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《Artificial Intelligence:A Modern Approach》教学资源(讲义,英文版)chapter20a

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learning tistical a St 1–3 Sections 20, Chapter 1 1–3 Sections 20, Chapter

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Example candies: of bags of kinds five re a there ose Supp candies cherry 100% : 1 h re a 10% candies lime 25% + candies cherry 75% : 2 h re a 20% candies lime 50% + candies cherry 50% : 3 h re a 40% candies lime 75% + candies cherry 25% : 4 h re a 20% candies lime 100% : 5 h re a 10% bag: some from wn dra candies observe e w Then e? b candy next the will flavour What it? is bag of kind What 4 1–3 Sections 20, Chapter

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otheses yp h of y probabilit osterior P 0 0.2 0.4 0.6 0.8 1 10 8 6 4 2 0 Posterior probability of hypothesis d Number of samples in ) d | 1 h( P ) d | 2 h( P ) d | 3 h( P ) d | 4 h( P ) d | 5 h( P 5 1–3 Sections 20, Chapter

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y probabilit Prediction 0.4 0.5 0.6 0.7 0.8 0.9 1 10 8 6 4 2 0 P(next candy is lime | d ) d Number of samples in 6 1–3 Sections 20, Chapter

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ximation appro MAP intractable often is space othesis hyp the over Summing attributes) 6 of functions olean Bo 18,446,744,073,709,551,616 (e.g., ) d|i h( P maximizing MAP h ose cho rning: lea (MAP) ri osterio p a Maximum h| d( P maximize I.e., r o )i h( P)i )i h( P log +)i h| d( P log ) of (negative as ed view eb can terms Log othesis hyp de enco to bits + othesis hyp given data de enco to bits rning lea (MDL) length description minimum of idea basic the is This otherwise 0 consistent, if 1 is )i h| d( P otheses, hyp deterministic r oF science) (cf. othesis hyp consistent simplest = MAP ⇒ 7 1–3 Sections 20, Chapter

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ximation appro ML irrelevant ecomes b r rio p sets, data rge la r oF )i h| d( P maximizing ML h ose cho rning: lea (ML) do eliho lik Maximum r rio p rm unifo r fo MAP to identical data; the to fit est b the get simply I.e., y) complexit same the of re a otheses hyp all if reasonable is (which d metho rning lea statistical esian) y (non-Ba rd” “standa the is ML 8 1–3 Sections 20, Chapter

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parameters Multiple ) F=cherry ( P r: flavo on robabilistically p ends dep er wrapp Red/green Flavor Wrapper ) F | W=red ( P F cherry 2 θ lime 1 θ θ er: wrapp green in candy cherry e.g., r, fo do eliho Lik )2 ,θ 1 ,θ θ h| en e gr = W, cherry = F( P )2 ,θ 1 ,θ θ h, cherry = F| en e gr = W( P)2 ,θ 1 ,θ θ h| cherry = F( P = )1 θ − (1 · θ = etc.: candies, cherry ed red-wrapp c r candies, N θ =)2 ,θ 1 ,θ θ h| d( P c ) θ − (1 ` θ· cr1 )1 θ − (1 c g θ· r` 2 )2 θ − (1 g` )] θ − (1 log ` +θ log c[ = L )] 1 θ − (1 log c g +1 θ log c r[ + )] 2 θ − (1 log ` g +2 θ log ` r[ + 10 1–3 Sections 20, Chapter

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