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Ahmet Selman Bozkır
[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
Let’s define three events: 1. A as “draw 47  resistor 2. B as “draw” a resistor with 5% 3. C as “draw” a “100  resistor P(A) = P(47  ) = 44/100 P(B) = P(5%) = 62/100 P(C) = P(100  ) = 32 /100 The joint probabilities are: P(A  B) = P(47   5%) = 28/100 P(A  C) = P(47   100  ) = 0 P(B  C) = P(5%  100  ) = 24/100 I f we use them the cond. prob. : Tolerance Resistance (  )‏ 5% 10% Total 22-  10 14 24 47-  28 26 44 100-  24 8 32 Total: 62 38 100
[object Object],A  B n A B1 B3 B2 Bn
[object Object]
[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],Prior P osterior
Let x be a document in the collection. Let R represent relevance of a document w.r.t. given (fixed) query and let NR represent non-relevance. p( x|R ), p( x|NR ) - probability that if a relevant (non-relevant) document is retrieved, it is x . Need to find p( R|x) - probability that a document x is relevant. p( R) ,p( NR ) - prior probability of retrieving a (non) relevant document R={0,1} vs. NR/R
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
Constant for a given query Needs estimation ,[object Object],[object Object]
[object Object],Then... This can be changed (e.g., in relevance feedback)‏ ,[object Object],[object Object]
All matching terms Non-matching query terms All matching terms All query terms
Constant for each query Only quantity to be estimated for rankings ,[object Object]
[object Object],[object Object],[object Object],For now, assume no zero terms.
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],κ is prior weight
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
a b c ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],For more information see: R.G. Cowell, A.P. Dawid, S.L. Lauritzen, and D.J. Spiegelhalter. 1999. Probabilistic Networks and Expert Systems . Springer Verlag. J. Pearl. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan-Kaufman. p(c|ab) for all values for a,b,c p(a)‏ p(b)‏ Conditional dependence
Gloom (g)‏ Finals (f)‏ No Sleep (n)‏ Triple Latte (t)‏ Project Due (d)‏
[object Object],[object Object],[object Object],[object Object],[object Object],Gloom (g)‏ Finals (f)‏ Project Due (d)‏ No Sleep (n)‏ Triple Latte (t)‏
[object Object],[object Object],[object Object],[object Object],[object Object]
I - goal node Document Network Query Network Large, but Compute once for each document collection Small, compute once for every query d1 d n d2 t1 t2 t n r1 r2 r3 r k d i - documents t i - document representations r i - “concepts” I q2 q1 c m c2 c1 c i - query concepts q i - high-level concepts
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
d 1 d 2 r 1 r 3 c 1 c 3 q 1 q 2 i r 2 c 2 Document Network Query Network Documents Terms/Concepts Concepts Query operators ( AND/OR/NOT )‏ Information need
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Hamlet Macbeth reason double reason two OR NOT User query trouble trouble Document Network Query Network
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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probabilistic ranking

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  • 4. Let’s define three events: 1. A as “draw 47  resistor 2. B as “draw” a resistor with 5% 3. C as “draw” a “100  resistor P(A) = P(47  ) = 44/100 P(B) = P(5%) = 62/100 P(C) = P(100  ) = 32 /100 The joint probabilities are: P(A  B) = P(47   5%) = 28/100 P(A  C) = P(47   100  ) = 0 P(B  C) = P(5%  100  ) = 24/100 I f we use them the cond. prob. : Tolerance Resistance (  )‏ 5% 10% Total 22-  10 14 24 47-  28 26 44 100-  24 8 32 Total: 62 38 100
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  • 9. 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
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  • 14. Let x be a document in the collection. Let R represent relevance of a document w.r.t. given (fixed) query and let NR represent non-relevance. p( x|R ), p( x|NR ) - probability that if a relevant (non-relevant) document is retrieved, it is x . Need to find p( R|x) - probability that a document x is relevant. p( R) ,p( NR ) - prior probability of retrieving a (non) relevant document R={0,1} vs. NR/R
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  • 24. All matching terms Non-matching query terms All matching terms All query terms
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  • 34. Gloom (g)‏ Finals (f)‏ No Sleep (n)‏ Triple Latte (t)‏ Project Due (d)‏
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  • 37. I - goal node Document Network Query Network Large, but Compute once for each document collection Small, compute once for every query d1 d n d2 t1 t2 t n r1 r2 r3 r k d i - documents t i - document representations r i - “concepts” I q2 q1 c m c2 c1 c i - query concepts q i - high-level concepts
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  • 39. d 1 d 2 r 1 r 3 c 1 c 3 q 1 q 2 i r 2 c 2 Document Network Query Network Documents Terms/Concepts Concepts Query operators ( AND/OR/NOT )‏ Information need
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  • 41. Hamlet Macbeth reason double reason two OR NOT User query trouble trouble Document Network Query Network
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  • 44. All sources served by Google!