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concept-learning-Mitchell-ch2 - Concept Learning CS 464...

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1 CS 464: Introduction to Machine Learning Concept Learning Slides adapted from Chapter 2, Machine Learning by Tom M. Mitchell http://www-2.cs.cmu.edu/afs/cs.cmu.edu/user/mitchell/ftp/mlbook.html 2 Concept Learning circle6 Acquiring the definition of a general category from given sample positive and negative training examples of the category. circle6 An example: learning “bird” concept from the given examples of birds (positive examples) and non-birds (negative examples). circle6 Inferring a boolean-valued function from training examples of its input and output. 3 Classification (Categorization) Given A fixed set of categories: C= { c 1 , c 2 ,… c k } A description of an instance x = (x 1 , x 2 ,…x n ) with n features, x X , where X is the instance space . Determine: The category of x : c ( x ) C, where c ( x ) is a categorization function whose domain is X and whose range is C . If c ( x ) is a binary function C ={1,0} ({true,false}, {positive, negative}) then it is called a concept . 4 Learning for Categorization A training example is an instance x X, paired with its correct category c ( x ): < x , c ( x )> for an unknown categorization function, c . Given a set of training examples, D . Find a hypothesized categorization function, h ( x ), such that: ) ( ) ( : ) ( , x c x h D x c x = > < Consistency 5 A Concept Learning Task – Enjoy Sport Training Examples Example 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 glyph1197O 4 Sunny Warm High Strong Warm Change YES • A set of example days, and each is described by six attributes. • The task is to learn to predict the value of EnjoySport for arbitrary day, based on the values of its attribute values. ATTRIBUTES COglyph1197CEPT 6 Hypothesis Space Restrict learned functions to a given hypothesis space , H , of functions h ( x ) that can be considered as definitions of c ( x ). For learning concepts on instances described by n discrete- valued features, consider the space of conjunctive hypotheses represented by a vector of n constraints < c 1 , c 2 , … c n > where each c i is either: ?, a wild card indicating no constraint on that feature A specific value from the domain of that feature Ø indicating no value is acceptable Sample conjunctive hypotheses are <Sunny, ?, ?, Strong, ?, ?> <?, ?, ?, ?, ?, ?> ( most general hypothesis ) < Ø, Ø, Ø, Ø, Ø, Ø> ( most specific hypothesis )
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7 EnjoySport Concept Learning Task Given circle6 Instances X : set of all possible days, each described by the attributes circle6 Sky – (values: Sunny, Cloudy, Rainy) circle6 AirTemp – (values: Warm, Cold) circle6 Humidity – (values: Normal, High) circle6 Wind – (values: Strong, Weak) circle6 Water – (values: Warm, Cold) circle6 Forecast – (values: Same, Change) circle6 Target Concept (Function) c : EnjoySport : X barb2right {0,1} circle6 Hypotheses H : Each hypothesis is described by a conjunction of constraints on the attributes. Example hypothesis: <Sunny, ?, ?, ?, ?, ?> circle6 Training Examples D
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