Artificial Intelligence6. Machine Learning, Version Space

Method

Japan Advanced Institute of Science and Technology (JAIST)Yoshimasa Tsuruoka

Outline• Introduction to machine learning

– What is machine learning?– Applications of machine learning

• Version space method– Representing hypotheses, version space– Find-S algorithm– Candidate-Elimination algorithm

• http://www.jaist.ac.jp/~tsuruoka/lectures/

Recognizing handwritten digits

Hastie, Tibshirani and Friedman (2008). The Elements of Statistical Learning (2nd edition). Springer-Verlag.

Natural language processing

• GENIA tagger– Tokenization– Part-of-speech tagging– Shallow parsing– Named entity recognition

http://www-tsujii.is.s.u-tokyo.ac.jp/GENIA/tagger/

Applications of machine learning

• Image/speech recognition• Part-of-speech tagging, syntactic parsing, word

sense disambiguation• Detection of spam emails• Intrusion detection• Credit card fraud detection• Automatic driving• AI players in computer games• etc.

Types of machine learning

• Supervised learning– “correct” output is given for each instance

• Unsupervised learning– No output is given– Analyses relations between instances

• Reinforcement learning– Supervision is given via “rewards”

Application of Unsupervised learning

http://clusty.com

• Search engine + clustering

Reinforcement learning

• Autonomous helicopters and robots

Inverted autonomous helicopter flight via reinforcement learning, Andrew Y. Ng, Adam Coates, Mark Diel, Varun Ganapathi, Jamie Schulte, Ben Tse, Eric Berger and Eric Liang. In International Symposium on Experimental Robotics, 2004

Quadruped Robot Obstacle Negotiation via Reinforcement Learning, Honglak Lee, Yirong Shen, Chih-Han Yu, Gurjeet Singh, and Andrew Y. Ng. In Proceedings of the IEEE International Conference on Robotics and Automation , 2006

What is machine learning?

• What does a machine learn?

• What “machine learning” can do:– Classification, regression, structured prediction– Clustering

• Machine learning involves– Numerical optimization, probabilistic modeling,

graphs, search, logic, etc.

Why machine learning?

• Why not write rules manually?– Detecting spam emails

• If the mail contains the word “Nigeria” then it is a spam• If the mail comes from IP X.X.X.X then it is a spam• If the mail contains a large image then it is a spam• …

• Too many rules• Hard to keep consistency• Each rule may not be completely correct

Version space methodChapter 2 of Mitchell, T., Machine Learning (1997)

• Concept Learning• Training examples• Representing hypotheses• Find-S algorithm• Version space• Candidate-Elimination algorithm

Learning a concept with examples

• Training examples

• The concept we want to learn– Days on which my friend Aldo enjoys his favorite

water sports

Ex. Sky AirTemp Humidity Wind Water Forecast EnjoySport

1 Sunny Warm Normal Strong Warm Same Yes

2 Sunny Warm High Strong Warm Same Yes

3 Rainy Cold High Strong Warm Change No

4 Sunny Warm High Strong Cool Change Yes

attributes

Hypotheses

• Representing hypothesesh1 = <Sunny, ?, ?, Strong, ?, ?>

Weather = Sunny, Wind = Strong(the other attributes can take any values)

h2 = <Sunny, ?, ?, ?, ?, ?>Weather = Sunny

• General and Specifich1 is more specific than h2 (h2 is more general than h1)

Find-S Algorithm

1. Initialize h to the most specific hypothesis in H2. For each positive training instance x

– For each attribute constraint ai in h• If the constraint ai is satisfied by x

• Then do nothing• Else replace ai in h by the next more general constraint

that is satisfied by x

3. Output hypothesis h

Example

h0 = <0, 0, 0, 0, 0, 0>

x1 = <Sunny, Warm, Normal, Strong, Warm, Same>, yes

h1 = <Sunny, Warm, Normal, Strong, Warm, Same>

x2 = <Sunny, Warm, High, Strong, Warm, Same>, yes

h2 = <Sunny, Warm, ?, Strong, Warm, Same>

x3 = <Rainy, Cold, High, Strong, Warm, Change>, no

h3 = <Sunny, Warm, ?, Strong, Warm, Same>

x4 = <Sunny, Warm, High, Strong, Cool, Change>, yes

h4 = <Sunny, Warm, ?, Strong, ?, ?>

Problems with the Find-S algorithm

• It is not clear whether the output hypothsis is the “correct” hypothesis– There can be other hypotheses that are consistent

with the training examples.– Why prefer the most specific hypothesis?

• Cannot detect when the training data is inconsistent

Version Space

• Definition– Hypothesis space H– Training examples D– Version space:

– The subset of hypotheses from H consistent with the training examples in D

DhConsistentHhVS DH ,,

LIST-THEN-ELIMINATE algorithm

1. VersionSpace ← initialized with a list containing every hypothesis in H

2. For each training example, <x, c(x)>– Remove from VersionSpace any hypothesis h for

which h(x) ≠ c(x)

3. Output the list of hypothesis in VersionSpace

Version Space• Specific boundary and General boundary

S: { <Sunny, Warm, ?, Strong, ?, ?> }

<Sunny, ?, ?, Strong, ?, ?> <Sunny, Warm, ?, ?, ?, ?> <?, Warm, ?, Strong, ?, ?>

G: { <Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?> }

• The version space can be represented with S and G. You don’t have to list all the hypotheses.

Candidate-Elimination algorithm• Initialization

– G: the set of maximally general hypotheses in H– S: the set of maximally specific hypotheses in H

• For each training example d, do– If d is a positive example

• Remove from G any hypothesis inconsistent with d• For each hypothesis s in S that is not consistent with d

– Remove s from S– Add to S all minimal generalization h of s such that

» h is consistent with d, and some member of G is more general than h• Remove from S any hypothesis that is more general than another

hypothesis in S– If d is a negative example

• …

Example

<Sunny, Warm, Normal, Strong, Warm, Same>, yes

S0: { <0, 0, 0, 0, 0, 0> }

S1: { <Sunny, Warm, Normal, Strong, Warm, Same> }

G0, G1: { <?, ?, ?, ?, ?, ?> }

1st training example

Example<Sunny, Warm, High, Strong, Warm, Same>, yes

S1: { <Sunny, Warm, Normal, Strong, Warm, Same> }

S2: { <Sunny, Warm, ?, Strong, Warm, Same> }

G0, G1 , G2 : { <?, ?, ?, ?, ?, ?> }

2nd training example

Example <Rainy, Cold, High, Strong, Warm, Change>, no

S2,S3 :{ <Sunny, Warm, ?, Strong, Warm, Same> }

G3: { <Sunny, ?, ?, ?, ?, ?> <?, Warm, ?, ?, ?, ?> <?, ?, ?, ?, ?, Same> }

G2 : { <?, ?, ?, ?, ?, ?> }

3rd training example

Example <Sunny, Warm, High, Strong, Cool, Change>, yes

S3 :{ <Sunny, Warm, ?, Strong, Warm, Same> }

S4 :{ <Sunny, Warm, ?, Strong, ?, ?> }

G4: { <Sunny, ?, ?, ?, ?, ?> <?, Warm, ?, ?, ?, ?> }

G3: { <Sunny, ?, ?, ?, ?, ?> <?, Warm, ?, ?, ?, ?> <?, ?, ?, ?, ?, Same> }

4th training example

The final version space

S4 :{ <Sunny, Warm, ?, Strong, ?, ?> }

<Sunny, ?, ?, Strong, ?, ?> <Sunny, Warm, ?, ?, ?, ?> <?, Warm, ?, Strong, ?, ?>

G4: { <Sunny, ?, ?, ?, ?, ?> <?, Warm, ?, ?, ?, ?> }