Transcript Slides - Asian Institute of Technology

Introduction to Information Retrieval
Information Retrieval and Data Mining
(AT71.07)
Comp. Sc. and Inf. Mgmt.
Asian Institute of Technology
Instructor: Dr. Sumanta Guha
Slide Sources: Introduction to
Information Retrieval book slides
from Stanford University, adapted
and supplemented
Chapter 11: Probabilistic information
retrieval
1
Introduction to Information Retrieval
Introduction to
Information Retrieval
CS276
Information Retrieval and Web Search
Christopher Manning and Prabhakar Raghavan
Lecture 11: Probabilistic information retrieval
Introduction to Information Retrieval
Recap of the last lecture
 Improving search results
 Especially for high recall. E.g., searching for aircraft so it
matches with plane; thermodynamics 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
Introduction to Information Retrieval
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.
Introduction to Information Retrieval
Why probabilities in IR?
User
Information Need
Query
Representation
Understanding
of user need is
uncertain
How to match?
Documents
Document
Representation
Uncertain guess of
whether document
has relevant content
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?
Introduction to Information Retrieval
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.
Introduction to Information Retrieval
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:
 In what order do we present documents to the user?
 We want the “best” document to be first, second best
second, etc….
 Idea: Rank by probability of relevance of the
document w.r.t. information need
 P(relevant|documenti, query)
Introduction to Information Retrieval
Recall a few probability basics
 For events a and b:
 Bayes’ Rule
p (a, b)  p (a  b)  p (a | b) p (b)  p (b | a ) p (a )
p (a | b) p (b)  p (b | a ) p (a )
Prior
p (b | a ) p (a )
p (b | a ) p (a )
p (a | b)Bayes’
 Rule

p (b)
xa,a p(b | x) p( x)
Posterior
p(a)
p(a)

 Odds: O(a) 
p(a ) 1  p(a)
p(b) = p(b|a)p(a) + p(b|a)p(a)
Introduction to Information Retrieval
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)
Introduction to Information Retrieval
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.
R={0,1} vs. NR/R
Need to find p(R|x) - probability that a document x is relevant.
p( x | R) p( R)
p( R | x) 
p( x)
p( x | NR) p( NR)
p( NR | x) 
p( x)
p(R), p(NR) – prior probability
of retrieving a (non) relevant
document
p( R | x)  p( NR | x)  1
p(x|R), p(x|NR) – probability that if a relevant (non-relevant)
document is retrieved, it is x.
Introduction to Information Retrieval
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]
Introduction to Information Retrieval
Probability Ranking Principle
 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
Introduction to Information Retrieval
Probabilistic Retrieval Strategy
 Estimate how terms contribute to relevance
 How do things like tf, df, 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
Introduction to Information Retrieval
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
Introduction to Information Retrieval
Binary Independence Model
 Traditionally used in conjunction with PRP
 “Binary” = Boolean: documents are represented as binary
incidence vectors of terms (cf. lecture 1):



x  ( x1 ,, xn )
iff term i is present in document x.
xi  1
 “Independence”: terms occur in documents independently
 Different documents can be modeled as same vector
 Bernoulli Naive Bayes model (cf. text categorization!)
Introduction to Information Retrieval
Binary Independence Model
 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
 Will use odds and Bayes’ Rule:

p ( R | q ) p ( x | R, q )



p ( R | q, x )
p( x | q)
O ( R | q, x ) 
  p ( NR | q ) p ( x | NR , q )
p ( NR | q, x )

p( x | q)
R=1
R=0
Introduction to Information Retrieval
Binary Independence Model



p ( R | q, x )
p ( R | q ) p ( x | R, q )
O ( R | q, x ) 
 
 
p( NR | q, x ) p( NR | q) p( x | NR, q)
O(R|q), which is constant for
a given query = does not
depend on the document
Needs estimation
• Using Independence Assumption:

n
p( xi | R, q)
p( x | R, q)


p( x | NR, q) i 1 p( xi | NR, q)
n

p( xi | R, q)
• So: O( R | q, x )  O( R | q)  
i 1 p ( xi | NR, q )
Introduction to Information Retrieval
Binary Independence Model
n
O( R | q, d )  O( R | q)  
i 1
p( xi | R, q)
p( xi | NR, q)
So all terms corresponding
to qi = 0 will have equal
values in numerator and
denominator and,
therefore, will vanish.
• Since xi is either 0 or 1:
p( xi  1 | R, q)
p( xi  0 | R, q)
O( R | q, d )  O( R | q)  

xi 1 p( xi  1 | NR, q) xi 0 p( xi  0 | NR, q)
• Let pi  prob( xi  1 | R, q); ui  prob( xi  1 | NR, q);
Term present
Term absent
Doc
xi = 1
xi = 0
• Assume, for
Relevant (R = 1)
pi
1 – pi
Non-relevant (R = 0)
ui
1 – ui
all terms not occurring in the query, i.e.,
qi = 0, that pi = ui (in other words, non-query terms are
equally likely to appear in relevant and non-relevant docs)
Introduction to Information Retrieval
Binary Independence Model

O ( R | q, x )  O ( R | q ) 
pi
1  pi


xi  qi 1 ui xi  0 1  ui
qi 1
Matching query terms
Non-matching query terms
pi
1  ui
1  pi
1  pi
 O( R | q)  



xi  qi 1 ui
xi 1 1  pi xi  0 1  ui
xi 1 1  ui
qi 1
qi 1
qi 1
Insert new terms which cancel!
pi (1  ui )
1  pi
 O( R | q)  

xi  qi 1 ui (1  pi ) qi 1 1  ui
Matching query terms
All query terms
Introduction to Information Retrieval
Binary Independence Model

O( R | q, x )  O( R | q) 
Constant for
each query, does
not depend on doc
• Retrieval Status Value:
pi (1  ui )
1  pi


xi  qi 1 ui (1  pi ) qi 1 1  ui
Only quantity to be estimated
for rankings
pi (1  ui )
pi (1  ui )
RSVd  log 
  log
ui (1  pi )
xi  qi 1
xi  qi 1 ui (1  pi )
Introduction to Information Retrieval
Binary Independence Model
• All boils down to computing RSV:
pi (1  ui )
pi (1  ui )
RSVd  log 
  log
ui (1  pi )
xi  qi 1
xi  qi 1 ui (1  pi )
• Equivalently,
pi (1  ui )
pi
1  ui
RSVd   ci ; ci  log
 log
 log
ui (1  pi )
1  pi
ui
xi qi 1
So, how do we compute ci’s from our data ?
Introduction to Information Retrieval
Binary Independence Model
• Estimating RSV coefficients.
• For each term i look at this table of document counts:
Docs
Relevant Non-Relevant
xi=1
xi=0
s
S–s
Total
S
Total
dfi – s
dfi
(N – dfi) – (S – s) N – dfi
N-S
N
s
df i  s
ui 
• Estimates: pi 
N S
S
pi (1  ui )
s ( S  s)
ci  K ( N , df i , S , s)  log
 log
ui (1  pi )
(df i  s) ((N  df i )  ( S  s))
Introduction to Information Retrieval
Binary Independence Model
• To avoid the possibility of zeroes (e.g., if every or no
relevant doc has a particular term) standard procedure
is to add ½ to each of the quantities in the center four
cells of the table of the previous slide. Accordingly:
( s  12 ) ( S  s  12 )
cˆi  K ( N , df i , S , s)  log
(df i  s  12 ) ( N  df i  S  s  12 )
Introduction to Information Retrieval
Estimation – key challenge
 If non-relevant documents are approximated by the
whole collection, then ui (prob. of occurrence in nonrelevant documents for query) is dfi /N and
 log (1– ui)/ui = log (N – dfi)/ dfi
≈ log N/dfi (assuming dfi small compared to N)
= IDF!
 pi (probability of occurrence in relevant documents)
can be estimated in various ways:
 from relevant documents if we 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)
Introduction to Information Retrieval
Iteratively estimating pi
1. Assume that pi constant over all xi in query

pi = 0.5 (even odds) for any given doc; in this case what is
RSVd   ci given ci  log
xi  qi 1
pi (1  ui )
pi
1  ui
?
 log
 log
ui (1  pi )
1  pi
ui
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 ui, 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

ui = (dfi – |Vi|) / (N – |V|)
4. Go to 2. until converges then return ranking
25
Introduction to Information Retrieval
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: partition
V into relevant VR and non-relevant VNR
3. Re-estimate pi and ui on the basis of these

Or can combine new information with original guess (use
(k )
|
VR
|


p
Bayesian prior):
i
i
pi( k 1) 
| VR | 
where  is prior weight and VRi is the set of docs in VR
containing xi.
4. Repeat, generating a succession of approximations to pi.
Introduction to Information Retrieval
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
Introduction to Information Retrieval
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