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L02n - Computer Science 165B Concept Learning Training...

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Computer Science 165B Concept Learning
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2 CS165B: Concept Learning Yes Change Cool Strong High Warm Sunny No Change Warm Strong High Cold Rainy Yes Yes EnjoySport Same Same Forecast Warm Strong High Warm Sunny Warm Strong Normal Warm Sunny Water Wind Humid AirTemp Sky Training Examples for EnjoySport c( )=1 c ( )=1 c ( )=1 c ( )=0 ± Concept learning : approximating a Boolean function from training examples
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3 CS165B: Concept Learning Representing Hypotheses ± Conjunction of constraints of the following form: A specific value : Water = Warm Don’t care : Water = ? No value allowed : Water = ∅ ± Hypotheses represented as vectors of form: Sky AirTemp Humid Wind Water Forecast Sunny ? ? Strong ? Same ± h ( x ) = 1 if h is true on x = 0 otherwise ± Other representations are possible
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4 CS165B: Concept Learning Prototypical Concept Learning Task ± Given: Instances X : Possible days, each described by the attributes Sky , AirTemp , Humidity , Wind , Water , Forecast Target function c or EnjoySport : X → {0, 1} Hypotheses H : Conjunctions of literals. E.g. ?, Cold, High, ?, ?, ? Training examples D : Positive and negative examples of the target function x 1 , c ( x 1 ) , . . . x m , c ( x m ) ± Determine: A hypothesis h in H such that h ( x ) = c ( x ) for all x in D
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5 CS165B: Concept Learning Inductive Learning Hypothesis Any hypothesis found to approximate the target function well over a sufficiently large set of training examples will also approximate the target function well over other unobserved examples
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6 CS165B: Concept Learning Ordering on Hypotheses Instances X Hypotheses H specific general ± h is more general than h , h g h if for each instance x , h ′( x ) = 1 → h ( x ) = 1 x 1 = Sunny Warm High Strong Cool Same x 2 = Sunny Warm High Light Warm Same h 1 = Sunny ? ? Strong ? ? h 2 = Sunny ? ? ? ? ? h 3 = Sunny ? ? ? Cool ? x 1 x 2 h 3 h 1 h 2
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7 CS165B: Concept Learning Find-S Algorithm 1. Initialize h to the most specific hypothesis in H 2. for each positive training instance x for each attribute constraint a i in h if the constraint a i in h is satisfied by x do nothing else replace a i in h by the next more general constraint that is satisfied by x 3. Output hypothesis h
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8 CS165B: Concept Learning x 1 = Sunny Warm Normal Strong Warm Same + x 2 = Sunny Warm High Strong Warm Same + x 3 = Rainy Cold High Strong Warm Change x 4 = Sunny Warm High Strong Cool Change + Example of Find-S Instances X Hypotheses H specific general h 0 = h 1 =
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