fall 2018 Some slides from Tom Mitchell, Dan Roth and others 1 Key issues in machine learning Modeling How to formulate your problem as a machine learning problem?

More information

CSC 411 Lecture 3: Decision Trees

CSC 411 Lecture 3: Decision Trees CSC 411 Lecture 3: Decision Trees Roger Grosse, Amir-massoud Farahmand, and Juan Carrasquilla University of Toronto UofT CSC 411: 03-Decision Trees 1 / 33 Today Decision Trees Simple but powerful learning

More information

Incremental Stochastic Gradient Descent

Incremental Stochastic Gradient Descent Incremental Stochastic Gradient Descent Batch mode : gradient descent w=w - η E D [w] over the entire data D E D [w]=1/2σ d (t d -o d ) 2 Incremental mode: gradient descent w=w - η E d [w] over individual

More information

Learning Decision Trees

Learning Decision Trees Learning Decision Trees Machine Learning Spring 2018 1 This lecture: Learning Decision Trees 1. Representation: What are decision trees? 2. Algorithm: Learning decision trees The ID3 algorithm: A greedy

More information

the tree till a class assignment is reached

the tree till a class assignment is reached Decision Trees Decision Tree for Playing Tennis Prediction is done by sending the example down Prediction is done by sending the example down the tree till a class assignment is reached Definitions Internal

More information

Assignment 1: Probabilistic Reasoning, Maximum Likelihood, Classification

Assignment 1: Probabilistic Reasoning, Maximum Likelihood, Classification Assignment 1: Probabilistic Reasoning, Maximum Likelihood, Classification For due date see https://courses.cs.sfu.ca This assignment is to be done individually. Important Note: The university policy on

More information

Introduction To Artificial Neural Networks

Introduction To Artificial Neural Networks Introduction To Artificial Neural Networks Machine Learning Supervised circle square circle square Unsupervised group these into two categories Supervised Machine Learning Supervised Machine Learning Supervised

More information

CS6375: Machine Learning Gautam Kunapuli. Decision Trees

CS6375: Machine Learning Gautam Kunapuli. Decision Trees Gautam Kunapuli Example: Restaurant Recommendation Example: Develop a model to recommend restaurants to users depending on their past dining experiences. Here, the features are cost (x ) and the user s

More information

Classification Algorithms

Classification Algorithms Classification Algorithms UCSB 290N, 2015. T. Yang Slides based on R. Mooney UT Austin 1 Table of Content roblem Definition Rocchio K-nearest neighbor case based Bayesian algorithm Decision trees 2 Given:

More information

Classification Algorithms

Classification Algorithms Classification Algorithms UCSB 293S, 2017. T. Yang Slides based on R. Mooney UT Austin 1 Table of Content Problem Definition Rocchio K-nearest neighbor case based Bayesian algorithm Decision trees 2 Classification

More information

Learning from Examples

Learning from Examples Learning from Examples Data fitting Decision trees Cross validation Computational learning theory Linear classifiers Neural networks Nonparametric methods: nearest neighbor Support vector machines Ensemble

More information

Administrative notes. Computational Thinking ct.cs.ubc.ca

Administrative notes. Computational Thinking ct.cs.ubc.ca Administrative notes Labs this week: project time. Remember, you need to pass the project in order to pass the course! (See course syllabus.) Clicker grades should be on-line now Administrative notes March

More information

Data Mining. CS57300 Purdue University. Bruno Ribeiro. February 8, 2018

Data Mining. CS57300 Purdue University. Bruno Ribeiro. February 8, 2018 Data Mining CS57300 Purdue University Bruno Ribeiro February 8, 2018 Decision trees Why Trees? interpretable/intuitive, popular in medical applications because they mimic the way a doctor thinks model

More information

16.4 Multiattribute Utility Functions

16.4 Multiattribute Utility Functions 285 Normalized utilities The scale of utilities reaches from the best possible prize u to the worst possible catastrophe u Normalized utilities use a scale with u = 0 and u = 1 Utilities of intermediate

More information

brainlinksystem.com $25+ / hr AI Decision Tree Learning Part I Outline Learning 11/9/2010 Carnegie Mellon

brainlinksystem.com $25+ / hr AI Decision Tree Learning Part I Outline Learning 11/9/2010 Carnegie Mellon I Decision Tree Learning Part I brainlinksystem.com $25+ / hr Illah Nourbakhsh s version Chapter 8, Russell and Norvig Thanks to all past instructors Carnegie Mellon Outline Learning and philosophy Induction

More information

Decision Trees. Lewis Fishgold. (Material in these slides adapted from Ray Mooney's slides on Decision Trees)

Decision Trees. Lewis Fishgold. (Material in these slides adapted from Ray Mooney's slides on Decision Trees) Decision Trees Lewis Fishgold (Material in these slides adapted from Ray Mooney's slides on Decision Trees) Classification using Decision Trees Nodes test features, there is one branch for each value of

More information

Classification and Regression Trees

Classification and Regression Trees Classification and Regression Trees Ryan P Adams So far, we have primarily examined linear classifiers and regressors, and considered several different ways to train them When we ve found the linearity

More information

Lecture 3: Decision Trees

Lecture 3: Decision Trees Lecture 3: Decision Trees Cognitive Systems II - Machine Learning SS 2005 Part I: Basic Approaches of Concept Learning ID3, Information Gain, Overfitting, Pruning Lecture 3: Decision Trees p. Decision

More information

Introduction. Decision Tree Learning. Outline. Decision Tree 9/7/2017. Decision Tree Definition

Introduction. Decision Tree Learning. Outline. Decision Tree 9/7/2017. Decision Tree Definition Introduction Decision Tree Learning Practical methods for inductive inference Approximating discrete-valued functions Robust to noisy data and capable of learning disjunctive expression ID3 earch a completely

More information

Decision Trees. CS57300 Data Mining Fall Instructor: Bruno Ribeiro

Decision Trees. CS57300 Data Mining Fall Instructor: Bruno Ribeiro Decision Trees CS57300 Data Mining Fall 2016 Instructor: Bruno Ribeiro Goal } Classification without Models Well, partially without a model } Today: Decision Trees 2015 Bruno Ribeiro 2 3 Why Trees? } interpretable/intuitive,

More information

Imagine we ve got a set of data containing several types, or classes. E.g. information about customers, and class=whether or not they buy anything.

Imagine we ve got a set of data containing several types, or classes. E.g. information about customers, and class=whether or not they buy anything. Decision Trees Defining the Task Imagine we ve got a set of data containing several types, or classes. E.g. information about customers, and class=whether or not they buy anything. Can we predict, i.e

More information

Supervised Learning (contd) Decision Trees. Mausam (based on slides by UW-AI faculty)

Supervised Learning (contd) Decision Trees. Mausam (based on slides by UW-AI faculty) Supervised Learning (contd) Decision Trees Mausam (based on slides by UW-AI faculty) Decision Trees To play or not to play? http://www.sfgate.com/blogs/images/sfgate/sgreen/2007/09/05/2240773250x321.jpg

More information

Decision Trees Part 1. Rao Vemuri University of California, Davis

Decision Trees Part 1. Rao Vemuri University of California, Davis Decision Trees Part 1 Rao Vemuri University of California, Davis Overview What is a Decision Tree Sample Decision Trees How to Construct a Decision Tree Problems with Decision Trees Classification Vs Regression

More information

Tutorial 6. By:Aashmeet Kalra

Tutorial 6. By:Aashmeet Kalra Tutorial 6 By:Aashmeet Kalra AGENDA Candidate Elimination Algorithm Example Demo of Candidate Elimination Algorithm Decision Trees Example Demo of Decision Trees Concept and Concept Learning A Concept

More information

Notes on Machine Learning for and

Notes on Machine Learning for and Notes on Machine Learning for 16.410 and 16.413 (Notes adapted from Tom Mitchell and Andrew Moore.) Learning = improving with experience Improve over task T (e.g, Classification, control tasks) with respect

More information

Decision T ree Tree Algorithm Week 4 1

Decision T ree Tree Algorithm Week 4 1 Decision Tree Algorithm Week 4 1 Team Homework Assignment #5 Read pp. 105 117 of the text book. Do Examples 3.1, 3.2, 3.3 and Exercise 3.4 (a). Prepare for the results of the homework assignment. Due date

More information

Decision Trees. Gavin Brown

Decision Trees. Gavin Brown Decision Trees Gavin Brown Every Learning Method has Limitations Linear model? KNN? SVM? Explain your decisions Sometimes we need interpretable results from our techniques. How do you explain the above

More information

Decision Trees. CSC411/2515: Machine Learning and Data Mining, Winter 2018 Luke Zettlemoyer, Carlos Guestrin, and Andrew Moore

Decision Trees. CSC411/2515: Machine Learning and Data Mining, Winter 2018 Luke Zettlemoyer, Carlos Guestrin, and Andrew Moore Decision Trees Claude Monet, The Mulberry Tree Slides from Pedro Domingos, CSC411/2515: Machine Learning and Data Mining, Winter 2018 Luke Zettlemoyer, Carlos Guestrin, and Andrew Moore Michael Guerzhoy

More information

Machine Learning

Machine Learning Machine Learning 10-601 Tom M. Mitchell Machine Learning Department Carnegie Mellon University January 14, 2015 Today: The Big Picture Overfitting Review: probability Readings: Decision trees, overfiting

More information

Allocation of multiple processors to lazy boolean function trees justification of the magic number 2/3

Allocation of multiple processors to lazy boolean function trees justification of the magic number 2/3 Allocation of multiple processors to lazy boolean function trees justification of the magic number 2/3 Alan Dix Computer Science Department University of York, York, YO1 5DD, U.K. alan@uk.ac.york.minster

More information

CS 6375 Machine Learning

CS 6375 Machine Learning CS 6375 Machine Learning Decision Trees Instructor: Yang Liu 1 Supervised Classifier X 1 X 2. X M Ref class label 2 1 Three variables: Attribute 1: Hair = {blond, dark} Attribute 2: Height = {tall, short}

More information

Machine Learning 2nd Edi7on

Machine Learning 2nd Edi7on Lecture Slides for INTRODUCTION TO Machine Learning 2nd Edi7on CHAPTER 9: Decision Trees ETHEM ALPAYDIN The MIT Press, 2010 Edited and expanded for CS 4641 by Chris Simpkins alpaydin@boun.edu.tr h1p://www.cmpe.boun.edu.tr/~ethem/i2ml2e

More information

Decision Trees. Tirgul 5

Decision Trees. Tirgul 5 Decision Trees Tirgul 5 Using Decision Trees It could be difficult to decide which pet is right for you. We ll find a nice algorithm to help us decide what to choose without having to think about it. 2

More information

Name (NetID): (1 Point)

Name (NetID): (1 Point) CS446: Machine Learning Fall 2016 October 25 th, 2016 This is a closed book exam. Everything you need in order to solve the problems is supplied in the body of this exam. This exam booklet contains four

More information

Decision Trees / NLP Introduction

Decision Trees / NLP Introduction Decision Trees / NLP Introduction Dr. Kevin Koidl School of Computer Science and Statistic Trinity College Dublin ADAPT Research Centre The ADAPT Centre is funded under the SFI Research Centres Programme

More information

Decision Trees.

Decision Trees. . Machine Learning Decision Trees 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

Decision Trees. Data Science: Jordan Boyd-Graber University of Maryland MARCH 11, Data Science: Jordan Boyd-Graber UMD Decision Trees 1 / 1

Decision Trees. Data Science: Jordan Boyd-Graber University of Maryland MARCH 11, Data Science: Jordan Boyd-Graber UMD Decision Trees 1 / 1 Decision Trees Data Science: Jordan Boyd-Graber University of Maryland MARCH 11, 2018 Data Science: Jordan Boyd-Graber UMD Decision Trees 1 / 1 Roadmap Classification: machines labeling data for us Last

More information

CMPT 310 Artificial Intelligence Survey. Simon Fraser University Summer Instructor: Oliver Schulte

CMPT 310 Artificial Intelligence Survey. Simon Fraser University Summer Instructor: Oliver Schulte CMPT 310 Artificial Intelligence Survey Simon Fraser University Summer 2017 Instructor: Oliver Schulte Assignment 3: Chapters 13, 14, 18, 20. Probabilistic Reasoning and Learning Instructions: The university

More information

Generative v. Discriminative classifiers Intuition

Generative v. Discriminative classifiers Intuition Logistic Regression (Continued) Generative v. Discriminative Decision rees Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University January 31 st, 2007 2005-2007 Carlos Guestrin 1 Generative

More information

Decision Tree Learning

Decision Tree Learning Topics Decision Tree Learning Sattiraju Prabhakar CS898O: DTL Wichita State University What are decision trees? How do we use them? New Learning Task ID3 Algorithm Weka Demo C4.5 Algorithm Weka Demo Implementation

More information

Decision Tree Learning

Decision Tree Learning Decision Tree Learning Berlin Chen Department of Computer Science & Information Engineering National Taiwan Normal University References: 1. Machine Learning, Chapter 3 2. Data Mining: Concepts, Models,

More information

Machine Learning

Machine Learning Machine Learning 10-701 Tom M. Mitchell Machine Learning Department Carnegie Mellon University January 13, 2011 Today: The Big Picture Overfitting Review: probability Readings: Decision trees, overfiting

More information

Introduction to Statistical Learning Theory. Material para Máster en Matemáticas y Computación

Introduction to Statistical Learning Theory. Material para Máster en Matemáticas y Computación Introduction to Statistical Learning Theory Material para Máster en Matemáticas y Computación 1 Learning agents Inductive learning Decision tree learning First Part: Outline 2 Learning Learning is essential

More information

A Problem Involving Games. Paccioli s Solution. Problems for Paccioli: Small Samples. n / (n + m) m / (n + m)

A Problem Involving Games. Paccioli s Solution. Problems for Paccioli: Small Samples. n / (n + m) m / (n + m) Class #10: Introduction to Probability Theory Artificial Intelligence (CS 452/552): M. Allen, 27 Sept. 17 A Problem Involving Games } Two players put money in on a game of chance } First one to certain

More information

Induction on Decision Trees

Induction on Decision Trees Séance «IDT» de l'ue «apprentissage automatique» Bruno Bouzy bruno.bouzy@parisdescartes.fr www.mi.parisdescartes.fr/~bouzy Outline Induction task ID3 Entropy (disorder) minimization Noise Unknown attribute

More information

Decision Tree Learning Lecture 2

Decision Tree Learning Lecture 2 Machine Learning Coms-4771 Decision Tree Learning Lecture 2 January 28, 2008 Two Types of Supervised Learning Problems (recap) Feature (input) space X, label (output) space Y. Unknown distribution D over

More information

Induction of Decision Trees

Induction of Decision Trees Induction of Decision Trees Peter Waiganjo Wagacha This notes are for ICS320 Foundations of Learning and Adaptive Systems Institute of Computer Science University of Nairobi PO Box 30197, 00200 Nairobi.

More information

Supervised Learning! Algorithm Implementations! Inferring Rudimentary Rules and Decision Trees!

Supervised Learning! Algorithm Implementations! Inferring Rudimentary Rules and Decision Trees! Supervised Learning! Algorithm Implementations! Inferring Rudimentary Rules and Decision Trees! Summary! Input Knowledge representation! Preparing data for learning! Input: Concept, Instances, Attributes"

More information

Decision Tree Learning and Inductive Inference

Decision Tree Learning and Inductive Inference Decision Tree Learning and Inductive Inference 1 Widely used method for inductive inference Inductive Inference Hypothesis: Any hypothesis found to approximate the target function well over a sufficiently

More information

Decision Trees.

Decision Trees. . Machine Learning Decision Trees 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

Classification: Decision Trees

Classification: Decision Trees Classification: Decision Trees These slides were assembled by Byron Boots, with grateful acknowledgement to Eric Eaton and the many others who made their course materials freely available online. Feel

More information

Machine Learning

Machine Learning Machine Learning 10-601 Tom M. Mitchell Machine Learning Department Carnegie Mellon University August 30, 2017 Today: Decision trees Overfitting The Big Picture Coming soon Probabilistic learning MLE,

More information

CHAPTER-17. Decision Tree Induction

CHAPTER-17. Decision Tree Induction CHAPTER-17 Decision Tree Induction 17.1 Introduction 17.2 Attribute selection measure 17.3 Tree Pruning 17.4 Extracting Classification Rules from Decision Trees 17.5 Bayesian Classification 17.6 Bayes

More information

Decision-Tree Learning. Chapter 3: Decision Tree Learning. Classification Learning. Decision Tree for PlayTennis

Decision-Tree Learning. Chapter 3: Decision Tree Learning. Classification Learning. Decision Tree for PlayTennis Decision-Tree Learning Chapter 3: Decision Tree Learning CS 536: Machine Learning Littman (Wu, TA) [read Chapter 3] [some of Chapter 2 might help ] [recommended exercises 3.1, 3.2] Decision tree representation

More information

Decision trees. Special Course in Computer and Information Science II. Adam Gyenge Helsinki University of Technology

Decision trees. Special Course in Computer and Information Science II. Adam Gyenge Helsinki University of Technology Decision trees Special Course in Computer and Information Science II Adam Gyenge Helsinki University of Technology 6.2.2008 Introduction Outline: Definition of decision trees ID3 Pruning methods Bibliography:

More information

Statistics and learning: Big Data

Statistics and learning: Big Data Statistics and learning: Big Data Learning Decision Trees and an Introduction to Boosting Sébastien Gadat Toulouse School of Economics February 2017 S. Gadat (TSE) SAD 2013 1 / 30 Keywords Decision trees

More information

CSCI 5622 Machine Learning

CSCI 5622 Machine Learning CSCI 5622 Machine Learning DATE READ DUE Mon, Aug 31 1, 2 & 3 Wed, Sept 2 3 & 5 Wed, Sept 9 TBA Prelim Proposal www.rodneynielsen.com/teaching/csci5622f09/ Instructor: Rodney Nielsen Assistant Professor

More information

Decision Trees. Nicholas Ruozzi University of Texas at Dallas. Based on the slides of Vibhav Gogate and David Sontag

Decision Trees. Nicholas Ruozzi University of Texas at Dallas. Based on the slides of Vibhav Gogate and David Sontag Decision Trees Nicholas Ruozzi University of Texas at Dallas Based on the slides of Vibhav Gogate and David Sontag Supervised Learning Input: labelled training data i.e., data plus desired output Assumption:

More information

Lecture 3: Decision Trees

Lecture 3: Decision Trees Lecture 3: Decision Trees Cognitive Systems - Machine Learning Part I: Basic Approaches of Concept Learning ID3, Information Gain, Overfitting, Pruning last change November 26, 2014 Ute Schmid (CogSys,

More information

DECISION TREE LEARNING. [read Chapter 3] [recommended exercises 3.1, 3.4]

DECISION TREE LEARNING. [read Chapter 3] [recommended exercises 3.1, 3.4] 1 DECISION TREE LEARNING [read Chapter 3] [recommended exercises 3.1, 3.4] Decision tree representation ID3 learning algorithm Entropy, Information gain Overfitting Decision Tree 2 Representation: Tree-structured

More information

Decision Tree Learning

Decision Tree Learning Topics Decision Tree Learning Sattiraju Prabhakar CS898O: DTL Wichita State University What are decision trees? How do we use them? New Learning Task ID3 Algorithm Weka Demo C4.5 Algorithm Weka Demo Implementation

More information

Introduction to Machine Learning CMU-10701

Introduction to Machine Learning CMU-10701 Introduction to Machine Learning CMU-10701 23. Decision Trees Barnabás Póczos Contents Decision Trees: Definition + Motivation Algorithm for Learning Decision Trees Entropy, Mutual Information, Information

More information

CIS519: Applied Machine Learning Fall Homework 5. Due: December 10 th, 2018, 11:59 PM

CIS519: Applied Machine Learning Fall Homework 5. Due: December 10 th, 2018, 11:59 PM CIS59: Applied Machine Learning Fall 208 Homework 5 Handed Out: December 5 th, 208 Due: December 0 th, 208, :59 PM Feel free to talk to other members of the class in doing the homework. I am more concerned

More information

Administrative notes February 27, 2018

Administrative notes February 27, 2018 Administrative notes February 27, 2018 Welcome back! Reminder: In the News Call #2 due tomorrow Reminder: Midterm #2 is on March 13 Project proposals are all marked. You can resubmit your proposal after

More information

Classification Using Decision Trees

Classification Using Decision Trees Classification Using Decision Trees 1. Introduction Data mining term is mainly used for the specific set of six activities namely Classification, Estimation, Prediction, Affinity grouping or Association

More information

Machine Learning 3. week

Machine Learning 3. week Machine Learning 3. week Entropy Decision Trees ID3 C4.5 Classification and Regression Trees (CART) 1 What is Decision Tree As a short description, decision tree is a data classification procedure which

More information

Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation

Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation Lecture Notes for Chapter 4 Part I Introduction to Data Mining by Tan, Steinbach, Kumar Adapted by Qiang Yang (2010) Tan,Steinbach,

More information

Decision Trees. Each internal node : an attribute Branch: Outcome of the test Leaf node or terminal node: class label.

Decision Trees. Each internal node : an attribute Branch: Outcome of the test Leaf node or terminal node: class label. Decision Trees Supervised approach Used for Classification (Categorical values) or regression (continuous values). The learning of decision trees is from class-labeled training tuples. Flowchart like structure.

More information

Chapter 3: Decision Tree Learning

Chapter 3: Decision Tree Learning Chapter 3: Decision Tree Learning CS 536: Machine Learning Littman (Wu, TA) Administration Books? New web page: http://www.cs.rutgers.edu/~mlittman/courses/ml03/ schedule lecture notes assignment info.

More information

Decision Tree Learning Mitchell, Chapter 3. CptS 570 Machine Learning School of EECS Washington State University

Decision Tree Learning Mitchell, Chapter 3. CptS 570 Machine Learning School of EECS Washington State University Decision Tree Learning Mitchell, Chapter 3 CptS 570 Machine Learning School of EECS Washington State University Outline Decision tree representation ID3 learning algorithm Entropy and information gain

More information

Classification: Decision Trees

Classification: Decision Trees Classification: Decision Trees Outline Top-Down Decision Tree Construction Choosing the Splitting Attribute Information Gain and Gain Ratio 2 DECISION TREE An internal node is a test on an attribute. A

More information

CS 395T Computational Learning Theory. Scribe: Mike Halcrow. x 4. x 2. x 6

CS 395T Computational Learning Theory. Scribe: Mike Halcrow. x 4. x 2. x 6 CS 395T Computational Learning Theory Lecture 3: September 0, 2007 Lecturer: Adam Klivans Scribe: Mike Halcrow 3. Decision List Recap In the last class, we determined that, when learning a t-decision list,

More information

2018 CS420, Machine Learning, Lecture 5. Tree Models. Weinan Zhang Shanghai Jiao Tong University

2018 CS420, Machine Learning, Lecture 5. Tree Models. Weinan Zhang Shanghai Jiao Tong University 2018 CS420, Machine Learning, Lecture 5 Tree Models Weinan Zhang Shanghai Jiao Tong University http://wnzhang.net http://wnzhang.net/teaching/cs420/index.html ML Task: Function Approximation Problem setting

More information

Notes on induction proofs and recursive definitions

Notes on induction proofs and recursive definitions Notes on induction proofs and recursive definitions James Aspnes December 13, 2010 1 Simple induction Most of the proof techniques we ve talked about so far are only really useful for proving a property

More information

Decision Trees. CSC411/2515: Machine Learning and Data Mining, Winter 2018 Luke Zettlemoyer, Carlos Guestrin, and Andrew Moore

Decision Trees. CSC411/2515: Machine Learning and Data Mining, Winter 2018 Luke Zettlemoyer, Carlos Guestrin, and Andrew Moore Decision Trees Claude Monet, The Mulberry Tree Slides from Pedro Domingos, CSC411/2515: Machine Learning and Data Mining, Winter 2018 Luke Zettlemoyer, Carlos Guestrin, and Andrew Moore Michael Guerzhoy

More information

Decision Trees. Robot Image Credit: Viktoriya Sukhanova 123RF.com

Decision Trees. Robot Image Credit: Viktoriya Sukhanova 123RF.com Decision Trees These slides were assembled by Eric Eaton, with grateful acknowledgement of the many others who made their course materials freely available online. Feel free to reuse or adapt these slides

More information

Machine Learning & Data Mining

Machine Learning & Data Mining Group M L D Machine Learning M & Data Mining Chapter 7 Decision Trees Xin-Shun Xu @ SDU School of Computer Science and Technology, Shandong University Top 10 Algorithm in DM #1: C4.5 #2: K-Means #3: SVM

More information

Lecture 7: DecisionTrees

Lecture 7: DecisionTrees Lecture 7: DecisionTrees What are decision trees? Brief interlude on information theory Decision tree construction Overfitting avoidance Regression trees COMP-652, Lecture 7 - September 28, 2009 1 Recall:

More information

CS 151. Red Black Trees & Structural Induction. Thursday, November 1, 12

CS 151. Red Black Trees & Structural Induction. Thursday, November 1, 12 CS 151 Red Black Trees & Structural Induction 1 Announcements Majors fair tonight 4:30-6:30pm in the Root Room in Carnegie. Come and find out about the CS major, or some other major. Winter Term in CS

More information

Decision Trees Entropy, Information Gain, Gain Ratio

Decision Trees Entropy, Information Gain, Gain Ratio Changelog: 14 Oct, 30 Oct Decision Trees Entropy, Information Gain, Gain Ratio Lecture 3: Part 2 Outline Entropy Information gain Gain ratio Marina Santini Acknowledgements Slides borrowed and adapted

More information

Dan Roth 461C, 3401 Walnut

Dan Roth   461C, 3401 Walnut CIS 519/419 Applied Machine Learning www.seas.upenn.edu/~cis519 Dan Roth danroth@seas.upenn.edu http://www.cis.upenn.edu/~danroth/ 461C, 3401 Walnut Slides were created by Dan Roth (for CIS519/419 at Penn

More information

Decision Trees. Danushka Bollegala

Decision Trees. Danushka Bollegala Decision Trees Danushka Bollegala Rule-based Classifiers In rule-based learning, the idea is to learn a rule from train data in the form IF X THEN Y (or a combination of nested conditions) that explains

More information

Tutorial 2. Fall /21. CPSC 340: Machine Learning and Data Mining

Tutorial 2. Fall /21. CPSC 340: Machine Learning and Data Mining 1/21 Tutorial 2 CPSC 340: Machine Learning and Data Mining Fall 2016 Overview 2/21 1 Decision Tree Decision Stump Decision Tree 2 Training, Testing, and Validation Set 3 Naive Bayes Classifier Decision

More information