1. Artificial Intelligence 6. Machine Learning, Version Space Method
Japan Advanced Institute of Science and Technology (JAIST)
Yoshimasa Tsuruoka

2. Outline Introduction to machine learning Version space method
What is machine learning?
Applications of machine learning
Version space method
Representing hypotheses, version space
Find-S algorithm
Candidate-Elimination algorithm

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

4. Natural language processing
GENIA tagger
Tokenization
Part-of-speech tagging
Shallow parsing
Named entity recognition

5. Applications of machine learning
Image/speech recognition
Part-of-speech tagging, syntactic parsing, word sense disambiguation
Detection of spam s
Intrusion detection
Credit card fraud detection
Automatic driving
AI players in computer games
etc.

6. 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”

7. Application of Unsupervised learning
Search engine + clustering

8. 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

9. 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.

10. Why machine learning? Why not write rules manually? Too many rules
Detecting spam s
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

11. Version space method Chapter 2 of Mitchell, T
Version space method Chapter 2 of Mitchell, T., Machine Learning (1997)
Concept Learning
Training examples
Representing hypotheses
Find-S algorithm
Version space
Candidate-Elimination algorithm

12. Learning a concept with examples
Training examples
The concept we want to learn
Days on which my friend Aldo enjoys his favorite water sports
attributes
Ex.
Sky
AirTemp
Humidity
Wind
Water
Forecast
EnjoySport 1
Sunny
Warm
Normal
Strong
Same
Yes 2
High 3
Rainy
Cold
Change No 4
Cool

13. Hypotheses Representing hypotheses General and Specific
h1 = <Sunny, ?, ?, Strong, ?, ?>
Weather = Sunny, Wind = Strong
(the other attributes can take any values)
h2 = <Sunny, ?, ?, ?, ?, ?>
Weather = Sunny
General and Specific
h1 is more specific than h2
(h2 is more general than h1)

14. Find-S Algorithm Initialize h to the most specific hypothesis in H
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
Output hypothesis h

15. 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, ?, ?>

16. 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

17. Version Space Definition Hypothesis space H Training examples D
The subset of hypotheses from H consistent with the training examples in D

18. LIST-THEN-ELIMINATE algorithm
VersionSpace ← initialized with a list containing every hypothesis in H
For each training example, <x, c(x)>
Remove from VersionSpace any hypothesis h for which h(x) ≠ c(x)
Output the list of hypothesis in VersionSpace

19. 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.

20. 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 …

21. Example
1st training example
<Sunny, Warm, Normal, Strong, Warm, Same>, yes S0: { <0, 0, 0, 0, 0, 0> } S1: { <Sunny, Warm, Normal, Strong, Warm, Same> } G0, G1: { <?, ?, ?, ?, ?, ?> }

22. Example
2nd training example
<Sunny, Warm, High, Strong, Warm, Same>, yes S1: { <Sunny, Warm, Normal, Strong, Warm, Same> } S2: { <Sunny, Warm, ?, Strong, Warm, Same> } G0, G1 , G2 : { <?, ?, ?, ?, ?, ?> }

23. Example 3rd training example
<Rainy, Cold, High, Strong, Warm, Change>, no S2,S3 :{ <Sunny, Warm, ?, Strong, Warm, Same> } G3: { <Sunny, ?, ?, ?, ?, ?> <?, Warm, ?, ?, ?, ?> <?, ?, ?, ?, ?, Same> } G2 : { <?, ?, ?, ?, ?, ?> }

24. Example 4th training 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> }

25. The final version space
S4 :{ <Sunny, Warm, ?, Strong, ?, ?> } <Sunny, ?, ?, Strong, ?, ?> <Sunny, Warm, ?, ?, ?, ?> <?, Warm, ?, Strong, ?, ?> G4: { <Sunny, ?, ?, ?, ?, ?> <?, Warm, ?, ?, ?, ?> }