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

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 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 Search engine + clustering http://clusty.com

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? Too many rules 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 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

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

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)

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

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

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

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

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

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

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> }

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