lecture11-prohdhhdhdhdhdhdhdhdbir(2).ppt

CS276
Information Retrieval and Web Search
Lecture 11: Probabilistic Information
Retrieval

Recap of the last lecture
 Improving search results
 Especially for high recall. E.g., searching for
aircraft so it matches with plane; thermodynamic
with heat
 Options for improving results…
 Global methods

Query expansion
 Thesauri
 Automatic thesaurus generation

Global indirect relevance feedback
 Local methods

Relevance feedback

Pseudo relevance feedback

Probabilistic relevance feedback
 Rather than reweighting in a vector space…
 If user has told us some relevant and some
irrelevant documents, then we can proceed to
build a probabilistic classifier, such as a Naive
Bayes model:
 P(tk|R) = |Drk| / |Dr|
 P(tk|NR) = |Dnrk| / |Dnr|
 tk is a term; Dr is the set of known relevant documents;
Drk is the subset that contain tk; Dnr is the set of known
irrelevant documents; Dnrk is the subset that contain tk.

Why probabilities in IR?
User
Information Need
Documents
Document
Representation
Query
Representation
How to match?
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.
Uncertain guess of
whether document
has relevant content
Understanding
of user need is
uncertain

Probabilistic IR topics
 Classical probabilistic retrieval model
 Probability ranking principle, etc.
 (Naïve) Bayesian Text Categorization
 Bayesian networks for text retrieval
 Language model approach to IR
 An important emphasis in recent work
 Probabilistic methods are one of the oldest but also
one of the currently hottest topics in IR.
 Traditionally: neat ideas, but they’ve never won on
performance. It may be different now.

The document ranking problem
 We have a collection of documents
 User issues a query
 A list of documents needs to be returned

Ranking method is core of an IR system:
Ranking method is core of an IR system:

In what order do we present documents to the
In what order do we present documents to the
user?
user?

We want the “best” document to be first, second
best second, etc….

Idea: Rank by probability of relevance of the
Idea: Rank by probability of relevance of the
document w.r.t. information need
document w.r.t. information need
 P(relevant|documenti, query)

Recall a few probability basics
 For events a and b:
 Bayes’ Rule
 Odds:
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Posterior
Prior

The Probability Ranking Principle
“If a reference retrieval system's response to each request
is a ranking of the documents in the collection in order of
decreasing probability of relevance to the user who
submitted the request, where the probabilities are
estimated as accurately as possible on the basis of
whatever data have been made available to the system for
this purpose, the overall effectiveness of the system to its
user will be the best that is obtainable on the basis of
those data.”

[1960s/1970s] S. Robertson, W.S. Cooper, M.E. Maron;
van Rijsbergen (1979:113); Manning & Schütze (1999:538)

Probability Ranking Principle
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.
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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
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Probability Ranking Principle (PRP)
 Simple case: no selection costs or other utility
concerns that would differentially weight errors
 Bayes’ Optimal Decision Rule
 x is relevant iff p(R|x) > p(NR|x)
 PRP in action: Rank all documents by p(R|x)
 Theorem:
 Using the PRP is optimal, in that it minimizes the
loss (Bayes risk) under 1/0 loss
 Provable if all probabilities correct, etc. [e.g.,
Ripley 1996]

 More complex case: retrieval costs.
 Let d be a document
 C - cost of retrieval of relevant document
 C’ - cost of retrieval of non-relevant document
 Probability Ranking Principle: if
for all d’ not yet retrieved, then d is the next
document to be retrieved
 We won’t further consider loss/utility from
now on
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 How do we compute all those probabilities?
 Do not know exact probabilities, have to use estimates
 Binary Independence Retrieval (BIR) – which we
discuss later today – is the simplest model
 Questionable assumptions
 “Relevance” of each document is independent of
relevance of other documents.

Really, it’s bad to keep on returning duplicates
 Boolean model of relevance
 That one has a single step information need

Seeing a range of results might let user refine query

Probabilistic Retrieval Strategy
 Estimate how terms contribute to relevance
 How do things like tf, idf, and length influence your
judgments about document relevance?

One answer is the Okapi formulae (S. Robertson)
 Combine to find document relevance probability
 Order documents by decreasing probability

Probabilistic Ranking
Basic concept:
"For a given query, if we know some documents that are
relevant, terms that occur in those documents should be
given greater weighting in searching for other relevant
documents.
By making assumptions about the distribution of terms
and applying Bayes Theorem, it is possible to derive
weights theoretically."
Van Rijsbergen

Binary Independence Model
 Traditionally used in conjunction with PRP
 “Binary” = Boolean: documents are represented as
binary incidence vectors of terms (cf. lecture 1):

 iff term i is present in document x.
 “Independence”: terms occur in documents
independently
 Different documents can be modeled as same vector
 Bernoulli Naive Bayes model (cf. text categorization!)
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 Queries: binary term incidence vectors
 Given query q,
 for each document d need to compute p(R|q,d).
 replace with computing p(R|q,x) where x is binary
term incidence vector representing d Interested
only in ranking
 Will use odds and Bayes’ Rule:
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• All boils down to computing RSV.
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So, how do we compute ci’s from our data ?

• Estimating RSV coefficients.
• For each term i look at this table of document counts:
Documens Relevant Non-Relevant Total
Xi=1 s n-s n
Xi=0 S-s N-n-S+s N-n
Total S N-S N
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• Estimates: For now,
assume no
zero terms.
More next
lecture.

Estimation – key challenge
 If non-relevant documents are approximated by the
whole collection, then ri (prob. of occurrence in non-
relevant documents for query) is n/N and
 log (1– ri)/ri = log (N– n)/n ≈ log N/n = IDF!
 pi (probability of occurrence in relevant documents)
can be estimated in various ways:
 from relevant documents if know some

Relevance weighting can be used in feedback loop

constant (Croft and Harper combination match) – then
just get idf weighting of terms

proportional to prob. of occurrence in collection

more accurately, to log of this (Greiff, SIGIR 1998)

25
Iteratively estimating pi
1. Assume that pi constant over all xi in query

pi = 0.5 (even odds) for any given doc
2. Determine guess of relevant document set:
 V is fixed size set of highest ranked documents on
this model (note: now a bit like tf.idf!)
3. We need to improve our guesses for pi and ri, so

Use distribution of xi in docs in V. Let Vi be set of
documents containing xi

pi = |Vi| / |V|
 Assume if not retrieved then not relevant

ri = (ni – |Vi|) / (N – |V|)
4. Go to 2. until converges then return ranking

Probabilistic Relevance Feedback
1. Guess a preliminary probabilistic description of
R and use it to retrieve a first set of documents
V, as above.
2. Interact with the user to refine the description:
learn some definite members of R and NR
3. Reestimate pi and ri on the basis of these

Or can combine new information with original
guess (use Bayesian prior):
4. Repeat, thus generating a succession of
approximations to R.

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κ is
prior
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PRP and BIR
 Getting reasonable approximations of probabilities
is possible.
 Requires restrictive assumptions:
 term independence
 terms not in query don’t affect the outcome
 boolean representation of
documents/queries/relevance
 document relevance values are independent
 Some of these assumptions can be removed
 Problem: either require partial relevance information or only
can derive somewhat inferior term weights

Removing term independence
 In general, index terms aren’t
independent
 Dependencies can be complex
 van Rijsbergen (1979)
proposed model of simple tree
dependencies
 Exactly Friedman and
Goldszmidt’s Tree Augmented
Naive Bayes (AAAI 13, 1996)
 Each term dependent on one
other
 In 1970s, estimation problems
held back success of this
model

Food for thought
 Think through the differences between standard
tf.idf and the probabilistic retrieval model in the
first iteration
 Think through the differences between vector
space (pseudo) relevance feedback and
probabilistic (pseudo) relevance feedback

Good and Bad News
 Standard Vector Space Model
 Empirical for the most part; success measured by results
 Few properties provable
 Probabilistic Model Advantages
 Based on a firm theoretical foundation
 Theoretically justified optimal ranking scheme
 Disadvantages
 Making the initial guess to get V
 Binary word-in-doc weights (not using term frequencies)
 Independence of terms (can be alleviated)
 Amount of computation
 Has never worked convincingly better in practice

Bayesian Networks for Text
Retrieval (Turtle and Croft 1990)
 Standard probabilistic model assumes you can’t
estimate P(R|D,Q)

Instead assume independence and use P(D|R)
 But maybe you can with a Bayesian network*
 What is a Bayesian network?

A directed acyclic graph
 Nodes

Events or Variables

Assume values.

For our purposes, all Boolean
 Links

model direct dependencies between nodes

Bayesian Networks
a b
c
a,b,c - propositions (events).
p(c|ab) for all values
for a,b,c
p(a)
p(b)
• Bayesian networks model causal
relations between events
•Inference in Bayesian Nets:
•Given probability distributions
for roots and conditional
probabilities can compute
apriori probability of any
instance
• Fixing assumptions (e.g., b
was observed) will cause
recomputation of probabilities
Conditional
dependence
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.

Toy Example
Gloom
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Project Due
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No Sleep
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Triple Latte
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Chained inference
 Evidence - a node takes on some value
 Inference
 Compute belief (probabilities) of other nodes

conditioned on the known evidence
 Two kinds of inference: Diagnostic and Predictive
 Computational complexity
 General network: NP-hard

Tree-like networks are easily tractable

Much other work on efficient exact and approximate
Bayesian network inference
 Clever dynamic programming
 Approximate inference (“loopy belief propagation”)

Model for Text Retrieval
 Goal
 Given a user’s information need (evidence), find
probability a doc satisfies need
 Retrieval model
 Model docs in a document network
 Model information need in a query network

Bayesian Nets for IR: Idea
Document Network
Query Network
Large, but
Compute once for each
document collection
Small, compute once for
every query
d1 dn
d2
t1 t2 tn
r1 r2 r3
rk
di -documents
ti - document representations
ri - “concepts”
I
q2
q1
cm
c2
c1
ci - query concepts
qi - high-level concepts
I - goal node

Bayesian Nets for IR
 Construct Document Network (once !)
 For each query
 Construct best Query Network
 Attach it to Document Network
 Find subset of di’s which maximizes the
probability value of node I (best subset).
 Retrieve these di’s as the answer to query.

Bayesian nets for text retrieval
d1 d2
r1 r3
c1 c3
q1 q2
i
r2
c2
Document
Network
Query
Network
Documents
Terms/Concepts
Concepts
Query operators
(AND/OR/NOT)
Information need

Link matrices and probabilities
 Prior doc probability P(d)
= 1/n
 P(r|d)
 within-document term
frequency
 tf  idf - based
 P(c|r)
 1-to-1
 thesaurus
 P(q|c): canonical forms of
query operators
 Always use things like
AND and NOT – never
store a full CPT*
*conditional probability table

Example: “reason trouble –two”
Hamlet Macbeth
reason double
reason two
OR NOT
User query
trouble
trouble
Document
Network
Query
Network

Extensions
 Prior probs don’t have to be 1/n.
 “User information need” doesn’t have to be a
query - can be words typed, in docs read, any
combination …
 Phrases, inter-document links
 Link matrices can be modified over time.
 User feedback.
 The promise of “personalization”

Computational details
 Document network built at indexing time
 Query network built/scored at query time
 Representation:
 Link matrices from docs to any single term are like
the postings entry for that term
 Canonical link matrices are efficient to store and
compute
 Attach evidence only at roots of network
 Can do single pass from roots to leaves

Bayes Nets in IR
 Flexible ways of combining term weights, which can
generalize previous approaches
 Boolean model
 Binary independence model
 Probabilistic models with weaker assumptions
 Efficient large-scale implementation
 InQuery text retrieval system from U Mass

Turtle and Croft (1990) [Commercial version defunct?]
 Need approximations to avoid intractable inference
 Need to estimate all the probabilities by some means
(whether more or less ad hoc)
 Much new Bayes net technology yet to be applied?

Resources
S. E. Robertson and K. Spärck Jones. 1976. Relevance Weighting
of Search Terms. Journal of the American Society for Information
Sciences 27(3): 129–146.
C. J. van Rijsbergen. 1979. Information Retrieval. 2nd ed. London:
Butterworths, chapter 6. [Most details of math]
http://www.dcs.gla.ac.uk/Keith/Preface.html
N. Fuhr. 1992. Probabilistic Models in Information Retrieval. The
Computer Journal, 35(3),243–255. [Easiest read, with BNs]
F. Crestani, M. Lalmas, C. J. van Rijsbergen, and I. Campbell. 1998.
Is This Document Relevant? ... Probably: A Survey of
Probabilistic Models in Information Retrieval. ACM Computing
Surveys 30(4): 528–552.
http://www.acm.org/pubs/citations/journals/surveys/1998-30-4/p528-crestani/
[Adds very little material that isn’t in van Rijsbergen or Fuhr ]

Resources
H.R. Turtle and W.B. Croft. 1990. Inference Networks for Document
Retrieval. Proc. ACM SIGIR: 1-24.
E. Charniak. Bayesian nets without tears. AI Magazine 12(4): 50-63
(1991). http://www.aaai.org/Library/Magazine/Vol12/12-04/vol12-04.html
D. Heckerman. 1995. A Tutorial on Learning with Bayesian Networks.
Microsoft Technical Report MSR-TR-95-06
http://www.research.microsoft.com/~heckerman/
N. Fuhr. 2000. Probabilistic Datalog: Implementing Logical Information
Retrieval for Advanced Applications. Journal of the American Society
for Information Science 51(2): 95–110.
R. K. Belew. 2001. Finding Out About: A Cognitive Perspective on Search
Engine Technology and the WWW. Cambridge UP 2001.
MIR 2.5.4, 2.8

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