statistical models for information retrieval and text mining
DESCRIPTION
Statistical Models for Information Retrieval and Text Mining. ChengXiang Zhai (翟成祥) Department of Computer Science Graduate School of Library & Information Science Institute for Genomic Biology, Statistics University of Illinois, Urbana-Champaign - PowerPoint PPT PresentationTRANSCRIPT
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 1
Statistical Models for Information
Retrieval and Text MiningChengXiang Zhai (翟成祥 )
Department of Computer Science
Graduate School of Library & Information Science
Institute for Genomic Biology, Statistics
University of Illinois, Urbana-Champaign
http://www-faculty.cs.uiuc.edu/~czhai, [email protected]
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 2
Course Overview
Statistics
Machine Learning
Computer VisionNatural Language Processing
Information Retrieval
Multimedia Data Text Data
Scope of the course
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 3
Goal of the Course
• Overview of techniques for information retrieval (IR)
• Detailed explanation of a few statistical models for IR and text mining
– Probabilistic retrieval models (for search)
– Probabilistic topic models (for text mining)
• Potential benefit for you:
– Some ideas working well for text retrieval may also work for computer vision
– Techniques for computer vision may be applicable to IR
– IR and text mining raise new challenges as well as opportunities for machine learning
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 4
Course Plan
• Lecture 1: Overview of information retrieval
• Lecture 2: Statistical language models for IR: Part 1
• Lecture 3: Statistical language models for IR: Part 2
• Lecture 4: Formal retrieval frameworks
• Lecture 5: Probabilistic topic models for text mining
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 5
Lecture 1: Overview of IR
• Basic Concepts in Text Retrieval (TR)
• Evaluation of TR
• Common Components of a TR system
• Overview of Retrieval Models
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 6
Basic Concepts in TR
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 7
What is Text Retrieval (TR)?
• There exists a collection of text documents
• User gives a query to express the information need
• A retrieval system returns relevant documents to users
• Known as “search technology” in industry
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 8
History of TR on One Slide• Birth of TR
– 1945: V. Bush’s article “As we may think”
– 1957: H. P. Luhn’s idea of word counting and matching
• Indexing & Evaluation Methodology (1960’s)
– Smart system (G. Salton’s group)
– Cranfield test collection (C. Cleverdon’s group)
– Indexing: automatic can be as good as manual (controlled vocabulary)
• TR Models (1970’s & 1980’s) …
• Large-scale Evaluation & Applications (1990’s-Present)
– TREC (D. Harman & E. Voorhees, NIST)
– Web search, PubMed, …
– Boundary with related areas are disappearing
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 9
Short vs. Long Term Info Need
• Short-term information need (Ad hoc retrieval)
– “Temporary need”, e.g., info about used cars
– Information source is relatively static
– User “pulls” information
– Application example: library search, Web search
• Long-term information need (Filtering)
– “Stable need”, e.g., new data mining algorithms
– Information source is dynamic
– System “pushes” information to user
– Applications: news filter
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 10
Importance of Ad hoc Retrieval
• Directly manages any existing large collection of information
• There are many many “ad hoc” information needs
• A long-term information need can be satisfied through frequent ad hoc retrieval
• Basic techniques of ad hoc retrieval can be used for filtering and other “non-retrieval” tasks, such as automatic summarization.
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 11
Formal Formulation of TR• Vocabulary V={w1, w2, …, wN} of language
• Query q = q1,…,qm, where qi V
• Document di = di1,…,dimi, where dij V
• Collection C= {d1, …, dk}
• Set of relevant documents R(q) C
– Generally unknown and user-dependent
– Query is a “hint” on which doc is in R(q)
• Task = compute R’(q), an “approximate R(q)”
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 12
Computing R(q)
• Strategy 1: Document selection
– R(q)={dC|f(d,q)=1}, where f(d,q) {0,1} is an indicator function or classifier
– System must decide if a doc is relevant or not (“absolute relevance”)
• Strategy 2: Document ranking
– R(q) = {dC|f(d,q)>}, where f(d,q) is a relevance measure function; is a cutoff
– System must decide if one doc is more likely to be relevant than another (“relative relevance”)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 13
Document Selection vs. Ranking
++
+ +-- -
- - - -
- - - -
-
- - +- -
Doc Selectionf(d,q)=?
++
++
--+
-+
--
- --
---
Doc Rankingf(d,q)=?
1
0
0.98 d1 +0.95 d2 +0.83 d3 -0.80 d4 +0.76 d5 -0.56 d6 -0.34 d7 -0.21 d8 +0.21 d9 -
R’(q)
R’(q)
True R(q)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 14
Problems of Doc Selection
• The classifier is unlikely accurate
– “Over-constrained” query (terms are too specific): no relevant documents found
– “Under-constrained” query (terms are too general): over delivery
– It is extremely hard to find the right position between these two extremes
• Even if it is accurate, all relevant documents are not equally relevant
• Relevance is a matter of degree!
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 15
Ranking is often preferred
• Relevance is a matter of degree
• A user can stop browsing anywhere, so the boundary is controlled by the user
– High recall users would view more items
– High precision users would view only a few
• Theoretical justification: Probability Ranking Principle [Robertson 77]
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 16
Probability Ranking Principle[Robertson 77]
• As stated by Cooper
• Robertson provides two formal justifications
• Assumptions: Independent relevance and sequential browsing (not necessarily all hold in reality)
“If a reference retrieval system’s response to each request is a ranking of the documents in the collections in order of decreasing probability of usefulness to the user who submitted the request, where the probabilities are estimated as accurately a possible on the basis of whatever data made available to the system for this purpose, then the overall effectiveness of the system to its users will be the best that is obtainable on the basis of that data.”
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 17
According to the PRP, all we need is
“A relevance measure function f”
which satisfies
For all q, d1, d2, f(q,d1) > f(q,d2) iff p(Rel|q,d1) >p(Rel|q,d2)
Most IR research has focused on finding a good function f
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 18
Evaluation in Information Retrieval
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 19
Evaluation Criteria
• Effectiveness/Accuracy
– Precision, Recall
• Efficiency
– Space and time complexity
• Usability
– How useful for real user tasks?
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 20
Methodology: Cranfield Tradition
• Laboratory testing of system components
– Precision, Recall
– Comparative testing
• Test collections
– Set of documents
– Set of questions
– Relevance judgments
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 21
The Contingency Table
Relevant Retrieved
Irrelevant Retrieved Irrelevant Rejected
Relevant RejectedRelevant
Not relevant
Retrieved Not RetrievedDocAction
Relevant
RetrievedRelevant Recall
Retrieved
RetrievedRelevant Precision
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 22
How to measure a ranking?
• Compute the precision at every recall point
• Plot a precision-recall (PR) curve
precision
recall
x
x
x
x
precision
recall
x
x
x
x
Which is better?
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 23
Summarize a Ranking: MAP• Given that n docs are retrieved
– Compute the precision (at rank) where each (new) relevant document is retrieved => p(1),…,p(k), if we have k rel. docs
– E.g., if the first rel. doc is at the 2nd rank, then p(1)=1/2.
– If a relevant document never gets retrieved, we assume the precision corresponding to that rel. doc to be zero
• Compute the average over all the relevant documents– Average precision = (p(1)+…p(k))/k
• This gives us (non-interpolated) average precision, which captures both precision and recall and is sensitive to the rank of each relevant document
• Mean Average Precisions (MAP)– MAP = arithmetic mean average precision over a set of topics
– gMAP = geometric mean average precision over a set of topics (more affected by difficult topics)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 24
Summarize a Ranking: NDCG• What if relevance judgments are in a scale of [1,r]? r>2
• Cumulative Gain (CG) at rank n– Let the ratings of the n documents be r1, r2, …rn (in ranked order)
– CG = r1+r2+…rn
• Discounted Cumulative Gain (DCG) at rank n– DCG = r1 + r2/log22 + r3/log23 + … rn/log2n
– We may use any base for the logarithm, e.g., base=b
– For rank positions above b, do not discount
• Normalized Cumulative Gain (NDCG) at rank n– Normalize DCG at rank n by the DCG value at rank n of the ideal
ranking
– The ideal ranking would first return the documents with the highest relevance level, then the next highest relevance level, etc
– Compute the precision (at rank) where each (new) relevant document is retrieved => p(1),…,p(k), if we have k rel. docs
• NDCG is now quite popular in evaluating Web search
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 25
When There’s only 1 Relevant Document
• Scenarios:
– known-item search
– navigational queries
• Search Length = Rank of the answer:
– measures a user’s effort
• Mean Reciprocal Rank (MRR):
– Reciprocal Rank: 1/Rank-of-the-answer
– Take an average over all the queries
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 26
Precion-Recall Curve
Mean Avg. Precision (MAP)
Recall=3212/4728
Breakeven Point (prec=recall)
Out of 4728 rel docs, we’ve got 3212
D1 +D2 +D3 –D4 –D5 +D6 -
Total # rel docs = 4System returns 6 docs
Average Prec = (1/1+2/2+3/5+0)/4
about 5.5 docsin the top 10 docs
are relevant
Precision@10docs
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 27
What Query Averaging Hides
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Recall
Prec
isio
n
Slide from Doug Oard’s presentation, originally from Ellen Voorhees’ presentation
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 28
The Pooling Strategy• When the test collection is very large, it’s impossible to
completely judge all the documents
• TREC’s strategy: pooling – Appropriate for relative comparison of different systems
– Given N systems, take top-K from the result of each, combine them to form a “pool”
– Users judge all the documents in the pool; unjudged documents are assumed to be non-relevant
• Advantage: less human effort
• Potential problem: – bias due to incomplete judgments (okay for relative comparison)
– Favor a system contributing to the pool, but when reused, a new system’s performance may be under-estimated
• Reuse the data set with caution!
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 29
User Studies• Limitations of Cranfield evaluation strategy:
– How do we evaluate a technique for improving the interface of a search engine?
– How do we evaluate the overall utility of a system?
• User studies are needed
• General user study procedure:– Experimental systems are developed
– Subjects are recruited as users
– Variation can be in the system or the users
– Users use the system and user behavior is logged
– User information is collected (before: background, after: experience with the system)
• Clickthrough-based real-time user studies: – Assume clicked documents to be relevant
– Mix results from multiple methods and compare their clickthroughs
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 30
Common Components in a TR System
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 31
Typical TR System Architecture
User
querydocs
results
Query Rep
Doc Rep (Index)
ScorerIndexer
Tokenizer
Index
judgmentsFeedback
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 32
Text Representation/Indexing
• Making it easier to match a query with a document
• Query and document should be represented using the same units/terms
• Controlled vocabulary vs. full text indexing
• Full-text indexing is more practically useful and has proven to be as effective as manual indexing with controlled vocabulary
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 33
What is a good indexing term?
• Specific (phrases) or general (single word)?
• Luhn found that words with middle frequency are most useful
– Not too specific (low utility, but still useful!)
– Not too general (lack of discrimination, stop words)
– Stop word removal is common, but rare words are kept
• All words or a (controlled) subset? When term weighting is used, it is a matter of weighting not selecting of indexing terms
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 34
Tokenization• Word segmentation is needed for some languages
– Is it really needed?
• Normalize lexical units: Words with similar meanings should be mapped to the same indexing term– Stemming: Mapping all inflectional forms of words to the same root form, e.g.
• computer -> compute
• computation -> compute
• computing -> compute (but king->k?)
– Are we losing finer-granularity discrimination?
• Stop word removal – What is a stop word? What about a query like “to be or not to be”?
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 35
Relevance Feedback
Updatedquery
Feedback
Judgments:d1 +d2 -d3 +
…dk -...
Query RetrievalEngine
Results:d1 3.5d2 2.4…dk 0.5...
UserDocumentcollection
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 36
Pseudo/Blind/Automatic Feedback
Query RetrievalEngine
Results:d1 3.5d2 2.4…dk 0.5...
Judgments:d1 +d2 +d3 +
…dk -...
Documentcollection
Feedback
Updatedquery
top 10
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 37
Implicit Feedback
Updatedquery
Feedback
Query RetrievalEngine
Results:d1 3.5d2 2.4…dk 0.5...
UserDocumentcollection
User Activitiese.g. clickthroughs
Judgments:d1 +d2 -d3 +
…dk -...
infer
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 38
Important Points to Remember
• PRP provides a justification for ranking, which is generally preferred to document selection
• How to compute the major evaluation measure (precision, recall, precision-recall curve, MAP, gMAP, breakeven precision, NDCG, MRR)
• What is pooling
• What is tokenization (word segmentation, stemming, stop word removal)
• What are relevance feedback, pseudo relevance feedback, and implicit feedback
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 39
Overview of Retrieval ModelsRelevance
(Rep(q), Rep(d)) Similarity
P(r=1|q,d) r {0,1} Probability of Relevance
P(d q) or P(q d) Probabilistic inference
Different rep & similarity
Vector spacemodel
(Salton et al., 75)
Prob. distr.model
(Wong & Yao, 89)
…
GenerativeModel
RegressionModel
(Fox 83)
Classicalprob. Model(Robertson &
Sparck Jones, 76)
Docgeneration
Querygeneration
LMapproach
(Ponte & Croft, 98)(Lafferty & Zhai, 01a)
Prob. conceptspace model
(Wong & Yao, 95)
Differentinference system
Inference network model
(Turtle & Croft, 91)
Learn toRank
(Joachims 02)(Burges et al. 05)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 40
Retrieval Models: Vector Space
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 41
Relevance = Similarity
• Assumptions
– Query and document are represented similarly
– A query can be regarded as a “document”
– Relevance(d,q) similarity(d,q)
• R(q) = {dC|f(d,q)>}, f(q,d)=(Rep(q), Rep(d))
• Key issues
– How to represent query/document?
– How to define the similarity measure ?
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 42
Vector Space Model
• Represent a doc/query by a term vector
– Term: basic concept, e.g., word or phrase
– Each term defines one dimension
– N terms define a high-dimensional space
– Element of vector corresponds to term weight
– E.g., d=(x1,…,xN), xi is “importance” of term i
• Measure relevance by the distance between the query vector and document vector in the vector space
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 43
VS Model: illustration
Java
Microsoft
Starbucks
D6
D10
D9
D4
D7
D8
D5
D11
D2 ? ?
D1
? ?
D3
? ?
Query
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 44
What the VS model doesn’t say
• How to define/select the “basic concept”
– Concepts are assumed to be orthogonal
• How to assign weights
– Weight in query indicates importance of term
– Weight in doc indicates how well the term characterizes the doc
• How to define the similarity/distance measure
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 45
What’s a good “basic concept”?
• Orthogonal
– Linearly independent basis vectors
– “Non-overlapping” in meaning
• No ambiguity
• Weights can be assigned automatically and hopefully accurately
• Many possibilities: Words, stemmed words, phrases, “latent concept”, …
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 46
How to Assign Weights?
• Very very important!
• Why weighting– Query side: Not all terms are equally important
– Doc side: Some terms carry more information about contents
• How?
– Two basic heuristics
• TF (Term Frequency) = Within-doc-frequency
• IDF (Inverse Document Frequency)
– TF normalization
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 47
TF Weighting
• Idea: A term is more important if it occurs more frequently in a document
• Some formulas: Let f(t,d) be the frequency count of term t in doc d
– Raw TF: TF(t,d) = f(t,d)
– Log TF: TF(t,d)=log f(t,d)
– Maximum frequency normalization: TF(t,d) = 0.5 +0.5*f(t,d)/MaxFreq(d)
– “Okapi/BM25 TF”: TF(t,d) = k f(t,d)/(f(t,d)+k(1-b+b*doclen/avgdoclen))
• Normalization of TF is very important!
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 48
TF Normalization
• Why?
– Document length variation
– “Repeated occurrences” are less informative than the “first occurrence”
• Two views of document length
– A doc is long because it uses more words
– A doc is long because it has more contents
• Generally penalize long doc, but avoid over-penalizing (pivoted normalization)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 49
TF Normalization: How?
Norm. TF
Raw TF
Which curve is more reasonable? Should normalized-TF be up-bounded?
Normalization interacts with the similarity measure
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 50
Regularized/“Pivoted” Length Normalization
Norm. TF
Raw TF
“Pivoted normalization”: Using avg. doc length to regularize normalization
1-b+b*doclen/avgdoclen (b varies from 0 to 1)What would happen if doclen is {>, <,=} avgdoclen?
Advantage: stabalize parameter setting
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 51
IDF Weighting
• Idea: A term is more discriminative if it occurs only in fewer documents
• Formula:IDF(t) = 1+ log(n/k)
n – total number of docsk -- # docs with term t (doc freq)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 52
TF-IDF Weighting
• TF-IDF weighting : weight(t,d)=TF(t,d)*IDF(t)
– Common in doc high tf high weight
– Rare in collection high idf high weight
• Imagine a word count profile, what kind of terms would have high weights?
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 53
How to Measure Similarity?
product)dot normalized(
)()(
),( :Cosine
),( :similarityproduct Dot
absent is term a if 0 ),...,(
),...,(
1
2
1
2
1
1
1
1
N
jij
N
jqj
N
jijqj
i
N
jijqji
qNq
iNii
ww
ww
DQsim
wwDQsim
wwwQ
wwD
How about Euclidean?
N
jijqji wwDQsim
1
2)(),(
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 54
What Works the Best?
(Singhal 2001)
•Use single words
•Use stat. phrases
•Remove stop words
•Stemming
•Others(?)
Error
[ ]
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 55
“Extension” of VS Model
• Alternative similarity measures
– Many other choices (tend not to be very effective)
– P-norm (Extended Boolean): matching a Boolean query with a TF-IDF document vector
• Alternative representation
– Many choices (performance varies a lot)
– Latent Semantic Indexing (LSI) [TREC performance tends to be average]
• Generalized vector space model
– Theoretically interesting, not seriously evaluated
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 56
Relevance Feedback in VS
• Basic setting: Learn from examples– Positive examples: docs known to be relevant
– Negative examples: docs known to be non-relevant
– How do you learn from this to improve performance?
• General method: Query modification– Adding new (weighted) terms
– Adjusting weights of old terms
– Doing both
• The most well-known and effective approach is Rocchio [Rocchio 1971]
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 57
+
Rocchio Feedback: Illustration
qq+ ++++ +
++++
++
++
+---
----
-- --
------ --
-----
-
-
-+ + +
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 58
Rocchio Feedback: Formula
Origial query Rel docs Non-rel docs
ParametersNew query
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 59
Rocchio in Practice
• Negative (non-relevant) examples are not very important (why?)
• Often truncate the vector onto to lower dimension (i.e., consider only a small number of words that have high weights in the centroid vector) (efficiency concern)
• Avoid overfitting by keeping a relatively high weight on the original query weights (why?)
• Can be used for relevance feedback and pseudo feedback
• Usually robust and effective
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 60
Advantages of VS Model
• Empirically effective! (Top TREC performance)
• Intuitive
• Easy to implement
• Well-studied/Most evaluated
• The Smart system
– Developed at Cornell: 1960-1999
– Still available
• Warning: Many variants of TF-IDF!
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 61
Disadvantages of VS Model
• Assume term independence
• Assume query and document to be the same
• Lack of “predictive adequacy”
– Arbitrary term weighting
– Arbitrary similarity measure
• Lots of parameter tuning!
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 62
Probabilistic Retrieval Models
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 63
Overview of Retrieval ModelsRelevance
(Rep(q), Rep(d)) Similarity
P(r=1|q,d) r {0,1} Probability of Relevance
P(d q) or P(q d) Probabilistic inference
Different rep & similarity
Vector spacemodel
(Salton et al., 75)
Prob. distr.model
(Wong & Yao, 89)
…
GenerativeModel
RegressionModel
(Fox 83)
Classicalprob. Model(Robertson &
Sparck Jones, 76)
Docgeneration
Querygeneration
LMapproach
(Ponte & Croft, 98)(Lafferty & Zhai, 01a)
Prob. conceptspace model
(Wong & Yao, 95)
Differentinference system
Inference network model
(Turtle & Croft, 91)
Learn toRank
(Joachims 02)(Burges et al. 05)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 64
Probability of Relevance
• Three random variables
– Query Q
– Document D
– Relevance R {0,1}
• Goal: rank D based on P(R=1|Q,D)
– Evaluate P(R=1|Q,D)
– Actually, only need to compare P(R=1|Q,D1) with P(R=1|Q,D2), I.e., rank documents
• Several different ways to refine P(R=1|Q,D)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 65
Refining P(R=1|Q,D) Method 1: conditional models
• Basic idea: relevance depends on how well a query matches a document
– Define features on Q x D, e.g., #matched terms, # the highest IDF of a matched term, #doclen,..
– P(R=1|Q,D)=g(f1(Q,D), f2(Q,D),…,fn(Q,D), )
– Using training data (known relevance judgments) to estimate parameter
– Apply the model to rank new documents
• Early work (e.g., logistic regression [Cooper 92, Gey 94])
– Attempted to compete with other models
• Recent work (e.g. Ranking SVM [Joachims 02], RankNet (Burges et al. 05))
– Attempted to leverage other models
– More features (notably PageRank, anchor text)
– More sophisticated learning (Ranking SVM, RankNet, …)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 66
Logistic Regression (Cooper 92, Gey 94)
)exp(1
1),|1(
6
10
iiiX
DQRP
6
10),|1(1
),|1(log
iiiXDQRP
DQRP x
x
1loglogit function:
)exp(1
)exp(
)exp(1
1
x
x
x
logistic (sigmoid) function:
X
P(R=1|Q,D)
1.0Uses 6 features X1, …, X6
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 67
Features/Attributes
MX
n
nNIDF
IDFM
X
DLX
DAFM
X
QLX
QAFM
X
j
j
j
j
j
t
t
M
t
M
t
M
t
log
log1
log1
log1
6
15
4
13
2
11
Average Absolute Query Frequency
Query Length
Average Absolute Document Frequency
Document Length
Average Inverse Document Frequency
Inverse Document Frequency
Number of Terms in common between query and document -- logged
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 68
Learning to Rank
• Advantages
– May combine multiple features (helps improve accuracy and combat web spams)
– May re-use all the past relevance judgments (self-improving)
• Problems
– Don’t learn the semantic associations between query words and document words
– No much guidance on feature generation (rely on traditional retrieval models)
• All current Web search engines use some kind of learning algorithms to combine many features such as PageRank and many different representations of a page
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 69
The PageRank Algorithm (Page et al. 98)
1 1
1
0 0 1/ 2 1/ 2
1 0 0 0
0 1 0 0
1/ 2 1/ 2 0 0
1( ) (1 ) ( ) ( )
1[ (1 ) ] ( )
( (1 ) )
N N
i ki k kk k
N
ki kk
T
M
p d m p d p dN
m p dN
p I M p
d1
d2
d4
“Transition matrix”
d3
Iterate until converge
N= # pages
Stationary (“stable”) distribution, so we
ignore time
Random surfing model: At any page,
With prob. , randomly jumping to a pageWith prob. (1-), randomly picking a link to follow.
Iij = 1/N
Initial value p(d)=1/N
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 70
PageRank in Practice• Interpretation of the damping factor (0.15):
– Probability of a random jump
– Smoothing the transition matrix (avoid zero’s)
• Normalization doesn’t affect ranking, leading to some variants
• The zero-outlink problem: p(di)’s don’t sum to 1– One possible solution = page-specific damping factor (=1.0
for a page with no outlink)
1 1
1( ) (1 ) ( ) ( ) ( (1 ) )
N NT
i ki k kk k
p d m p d p d p I M pN
1 1
1 1
1
1'( ) ( ), , ( ) (1 ) ( ) ( )
1'( ) (1 ) '( ) '( )
'( ) (1 ) '( )
N N
i i i ki k kk k
N N
i ki k kk k
NC N
i ki kk
Let p d cp d c constant cp d m cp d cp dN
p d m p d p dN
p d m p d
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 71
HITS: Capturing Authorities & Hubs [Kleinberg 98]
• Intuitions
– Pages that are widely cited are good authorities
– Pages that cite many other pages are good hubs
• The key idea of HITS
– Good authorities are cited by good hubs
– Good hubs point to good authorities
– Iterative reinforcement…
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 72
The HITS Algorithm [Kleinberg 98]
d1
d2
d4( )
( )
0 0 1 1
1 0 0 0
0 1 0 0
1 1 0 0
( ) ( )
( ) ( )
;
;
j i
j i
i jd OUT d
i jd IN d
T
T T
A
h d a d
a d h d
h Aa a A h
h AA h a A Aa
“Adjacency matrix”
d3 Initial values: a(di)=h(di)=1
Iterate
Normalize: 2 2
( ) ( ) 1i ii i
a d h d
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 73
Refining P(R=1|Q,D) Method 2:generative models
• Basic idea
– Define P(Q,D|R)
– Compute O(R=1|Q,D) using Bayes’ rule
• Special cases
– Document “generation”: P(Q,D|R)=P(D|Q,R)P(Q|R)
– Query “generation”: P(Q,D|R)=P(Q|D,R)P(D|R)
)0(
)1(
)0|,(
)1|,(
),|0(
),|1(),|1(
RP
RP
RDQP
RDQP
DQRP
DQRPDQRO
Ignored for ranking D
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 74
Document Generation
)0,|(
)1,|(
)0|()0,|(
)1|()1,|(
)0|,(
)1|,(
),|0(
),|1(
RQDP
RQDP
RQPRQDP
RQPRQDP
RDQP
RDQP
DQRP
DQRP
Model of relevant docs for Q
Model of non-relevant docs for Q
Assume independent attributes A1…Ak ….(why?)Let D=d1…dk, where dk {0,1} is the value of attribute Ak (Similarly Q=q1…qk )
)0),0,|1()1,|1(()1,|0()0,|1(
)0,|0()1,|1(
)1,|0()0,|1(
)0,|0()1,|1(
)0,|0(
)1,|0(
)0,|1(
)1,|1(
)0,|(
)1,|(
),|0(
),|1(
1,1
1,1
0,11,1
1
iii
k
qdi ii
ii
k
di ii
ii
k
di i
ik
di i
i
k
i ii
ii
qifRQAPRQAPAssumeRQAPRQAP
RQAPRQAP
RQAPRQAP
RQAPRQAP
RQAP
RQAP
RQAP
RQAP
RQdAP
RQdAP
DQRP
DQRP
ii
i
ii
Non-query terms are equally likely to
appear in relevant and non-relevant docs
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 75
Robertson-Sparck Jones Model(Robertson & Sparck Jones 76)
Two parameters for each term Ai: pi = P(Ai=1|Q,R=1): prob. that term Ai occurs in a relevant doc qi = P(Ai=1|Q,R=0): prob. that term Ai occurs in a non-relevant doc
k
qdi ii
iiRank
iipq
qpDQRO
1,1 )1(
)1(log),|1(log (RSJ model)
How to estimate parameters?Suppose we have relevance judgments,
1).(#
5.0).(#ˆ
1).(#
5.0).(#ˆ
docnonrel
Awithdocnonrelq
docrel
Awithdocrelp i
ii
i
“+0.5” and “+1” can be justified by Bayesian estimation
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 76
RSJ Model: No Relevance Info(Croft & Harper 79)
k
qdi ii
iiRank
iipq
qpDQRO
1,1 )1(
)1(log),|1(log (RSJ model)
How to estimate parameters?Suppose we do not have relevance judgments,
- We will assume pi to be a constant - Estimate qi by assuming all documents to be non-relevant
k
qdi i
iRank
iin
nNDQRO
1,1 5.0
5.0log),|1(log
N: # documents in collectionni: # documents in which term Ai occurs
i
i
n
nNIDF
log'
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 77
Improving RSJ: Adding TF
Let D=d1…dk, where dk is the frequency count of term Ak
k
di iii
iii
k
di i
ik
di ii
ii
k
i ii
ii
i
ii
RQAPRQdAP
RQAPRQdAP
RQAP
RQAP
RQdAP
RQdAP
RQdAP
RQdAP
DQRP
DQRP
1,1
0,11,1
1
)1,|0()0,|(
)0,|0()1,|(
)0,|0(
)1,|0(
)0,|(
)1,|(
)0,|(
)1,|(
),|0(
),|1(
)0,|(
)1,|(
),|0(
),|1(
RQDP
RQDP
DQRP
DQRPBasic doc. generation model:
EE ef
RQEPef
RQEp
EfApRQEPEfApRQEpRQfApf
Ef
E
iii
!),|(
!),|(
)|(),|()|(),|(),|(
2-Poisson mixture model
Many more parameters to estimate! (how many exactly?)
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 78
BM25/Okapi Approximation(Robertson et al. 94)
• Idea: Approximate p(R=1|Q,D) with a simpler function that share similar properties
• Observations:
– log O(R=1|Q,D) is a sum of term weights Wi
– Wi= 0, if TFi=0
– Wi increases monotonically with TFi
– Wi has an asymptotic limit
• The simple function is
)1(
)1(log
)1(
1
1
ii
ii
i
ii pq
qp
TFk
kTFW
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 79
Adding Doc. Length & Query TF
• Incorporating doc length
– Motivation: The 2-Poisson model assumes equal document length
– Implementation: “Carefully” penalize long doc
• Incorporating query TF
– Motivation: Appears to be not well-justified
– Implementation: A similar TF transformation
• The final formula is called BM25, achieving top TREC performance
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 80
The BM25 Formula
“Okapi TF/BM25 TF”
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 81
Extensions of “Doc Generation” Models
• Capture term dependence (Rijsbergen & Harper 78)
• Alternative ways to incorporate TF (Croft 83, Kalt96)
• Feature/term selection for feedback (Okapi’s TREC reports)
• Other Possibilities (machine learning … )
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 82
Query Generation
))0|()0,|(()0|(
)1|()1,|(
)0|()0,|(
)1|()1,|(
)0|,(
)1|,(),|1(
RQPRDQPAssumeRDP
RDPRDQP
RDPRDQP
RDPRDQP
RDQP
RDQPDQRO
Assuming uniform prior, we have
Query likelihood p(q| d) Document prior
)1,|(),|1( RDQPDQRO
Now, the question is how to compute ?)1,|( RDQP
Generally involves two steps:(1) estimate a language model based on D(2) compute the query likelihood according to the estimated model
Leading to the so-called “Language Modeling Approach” …
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 83
Lecture 1: Key Points • Vector Space Model is a family of models, not a single model
• Many variants of TF-IDF weighting and some are more effective than others
• State of the art retrieval performance is achieved through– Bag of words representation
– TF-IDF weighting (BM25) + length normalization
– Pseudo relevance feedback (mostly for recall)
– For web search, add PageRank, anchor text, …, plus learning to rank
• Principled approaches didn’t lead to good performance directly (before the “language modeling approach” was proposed); heuristic modification has been necessary
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 84
Readings
• Amit Singhal’s overview:
– http://sifaka.cs.uiuc.edu/course/ds/mir.pdf
• My review of IR models:
– http://sifaka.cs.uiuc.edu/course/ds/irmod.pdf
2008 © ChengXiang Zhai China-US-France Summer School, Lotus Hill Inst., 2008 85
Discussion• Text retrieval and image retrieval
– Query language:
• keywords vs. image features
• By example
– Content representation
• Bag of words vs. “bag of image features”?
• Phrase indexing vs. units from image parsing?
• Sentiment analysis
– Retrieval heuristics
• TF-IDF weighting vs. ?
• Passage retrieval vs. image region retrieval?
• Proximity
• Text retrieval and video retrieval
• Multimedia retrieval?