Click Models for Web Search Lecture 1 Aleksandr Chuklin, Ilya Markov Maarten de Rijke a.chuklin@uva.nl i.markov@uva.nl derijke@uva.nl University of Amsterdam Google Research Europe AC IM MdR Click Models for Web Search 1
Aleksandr Chuklin Currently at Google Zürich Previously at Yandex Moscow Research interests: user experience evaluation and modelling Participated at RuSSIR 2009 in Petrozavodsk and RuSSIR 2011 in Saint Petersburg AC IM MdR Click Models for Web Search 2
Ilya Markov Postdoctoral researcher at the University of Amsterdam PhD at the University of Lugano Research interests: heterogeneous search environments Distributed IR, federated search, aggregated search User behavior, user-oriented evaluation Teach MSc courses on IR and Web Search AC IM MdR Click Models for Web Search 3
Long-term relations with RuSSIR RuSSIR 2007, student RuSSIR 2010, lecturer on Distributed IR (with Fabio Crestani) RuSSIR 2011, member of organizing committee RuSSIR 2015, chair of program committee RuSSIR 2016, lecturer AC IM MdR Click Models for Web Search 4
Course on Information Retrieval in St. Petersburg http://compsciclub.ru/courses/ information-retrieval/2016-autumn/ AC IM MdR Click Models for Web Search 5
Maarten de Rijke Currently at the University of Amsterdam Ongoing collaborations with Bloomberg Labs, Google, Microsoft Research, Yandex Moscow Research interests: semantic search, online learning to rank Always looking for strong new PhD students AC IM MdR Click Models for Web Search 6
The book http://clickmodels.weebly.com/the-book.html AC IM MdR Click Models for Web Search 7
Other course materials clickmodels.weebly.com/russir-2016-course.html Demos and practical sessions: clickmodels.weebly.com/russir-2016-setup.html github.com/markovi/pyclick AC IM MdR Click Models for Web Search 8
Course content Basic Click Models Parameter Estimation Evaluation Applications Results Data and Tools Advanced Models Recent Studies Future Research AC IM MdR Click Models for Web Search 9
Lectures Basic Click Models Parameter Estimation Evaluation Lecture 1 Lecture 2 Applications Lecture 2 Results Lecture 3 Practical 1 Data and Tools Advanced Models Recent Studies Lecture 4 Practical 2 Lecture 5 Future Research AC IM MdR Click Models for Web Search 10
Course overview Basic Click Models Parameter Estimation Evaluation Applications Results Data and Tools Advanced Models Recent Studies Future Research AC IM MdR Click Models for Web Search 11
This lecture Basic Click Models Parameter Estimation Evaluation Applications Results Data and Tools Advanced Models Recent Studies Future Research AC IM MdR Click Models for Web Search 12
Lecture outline 1 Introduction 2 Basic click models 3 Click probabilities AC IM MdR Click Models for Web Search 13
Web search AC IM MdR Click Models for Web Search 14
Why clicks? AC IM MdR Click Models for Web Search 15
Why clicks? Reflect user interests Help to improve search Help to evaluate search Ongoing and future research: other user search interactions mouse movements scrolling touch gestures AC IM MdR Click Models for Web Search 16
What can we do with clicks? AC IM MdR Click Models for Web Search 17
What can we do with clicks? count click-through rate (CTR) Global CTR = Rank-based CTR = Query-document CTR = # clicks # shown docs # clicks at rank r # shown docs at rank r # u is clicked for q # u is shown for q Some notation: u URL (or document), q query AC IM MdR Click Models for Web Search 18
Why click models? AC IM MdR Click Models for Web Search 19
Why click models? Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. Wikipedia, Scientific modelling AC IM MdR Click Models for Web Search 20
Why click models? Click models make user clicks in web search easier to understand, define, quantify, visualize, or simulate using (mostly) probabilistic graphical models. AC IM MdR Click Models for Web Search 21
Click log Yandex Relevance Prediction Challenge http://imat-relpred.yandex.ru/en AC IM MdR Click Models for Web Search 22
Why do we need click models? Understand users Simulate users Approximate document relevance Evaluate search AC IM MdR Click Models for Web Search 23
Lecture outline 1 Introduction 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model 3 Click probabilities AC IM MdR Click Models for Web Search 24
Lecture outline 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model AC IM MdR Click Models for Web Search 25
Random click model P click P click P click P click P click AC IM MdR Click Models for Web Search 26
Random click model Terminology C u binary random variable denoting a click on document u Document u is clicked: C u = 1 Document u is not clicked: C u = 0 P(C u = 1) probability of click on document u P(C u = 0) = 1 P(C u = 1) Random click model (RCM) Any document can be clicked with the same (fixed) probability P(C u = 1) = const = ρ AC IM MdR Click Models for Web Search 27
Random click model P(C u1 = 1) = ρ P(C u2 = 1) = ρ P(C u3 = 1) = ρ P(C u4 = 1) = ρ ρ = # clicks = Global CTR # shown docs P(C u5 = 1) = ρ AC IM MdR Click Models for Web Search 28
Lecture outline 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model AC IM MdR Click Models for Web Search 29
Rank-based CTR model P(C u1 = 1) = ρ 1 P(C u2 = 1) = ρ 2 P(C u3 = 1) = ρ 3 P(C u4 = 1) = ρ 4 P(C ur = 1) = ρ r = P(C u5 = 1) = ρ 5 # clicks at rank r # shown docs at rank r AC IM MdR Click Models for Web Search 30
Query-document CTR model P(C u1 = 1) = ρ u1 q P(C u2 = 1) = ρ u2 q P(C u3 = 1) = ρ u3 q P(C u4 = 1) = ρ u4 q P(C u = 1) = ρ uq = # u is clicked for q # u is shown for q P(C u5 = 1) = ρ u5 q AC IM MdR Click Models for Web Search 31
CTR models: summary Random click model (global CTR): Rank-based CTR: P(C u = 1) = ρ P(C ur = 1) = ρ r Query-document CTR: P(C u = 1) = ρ uq AC IM MdR Click Models for Web Search 32
CTR models: demo Demo AC IM MdR Click Models for Web Search 33
Lecture outline 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model AC IM MdR Click Models for Web Search 34
Position-based model P read (1), P click (u 1 q) P read (2), P click (u 2 q) P read (3), P click (u 3 q) P read (4), P click (u 4 q) P read (5), P click (u 5 q) AC IM MdR Click Models for Web Search 35
Position-based model: examination Terminology Examination = reading a snippet E r binary random variable denoting examination of a snippet at rank r Snippet at rank r is examined: E r = 1 Snippet at rank r is not examined: E r = 0 P(E r = 1) probability of examination of rank r P(E r = 0) = 1 P(E r = 1) Position-based model (PBM) Examination depends on rank P(E r = 1) = γ r AC IM MdR Click Models for Web Search 36
Position-based model γ 1, P click (u 1 q) γ 2, P click (u 2 q) γ 3, P click (u 3 q) γ 4, P click (u 4 q) γ 5, P click (u 5 q) AC IM MdR Click Models for Web Search 37
Position-based model: attractiveness Terminology Attractiveness = a user wants to click on a document after examining (reading) its snippet A u binary random variable showing whether document u is attractive to a user, given query q Document u is attractive: A u = 1 Document u is not attractive: A u = 0 P(A u = 1) probability of attractiveness of document u P(A u = 0) = 1 P(A u = 1) Position-based model (PBM) Attractiveness depends on a query-document pair P(A uq = 1) = α uq AC IM MdR Click Models for Web Search 38
Position-based model γ 1, α u1 q γ 2, α u2 q γ 3, α u3 q γ 4, α u4 q γ 5, α u5 q AC IM MdR Click Models for Web Search 39
Position-based model: summary P(E ru = 1) = γ ru P(A u = 1) = α uq P(C u = 1) = P(E ru = 1) P(A u = 1) AC IM MdR Click Models for Web Search 40
Position-based model: probabilistic graphical model ru uq E u A u C u document u AC IM MdR Click Models for Web Search 41
Position-based model: exercises P(E ru = 1) = γ ru P(A u = 1) = α uq P(C u = 1) = P(E ru = 1) P(A u = 1) E ru = 0 C u = 0 A u = 0 C u = 0 E ru = 1 (C u = 1 A u = 1) A u = 1 (C u = 1 E ru = 1) AC IM MdR Click Models for Web Search 42
Position-based model: demo Demo AC IM MdR Click Models for Web Search 43
Lecture outline 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model AC IM MdR Click Models for Web Search 44
Position-based model P(E ru = 1) = γ ru P(A u = 1) = α uq P(C u = 1) = P(E ru = 1) P(A u = 1) AC IM MdR Click Models for Web Search 45
Cascade model 1 Start from the first document 2 Examine documents one by one 3 If click, then stop 4 Otherwise, continue AC IM MdR Click Models for Web Search 46
Cascade model E r = 1 and A ur = 1 C r = 1 P(A ur = 1) = α ur q P(E 1 = 1) = 1 }{{} start from first P(E r = 1 E r 1 = 0) = 0 }{{} examine one by one P(E r = 1 C r 1 = 1) = 0 }{{} if click, then stop P(E r = 1 E r 1 = 1, C r 1 = 0) = 1 }{{} otherwise, continue AC IM MdR Click Models for Web Search 47
Cascade model: probabilistic graphical model ur 1q urq document u r 1 document u r Ar 1 Ar Cr 1 Cr... Er 1 Er... AC IM MdR Click Models for Web Search 48
Click models so far CTR models + count clicks (simple and fast) do not distinguish examination and attractiveness Position-based model (PBM) User browsing model + examination and attractiveness examination of a document at rank r does not depend on examinations and clicks above r Cascade model (CM) Dynamic Bayesian network + cascade dependency of examination at r on examinations and clicks above r only one click is allowed AC IM MdR Click Models for Web Search 49
Lecture outline 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model AC IM MdR Click Models for Web Search 50
Dynamic Bayesian network model Cascade model Dynamic Bayesian network AC IM MdR Click Models for Web Search 51
Dynamic Bayesian network model 1 Start from the first document 2 Examine documents one by one 3 If click, read actual document and can be satisfied 4 If satisfied, stop 5 Otherwise, continue with fixed probability AC IM MdR Click Models for Web Search 52
Dynamic Bayesian network model: satisfaction Terminology Satisfaction = a user reads the clicked document and satisfies his/her information need S u binary random variable showing whether document u is satisfactory for query q P(S u = 1) probability of satisfactoriness of document u, P(S u = 0) = 1 P(S u = 1) Dynamic Bayesian network model (DBN) If a user is satisfied, he/she stops Otherwise, continues with fixed probability P(E r = 1 S r 1 = 1) = 0 }{{} if satisfied, stop P(E r = 1 E r 1 = 1, S r 1 = 0) = γ }{{} otherwise, continue AC IM MdR Click Models for Web Search 53
Dynamic Bayesian network model: summary E r = 1 and A ur = 1 C r = 1 P(A ur = 1) = α ur q P(E 1 = 1) = 1 P(E r = 1 E r 1 = 0) = 0 P(S r = 1 C r = 1) = σ }{{} ur q if click, can be satisfied P(E r = 1 S r 1 = 1) = 0 }{{} if satisfied, stop P(E r = 1 E r 1 = 1, S r 1 = 0) = γ }{{} otherwise, continue AC IM MdR Click Models for Web Search 54
Dynamic Bayesian network: probabilistic graphical model ur 1q ur 1q urq urq A r 1 S r 1 A r S r C r 1 C r... E r 1 document u r 1 E r document u r... AC IM MdR Click Models for Web Search 55
Dynamic Bayesian network model: demo Demo AC IM MdR Click Models for Web Search 56
Lecture outline 2 Basic click models Random click model CTR models Position-based model Cascade model Dynamic Bayesian network model User browsing model AC IM MdR Click Models for Web Search 57
User browsing model Position-based model User browsing model AC IM MdR Click Models for Web Search 58
Position-based model γ 1, α u1 q γ 2, α u2 q γ 3, α u3 q γ 4, α u4 q γ 5, α u5 q P(E r = 1 C r = 1, C r +1 = 0,..., C r 1 = 0) = γ rr AC IM MdR Click Models for Web Search 59
User browsing model γ 10, α u1 q γ 21, α u2 q γ 31, α u3 q γ 41, α u4 q γ 54, α u5 q P(E r = 1 C r = 1, C r +1 = 0,..., C r 1 = 0) = γ rr AC IM MdR Click Models for Web Search 60
User browsing model: summary P(C u = 1) = P(E ru = 1) P(A u = 1) P(A u = 1) = α uq P(E r = 1 C r = 1, C r +1 = 0,..., C r 1 = 0) = γ rr AC IM MdR Click Models for Web Search 61
User browsing model: probabilistic graphical model urq document u r A r C r rr 0 E r... AC IM MdR Click Models for Web Search 62
Basic click models summary CTR models: counting clicks Position-based model (PBM): examination and attractiveness Cascade model (CM): previous examinations and clicks matter Dynamic Bayesian network model (DBN): satisfactoriness User browsing model (UBM): rank of previous click AC IM MdR Click Models for Web Search 63
Probability theory Partitioned probability: A = A 1 A 2, A 1 A 2 = P(A) = P(A 1, A 2 ) = P(A 1 ) + P(A 2 ) Bayes rule P(A B) P(B) = P(B A) P(A) B causes A: B A P(B) = P(B A) P(A) AC IM MdR Click Models for Web Search 64
Probability theory (cont d) B A, A = A 1 A 2, A 1 A 2 = P(B) = P(B A) P(A) = P(B A 1, A 2 ) P(A 1, A 2 ) = P(B A 1, A 2 ) (P(A 1 ) + P(A 2 )) = P(B A 1, A 2 ) P(A 1 ) + P(B A 1, A 2 ) P(A 2 ) = P(B A 1 ) P(A 1 ) + P(B A 2 ) P(A 2 ) P(B) = P(B A 1 ) P(A 1 ) + P(B A 2 ) P(A 2 ) AC IM MdR Click Models for Web Search 65
Lecture outline 1 Introduction 2 Basic click models 3 Click probabilities AC IM MdR Click Models for Web Search 66
Click probabilities Full probability probability that a user clicks on a document at rank r P(C r = 1) Conditional probability probability that a user clicks on a document at rank r given previous clicks P(C r = 1 C 1,..., C r 1 ) AC IM MdR Click Models for Web Search 67
Dependency between examination and clicks ru uq E u A u C u document u AC IM MdR Click Models for Web Search 68
Full click probability P(C r = 1) = + P(C r = 1 E r = 1) P(E r = 1) P(C r = 1 E r = 0) P(E r = 0) = P(A ur = 1) P(E r = 1) + 0 = α ur qɛ r AC IM MdR Click Models for Web Search 69
Cascade models: dependency between examinations ur 1q urq document ur 1 document ur Ar 1 Ar Cr 1 Cr... Er 1 Er... AC IM MdR Click Models for Web Search 70
Full click probability P(C r = 1) = P(A ur = 1) P(E r = 1) = α ur qɛ r ɛ r+1 = P(E r+1 = 1) = + P(E r = 1) P(E r+1 = 1 E r = 1) P(E r = 0) P(E r+1 = 1 E r = 0) = ɛ r P(E r+1 = 1 E r = 1) + 0 ( = ɛ r + P(E ) r+1 = 1 E r = 1, C r = 1) P(C r = 1 E r = 1) P(E r+1 = 1 E r = 1, C r = 0) P(C r = 0 E r = 1) AC IM MdR Click Models for Web Search 71
Full click probability: Dynamic Bayesian network model Dynamic Bayesian network model: satisfactoriness ur 1q ur 1q urq urq Ar 1 Sr 1 Ar Sr Cr 1 Cr... Er 1 document ur 1 Er document ur... ( P(C r+1 = 1) = α ur+1qɛ r + P(E ) r+1 = 1 E r = 1, C r = 1) P(C r = 1 E r = 1) P(E r+1 = 1 E r = 1, C r = 0) P(C r = 0 E r = 1) P(C r+1 = 1) = α ur+1qɛ r ( + (1 σ u r q)γ α ur q γ (1 α ur q) ) AC IM MdR Click Models for Web Search 72
Conditional click probability P(C r = 1 C 1,..., C r 1 ) = P(C r = 1 C <r ) = + P(C r = 1 E r = 1, C <r ) P(E r = 1 C <r ) P(C r = 1 E r = 0, C <r ) P(E r = 0 C <r ) = P(A ur = 1) P(E r = 1 C <r ) + 0 = α ur qɛ r P(E r+1 = 1 E r = 1, C r = 1) c r (s) ɛ r+1 = + P(E r+1 = 1 E r = 1, C r = 0) ɛr (1 α ur q) (1 c r (s) ) 1 α ur qɛ r c (s) r a click on rank r in query session s AC IM MdR Click Models for Web Search 73
Click probabilities summary Full probability P(C r+1 = 1) = ( α ur+1qɛ r Conditional probability + P(E r+1 = 1 E r = 1, C r = 1) P(C r = 1 E r = 1) P(E r+1 = 1 E r = 1, C r = 0) P(C r = 0 E r = 1) P(C r+1 = 1 C 1,..., C r ) P(E r+1 = 1 E r = 1, C r = 1) c r (s) = α ur+1q + P(E r+1 = 1 E r = 1, C r = 0) ɛr (1 α ur q) (1 c (s) r ) 1 α ur qɛ r ) AC IM MdR Click Models for Web Search 74
Lecture 1 summary CTR models: counting clicks Position-based model (PBM): examination and attractiveness Cascade model (CM): previous examinations and clicks matter Dynamic Bayesian network model (DBN): satisfactoriness User browsing model (UBM): rank of previous click AC IM MdR Click Models for Web Search 75
Lecture 1 summary What do click models give us? General Understanding of user behavior Specific Conditional click probabilities Full click probabilities Attractiveness and satisfactoriness for query-document pairs AC IM MdR Click Models for Web Search 76
Course overview Basic Click Models Parameter Estimation Evaluation Applications Results Data and Tools Advanced Models Recent Studies Future Research AC IM MdR Click Models for Web Search 77
Next lecture Basic Click Models Parameter Estimation Evaluation Applications Results Data and Tools Advanced Models Recent Studies Future Research AC IM MdR Click Models for Web Search 78
Acknowledgments All content represents the opinion of the authors which is not necessarily shared or endorsed by their respective employers and/or sponsors. AC IM MdR Click Models for Web Search 79