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class09-im - Three classic approaches to IR 1 Recall...

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Three “classic” approaches to IR 1 Recall: Boolean Retrieval 1 if play contains word, 0 otherwise Brutus AND Caesar but NOT Calpurnia 2
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Recall: Vector Space Retrieval 3 Probabilistic IR Chapter 11 Traditional Probabilistic IR model Traditionally: neat ideas, but they’ve never won on performance. Chapter 12 Statistical Language Models Very hot right now 4
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Why probabilities in IR? User Information Need Documents Document Representation Query Representation How to match? In traditional IR systems, matching between each document and query is attempted in a semantically imprecise space of index terms. Probabilities provide a principled foundation for uncertain reasoning. Can we use probabilities to quantify our uncertainties? Uncertain guess of whether document has relevant content Understanding of user need is uncertain 5 But first ... Probability review Independent events Let a, b be two events, with probability P ( a ) and P ( b ). The events a and b are independent if and only if: P ( a ! b ) = P ( a ) P ( b ) In general, a 1 , a 2 , ... , a n are independent if and only if: P ( a 1 ! a 2 ! ... ! a n ) = P ( a 1 ) P ( a 2 )... P ( a n ) 6
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Probability review Let a, b be two events, with probability P ( a ) and P ( b ). Conditional probability P ( a | b ) is the probability of a given b, also called the conditional probability of a given b . Conditional independence The events a 1 , ..., a n are conditionally independent if and only if: P ( a i | a j ) = P(a i ) for all i and j. 7 Example Independent a and b are the results of throwing two dice P ( a =5 | b =3) = P ( a =5) = 1 /6 Not independent a and b are the results of throwing two dice t is the sum of the two dice t = a + b P ( t =8 | a =2) = 1 /6 P ( t =8 | a =1) = 0 8
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Example P ( a ) = x + y P ( b ) = w + x P(a | b) = x / ( w + x ) P ( a | b) P ( b ) = P ( a ! b ) = P ( b | a ) P ( a ) a b w z y x a b where a is the event not a 9 Bayes theorem Notation Let a, b be two events. P ( a | b ) is the probability of a given b Bayes Theorem P ( a | b ) = Derivation P ( a | b) P ( b ) = P ( a ! b ) = P ( b | a ) P ( a ) P ( b | a ) P ( a ) P ( b ) 10
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Bayes theorem Terminology used with Bayes Theorem P ( a | b ) = P ( a ) is called the prior probability of a P ( a | b ) is called the posterior probability of a given b P ( b | a ) P ( a ) P ( b ) 11 Example of Bayes theorem Example a Weight over 200 lb. b Height over 6 ft. Over 200 lb Over 6 ft w z y x P ( a | b ) = x / ( w + x ) = x / P ( b ) P ( b | a ) = x / ( x + y ) = x / P ( a ) x is P ( a ! b ) 12
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IR based on Language Model (LM) query d1 d2 dn Information need document collection generation A common search heuristic is to use words that you expect to find in matching documents as your query The LM approach directly exploits that idea!
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