Text Retrieval Issues

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Ranked Retrieval

LBSC 796/INFM 718R

Session 3

September 24, 2007

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Agenda

•Ranked retrieval

•

•Similarit= y-based ranking

•

•Probabili= ty-based ranking

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The Perfect Query Paradox

&#= 8226;Every information need has a perfect result set

&= #8211;All the relevant documents, no others

• <= /div>

= 226;Every result set has a (nearly) perfect query

&= #8211;AND every word to get a query for document 1

&= #8226;Use AND NOT for every other known word

&= #8211;Repeat for each document in the result set

&= #8211;OR them to get a query that retrieves the result set

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Boolean Retrieval

&#= 8226;Strong points

&= #8211;Accurate, if you know the right strategies

&= #8211;Efficient for the computer

&#= 8226;Weaknesses

&= #8211;Often results in too many documents, or none

&= #8211;Users must learn Boolean logic

&= #8211;Sometimes finds relationships that don’t exist

&= #8211;Words can have many meanings

&= #8211;Choosing the right words is sometimes hard

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Leveraging the User

Source

Selection

Query

Selection

Ranked List

Examination

Document

Delivery

Document

Query

Formulation

IR System

Indexing

Index

Acquisition

Collection

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Where Ranked Retrieval Fits

Documents

Query

Hits

= Representation

= Function

= Representation

= Function

Query Representation

Document Representation

= Comparison

= Function

Index

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Ranked Retrieval Paradigm

&#= 8226;Perform a fairly general search

&= #8211;One designed to retrieve more than is needed

» <= /div>

&#= 8226;Rank the documents in “best-first” order

&= #8211;Where best means “most likely to be relevant”

» <= /div>

&#= 8226;Display as a list of easily skimmed “surrogates”

&= #8211;E.g., snippets of text that contain query terms

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Advantages of Ranked Retrieval

&#= 8226;Leverages human strengths, covers weaknesses

&= #8211;Formulating precise queries can be difficult

&= #8211;People are good at recognizing what they want

» <= /div>

&#= 8226;Moves decisions from query to selection time

&= #8211;Decide how far down the list to go as you read it

» <= /div>

&#= 8226;Best-first ranking is an understandable idea

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Ranked Retrieval Challenges

&#= 8226;“Best first” is easy to say but hard to do!

&= #8211;Computationally, we can only approximate it

» <= /div>

&#= 8226;Some details will be opaque to the user

&= #8211;Query reformulation requires more guesswork

– <= /div>

&#= 8226;More expensive than Boolean

&= #8211;Storing evidence for “best” requires more space

&= #8211;Query processing time increases with query length

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Simple Example:
Partial-Match Ranking

&#= 8226;Form all possible result sets in this order:

&= #8211;AND all the terms to get the first set

&= #8211;AND all but the 1st term, all but the 2nd, …

&= #8211;AND all but the first two terms, …

&= #8211;And so on until every combination has been done

= 226;Remove duplicates from subsequent sets

&#= 8226;Display the sets in the order they were made

&= #8211;Document rank within a set is arbitrary

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Partial-Match Ranking Example

information AND retrieval

Readings in Information Retrieval

Information Storage and Retrieval

Speech-Based Information Retrieval for Digital Libraries

Word Sense Disambiguation and Information Retrieva= l

information NOT retrieval

The S= tate of the Art in Information Filtering

Inference Networks for Document Retrieval

Content-Based Image Retrieval Systems <= /div>

Video Parsing, Retrieval and Browsing <= /div>

An Approach to Conceptual Text Retrieval Using the EuroWordNet …

Cross-Language Retrieval: English/Russian/French

retrieval NOT information

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Agenda

•Ranked retrieval

•

ØSimilarity-based ranking

•

•Probabili= ty-based ranking

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What’s a Model?

&#= 8226;A construct to help understand a complex system

&= #8211;A particular way of “looking at things”

•

&#= 8226;Models inevitably make simplifying assumptions

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Similarity-Based Queries

&#= 8226;Model relevance as “similarity”

&= #8211;Rank documents by their similarity to the query

&#= 8226;Treat the query as if it were a document

&= #8211;Create a query bag-of-words

&#= 8226;Find its similarity to each document

&#= 8226;Rank order the documents by similarity

&#= 8226;Surprisingly, this works pretty well!

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Similarity-Based Queries

&#= 8226;Treat the query as if it were a document

&= #8211;Create a query bag-of-words

&#= 8226;Find the similarity of each document

&= #8211;Using the coordination measure, for example

&#= 8226;Rank order the documents by similarity

&= #8211;Most similar to the query first

&#= 8226;Surprisingly, this works pretty well!

&= #8211;Especially for very short queries

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Document Similarity

&#= 8226;How similar are two documents?

&= #8211;In particular, how similar is their bag of words?

1: Nuclear fallout contaminated Monta= na.

2: Information retrieval is interesti= ng.

3: Information retrieval is complica= ted.

nuclear=

fallout=

siberia=

contam= inated

intere= sting

compli= cated

inform= ation

retriev= al

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The Coordination Measure

&#= 8226;Count the number of terms in common

&= #8211;Based on Boolean bag-of-words

&#= 8226;Documents 2 and 3 share two common terms

&= #8211;But documents 1 and 2 share no terms at all

&#= 8226;Useful for “more like this” queries

&= #8211;“more like doc 2” would rank doc 3 ahead of doc 1

&#= 8226;Where have you seen this before?

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Coordination Measure Example

nuclear<= /span>

fallout<= /span>

siberia<= /span>

contami= nated

interes= ting

complic= ated

informa= tion

retrieva= l

Query: complicated retrieval

Result: 3, 2

Query: information retrieval

Result: 2, 3

Query: interesting nuclear fallout

Result: 1, 2

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Vector Space Model

Postulate: Documents that are “close together” in vector = space “talk about” = the same things

Therefore, retrieve documents based on how close the= document is to the query (i.e., similarity ~ “closeness”)

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Counting Terms

&#= 8226;Terms tell us about documents

&= #8211;If “rabbit” appears a lot, it may be about rabbits

&#= 8226;Documents tell us about terms

&= #8211;“the” is in every document -- not discriminating

= 226;Documents are most likely described well by rare terms that occur in = them frequently

&= #8211;Higher “term frequency” is stronger evidence

&#= 8211;Low “document frequency” makes it stronger still

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•McDo= nald's slims down spuds

Fast-food chain to reduce certain types of = = fat in its french fries with new cooking oil. =

NEW YORK (CNN/Money) - McDonald's Corp. = is cutting the amount of "bad" fat in its french fries nearly in ha= lf, the fast-food chain said Tuesday as it moves to make all its fried menu items healthier.

But does that mean the popular shoestring fries = won't taste the same? The company says no. "I= t's = a win-win for our customers because they are getting the same great french-fry taste along = with an even healthier nutrition profile," sa= id Mike Roberts, president of McDonald's USA.

But others are not so sure. McDonald's will not = specifically discuss the kind of oil it plans to u= se, but at least one nutrition expert says playing with the formula could mean a different taste. = ;

Shares of Oak Brook, Ill.-based McDonald's = <= span style=3D'font-size:57%'>(MCD: down $0.54 to $23.22, Research, Estimates) were lower Tuesday afternoon. It was <= span style=3D'font-size:57%'>unclear Tuesday whether competitors Burger = King and Wendy's International (WEN: down <= /span>$0.80 to $34.91, Research, Estimates) would = follow suit. Neither company could immediately = be reached for comment.

•…=

16 ×= ; said

14 × McDonalds

12 × fat

11 × fries

8 × new

6 × company, french, nutrition

5 ×= food, oil, percent, reduce,

taste, Tuesday

…&#= 13;

“Bag of Words”

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A Partial Solution: TF*IDF

&#= 8226;High TF is evidence of meaning

&#= 8226;Low DF is evidence of term importance

&#= 8211;Equivalently high “IDF”

&#= 8226;Multiply them to get a “term weight”

= 226;Add up the weights for each query term

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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

TF*IDF Example

nuclear<= /span>

fallout<= /span>

siberia<= /span>

contami= nated

interes= ting

complic= ated

informa= tion

retrieva= l

0.50

0.63

0.90

0.13

0.60

0.75

1.51

0.38

0.50

2.11

0.13

1.20

0.60

0.38

0.50

0.301

0.125

0.602

0.301

0.000

0.602

query:

contaminated retrieval

Result: 2, 3, 1, 4

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The Document Length Effect

&#= 8226;People want documents with useful parts

&= #8211;But scores are computed for the whole document

– <= /div>

&#= 8226;Document lengths vary in many collections

&#= 8211;So frequency could yield inconsistent resutls

– <= /div>

&#= 8226;Two strategies

&= #8211;Adjust term frequencies for document length

&= #8211;Divide the documents into equal “passages”

------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0103.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

Document Length Normalization

&#= 8226;Long documents have an unfair advantage

&= #8211;They use a lot of terms

&= #8226;So they get more matches than short documents

&= #8211;And they use the same words repeatedly

&= #8226;So they have much higher term frequencies

• <= /div>

&#= 8226;Normalization seeks to remove these effects

&= #8211;Related somehow to maximum term frequency

–

------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

“Cosine” Normalization

&#= 8226;Compute the length of each document vector

&= #8211;Multiply each weight by itself

&= #8211;Add all the resulting values

&= #8211;Take the square root of that sum

&#= 8226;Divide each weight by that length

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Cosine Normalization Example

0.29

0.37

0.53

<= span style=3D'font-size:58%;mso-special-format:lastCR;display:none'>

0.13

0.62

0.77

0.57

0.14

0.19

0.79

0.05

0.71

0.69

0.44

0.57

nuclear<= /span>

fallout<= /span>

siberia<= /span>

contami= nated

interes= ting

complic= ated

informa= tion

retrieva= l

0.50

0.63

0.90

0.13

0.60

0.75

1.51

0.38

0.50

2.11

0.13

1.20

0.60

0.38

0.50

0.301

0.125

0.602

0.301

0.000

0.602

1.70

0.97

2.67

0.87

Length=

query: contaminated retrieval, Resu= lt: 2, 4, 1, 3 (compare to 2, 3, 1, 4)

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Formally …

Document Vector

Query Vector

Inner Product

Length

Normalization

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Why Call It “Cosine”?

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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

Interpreting the Cosine Measure

&#= 8226;Think of query and the document as vectors

&= #8211;Query normalization does not change the ranking

&#= 8211;Square root does not change the ranking

&#= 8226;Similarity is the angle between two vectors

&#= 8211;Small angle =3D very similar

&#= 8211;Large angle =3D little similarity

&#= 8226;Passes some key sanity checks

&= #8211;Depends on pattern of word use but not on length

&#= 8211;Every document is most similar to itself

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“Okapi BM-25” Term Weight= s

TF component

IDF component

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Content-Location: file:///C:/B278E2C3/796f073c_files/slide0108_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAAa AAwAhAAAAAAAAA0LCgcCAAACBgsLDAkGBgQHDA0LCAcGCgQABAkLDA0HBgcJDA0HBAAECAsGAg0J BgQGCgcCAgsGBAICBgcEBgIGCgcHDAQAAgsGBgcGCAECAwECAwECAwECAwViICCOZDkGaIqabMsK A0oUpUGLsHyP8GEiiVKPhVAsTIxGqXg0OR4sW+nZgvhKEYnJ+pooS5Qvz8uKVHY4CxpgXosgl1EE w9aW4HI6QEAGIDJKGk1jX39KDio6AhtTiQEzACEAOy== ------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0108_image078.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAAElAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQD+ ACQAgAAAAAAAAALUhI+py+0bnpy02ouz3rx7GH3iSJbmiXZBmLbuC8fwKtf2jedHxOr+DwxKQj2h 8YisEZPMppPEKj6n1GqiJ7Vqt0dplgsOKxlfsfkMdZTR7LZlbYC75/QdhVbP6/EVuf5fxXex4gdo GERY+EB42CiSCBkpKYkyaXmJmam5ydnp+dlpkuhIisiooliqGiP4lroKO5PaGlsLVPhqq+tCe7X7 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Passage Retrieval

&#= 8226;Another approach to long-document problem

&= #8211;E.g., break it up into coherent units

&#= 8226;Recognizing topic boundaries can be hard

&= #8211;Overlapping 300 word passages work well

&#= 8226;Use best passage rank as the document’s rank

&= #8211;Passage ranking can also help focus examination

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Summary

= 226;Goal: find documents most similar to the query

– <= /div>

&#= 8226;Compute normalized document term weights

&= #8211;Some combination of TF, DF, and Length

– <= /div>

&#= 8226;Sum the weights for each query term

&= #8211;In linear algebra, this is an “inner product” operation

------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0348.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

Agenda

•Ranked retrieval

•

•Similarit= y-based ranking

•

ØProbability-based ranking

------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0116.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

The Key Idea

&#= 8226;We ask “is this document relevant?”

&= #8211;Vector space: we answer “somewhat”

&= #8211;Probabilistic: we answer “probably”

– <= /div>

&#= 8226;The key is to know what “probably” means

&= #8211;First, we’ll formalize that notion

&= #8211;Then we’ll apply it to ranking

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“Noisy-Channel” Model of= IR

Information need

Query

User has a information need, = “thinks” of a releva= nt document…

and writes down some queries

Information retrieval: given the query, guess the document it came from.

d= 1=

d= 2=

d= n=

document collection

…

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Where do the probabilities fit?

Comparison Function

Representation Function

Query Formulation

Human Judgment

Representation Function<= /div>

Retrieval Status Value

Utility

Query=

Information Need

Docum= ent

Query Representation

Document Representation

Query Processing

Document Processing

P(d is Rel | q)

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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhtQAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACgAz AAYAgAAAADMzzAIbhBGny+3PgoS0Womz3rz7D4ZiaGDWiTpJylYFADs= ------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0202.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

Probabilistic Inference

•Suppose there’s a horrible, but = very rare disease

•

•But there’s a very accurate test= for it

•

•Unfortuna= tely, you tested positive…

The probability that you contrac= ted it is 0.01%

The test is 99% accurate<= /div>

Should you panic?

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Bayes’ Theorem

•You want = to find

• <= /div>

•But you o= nly know

<= span class=3DB1B style=3D'position:absolute;left:-4.23%'>–How rare= the disease is

<= span class=3DB1B style=3D'position:absolute;left:-4.23%'>–How accu= rate the test is

<= span class=3DBB style=3D'position:absolute;left:-4.58%'>•Use Bayes= ’ Theorem (hence Bayesian Inference)

P(“have disease” | “test positive”)

Prior probability

Posterior probability

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Applying Bayes’ Theorem

Two cases:

1.You have the disease, and you tested positive

<= span style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-3.64%'= >2.You don’t have the disease, but= you tested positive (error)

Case 1: (0.0001)(0.99) =3D 0.000099

Case 2: (0.9999)(0.01) =3D 0.009999

Case 1+2 = =3D 0.010098

P(“have disease” | “test positive”)

=3D (0.99)(0.0001) / 0.010098

=3D 0.009804 < 1%

Don’t worry!

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Another View

In a population of one million people

100 are infected

999,900 are not

<= b>99

= test positive

= 1

= test negative

<= b>9999

= test positive

= 989901

= test negative

10098 will test positive…

Of those, only 99 really have the diseas= e!

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Probability

&#= 8226;Alternative definitions

&= #8211;Statistical: relative frequency as n ® ¥ <= /span>

&= #8211;Subjective: degree of belief

• <= /div>
&#= 8226;Thinking statistically

&= #8211;Imagine a finite amount of “stuff”

&= #8211;Associate the number 1 with the total amount

&= #8211;Distribute that “mass” over the possible events

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Statistical Independence

<= span class=3DBB style=3D'position:absolute;left:-4.47%'>•A and B a= re independent if and only if:

–    P(A and B) =3D P(A) <= span style=3D'font-family:Symbol;mso-char-type:symbol'>´ P(B) =

– <= /div>
•Independen= ce formalizes “unrelated”

<= span class=3DB1B style=3D'position:absolute;left:-4.23%'>–P(“= ;being brown eyed”) =3D 85/100

<= span class=3DB1B style=3D'position:absolute;left:-4.23%'>–P(“= ;being a doctor”) =3D 1/1000

<= span class=3DB1B style=3D'position:absolute;left:-3.7%'>–P(“= being a brown eyed doctor”) =3D 85/100,000

R= 11;

= 226;

Think of it this way. Out of 100,000 people, you expect a thousandth to be doctors -- that’s 100 people.=

Out of those 100 people, you expect 85 to have brown eyes. So you expect 85 of the original 100,000 to be brown-eyed doctors.

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Dependent Events

<= span class=3DBB style=3D'position:absolute;left:-4.31%'>•Suppose&#= 8221;

<= span class=3DB1B style=3D'position:absolute;left:-3.85%'>–P(“= ;having a B.S. degree”) =3D 2/10

<= span class=3DB1B style=3D'position:absolute;left:-3.85%'>–P(“= ;being a doctor”) =3D 1/1000

<= span class=3DBB style=3D'position:absolute;left:-4.31%'>•Would you expect

<= span class=3DB1B style=3D'position:absolute;left:-3.76%'>–P(“= ;having a B.S. degree and being a doctor”)

–    =3D 2/10,000   ???

<= span class=3DBB style=3D'position:absolute;left:-4.31%'>•Extreme example:

<= span class=3DB1B style=3D'position:absolute;left:-3.85%'>–P(“= ;being a doctor”) =3D 1/1000

<= span class=3DB1B style=3D'position:absolute;left:-3.85%'>–P(“= ;having studied anatomy”) =3D 12/1000

You know 10/1000 are doctors, and more than your average number of them (2 out of = 10) are likely to have a B.S. degree. If you assume they’re independent, the probability you get is very much an underestimate of the true probability.

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Conditional Probability

•P(A | B) º P(A and B) / P(B)

A

B

A an= d B

•<= /span> P(A= ) =3D prob of A relative to the whole space

• P(A= |B) =3D prob of A considering only the       <= span style=3D'font-size:133%'>         = ; cases where B is known to be true

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More on Conditional Probability

<= span class=3DBB style=3D'position:absolute;left:-3.86%'>•Suppose&#= 13;

<= span class=3DB1B style=3D'position:absolute;left:-3.44%'>–P(“= ;having studied anatomy”) =3D 12/1000

<= span class=3DB1B style=3D'position:absolute;left:-2.94%'>–P(“= ;being a doctor and having studied anatomy”) =3D 1/1000

<= span class=3DBB style=3D'position:absolute;left:-3.86%'>•Consider&= #13;

<= span class=3DB1B style=3D'position:absolute;left:-3.12%'>–P(“= ;being a doctor” | “having studied anatomy”) =3D 1/12 =

<= span class=3DBB style=3D'position:absolute;left:-3.38%'>•But if yo= u assume all doctors have studied anatomy

<= span class=3DB1B style=3D'position:absolute;left:-3.32%'>–P(“= ;having studied anatomy” | “being a doctor”) =3D 1

Useful restatemen= t of definition: P(A and B) =3D P= (A|B) x P(B)

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Some Notation

•Consider <= /div>
–A set of hypotheses:    H1, H2, H3 =

–Some observable eviden= ce    O

•<= /span>

•P(O|H1) =3D probabilit= y of O being observed

• =    if we knew H1 were true

•P(O|H2) =3D probabilit= y of O being observed

• =    if we knew H2 were true

•P(O|H3) =3D probabilit= y of O being observed

• =    if we knew H3 were t= rue

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An Example

•L= et

–O = =3D “Joe earns more than $100,000/year”

–H1= =3D “Joe is a doctor”

–H2= =3D “Joe is a college professor”

–H3= =3D “Joe works in food services”

•S= uppose we do a survey and we find out

–P(= O|H1) =3D 0.6

–P(= O|H2) =3D 0.07

–P(= O|H3) =3D 0.001

•W= hat should be our guess about Joe’s profession?

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Bayes’ Rule

= 226;What’s P(H1|O)? P(H2|O)? P(H3|O)?

&#= 8226;Theorem:

R= 11;

P(H | O)   =3D

P(O | = H) x P(H)

        P(O)

Posterior

probability

Prior

probability

•<= /span>Notice that the prior is very important!

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Back to the Example

&#= 8226;Suppose we also have good data about priors:

&= #8211;P(O|H1) =3D 0.6 P(H1) =3D 0.000= 1 docto= r

&= #8211;P(O|H2) =3D 0.07 P(H2) =3D 0.001=     pro= f

&= #8211;P(O|H3) =3D 0.001 P(H3) =3D 0.2=         food

&#= 8226;We can calculate

&= #8211;P(H1|O) =3D 0.00006 / P(“earning > $100K/year”)

&= #8211;P(H2|O) =3D 0.0007 / P(“earning > $100K/year”)

&= #8211;P(H3|O) =3D 0.0002 / P(“earning > $100K/year”)

Notice that in this example, the prior probabilities reflect the likelihood of someone having a particular kind of job, ignoring any information about income. E.g. we’= ;re supposing food services workers are estimated at 20% of the population. Thus the best guess about profes= sion prior to info about income would be food services worker.

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Key Ideas

&#= 8226;Defining probability using frequency

– <= /div>
&#= 8226;Statistical independence

– <= /div>
&#= 8226;Conditional probability

– <= /div>
&#= 8226;Bayes’ rule

•

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Probability Ranking Principle

&#= 8226;Assume binary relevance, document independence

&= #8211;Each document is either relevant or it is not

&= #8211;Relevance of one doc reveals nothing about another

– <= /div>
&#= 8226;Assume the searcher works down a ranked list

&= #8211;Seeking some number of relevant documents

– <= /div>
&#= 8226;Theorem (provable from assumptions):

–Documents should be ranked in order of decreasing probability of relevance to the query,

R= 11; P(d relevant-to q)

Notion of “partly relevant” in vector space models has been replaced= by yes-or-no -- document d is relevant or it’s not. The focus is then on the probabi= lity of the event “document d is in fact relevant to query q”.

Question: what are some counter-examples that show the assumptions are too strong?<= /font>

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Language Models

<= span class=3DBB style=3D'position:absolute;left:-4.1%'>•Probability distribution over strings of text

<= span class=3DB1B style=3D'position:absolute;left:-3.78%'>–How like= ly is a string in a given “language”?

– <= /div>
– <= /div>
– <= /div>
–

–

–

–

<= span class=3DBB style=3D'position:absolute;left:-4.51%'>•Probabili= ties depend on what language we’re modeling

p= 1 =3D P(“a qu= ick brown dog”)

p2 =3D P(“dog quick a brownR= 21;)

p= 3 =3D P(“бm= 9;страя brown dog”)

p= 4 =3D P(“бm= 9;страя соб&= #1072;ка”)

In a language model for English:= p1 > p2 > p3 > p4

In a language model for Russian:= p1 < p2 < p3 < p4

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Unigram Language Model

•Assume ea= ch word is generated independently

<= span class=3DB1B style=3D'position:absolute;left:-4.23%'>–Obviousl= y, this is not true…

<= span class=3DB1B style=3D'position:absolute;left:-4.23%'>–But it s= eems to work well in practice!

<= span class=3DBB style=3D'position:absolute;left:-4.13%'>•The proba= bility of a string, given a model:

The probability of a sequence= of words decomposes into a product of the probabilities of individual words

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A Physical Metaphor

•Colored balls are ran= domly drawn from an urn (with replacement)

• P (    )

•P (        = ;         ) =3D

=3D (4/9) ´ (2/9) ´ (4/9= ) ´ (3/9= )

words

M

• P (    )

´

• P (    )

´

• P (    )

´

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An Example

the

man

likes

the

woman

0.2

0.01

0.02

0.2

0.01

multiply

P(s | M) =3D 0.00000008 <= /div>

P(“the man likes the woman”|M)

=3D P(the|M) ´ P(man|M) ´ P(likes|M) ´ P(the|M) ´ P(man|M)

=3D 0.00000008

P(w) = w

0.2 the

0.1 a

0.01 man

0.01 woman

0.03 said

0.02 likes

…

Model M<= /b>

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Comparing Language Models

P(w) w

0.2 the

0.0001 yon

0.01 class

0.0005 maiden

0.0003 sayst

0.0001 pleaseth

…

Model M1

P(w) w

0.2 the

0.1 yon

0.001 class

0.01 maiden

0.03 sayst

0.02 pleaseth

…

Model M2=

maiden

class

pleaseth

yon

the

0.0005

0.01

0.0001

0.0001

0.2

0.01

0.001

0.02

0.1

0.2

P(s|M2) > P(s|M1)
What exactly does this mean?

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Retrieval w/ Language Models

•Build a m= odel for every document

•Rank docum= ent d based on P(MD | q)

•Expand us= ing Bayes’ Theorem

•

•

•

•

•Same as r= anking by P(q | MD)

P(q) i= s same for all documents; doesn’t change ranks

P(MD) [= the prior] is assumed to be the same for all d

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Visually …

Ranking by P(MD | q)…

Hey, what’s the probability this query came from you?=

model1

Hey, what’s the probabilit= y <= span style=3D'font-family:Arial;font-size:58%'>that you generated this query?

model1

is the same as ranki= ng by P(q | MD)

Hey, what’s the probability this query came from you?=

model2

Hey, what’s the probabilit= y <= span style=3D'font-family:Arial;font-size:58%'>that you generated this query?

model2

Hey, what’s the probability this query came from you?=

modeln

Hey, what’s the probabilit= y <= span style=3D'font-family:Arial;font-size:58%'>that you generated this query?

modeln

…

…

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Ranking Models?

Hey, what’s the probabilit= y that you generated this query?

model1

Ranking by P(q | MD)

Hey, what’s the probabilit= y that you generated this query?

model2

Hey, what’s the probabilit= y that you generated this query?

modeln

…

… is a model of document1

… is a model of document2

… is a model of documentn

… is the same = as ranking documents

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Building Document Models

•How do we build a la= nguage model for a document?

What’s in the urn?

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Physical metaphor:

What colored balls and how many of each?

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A First Try

•Simply count the frequencies in the document =3D maximum likelihood estimate=

M

• P (    ) =3D 1/2

• P (    ) =3D 1/4

• P (    ) =3D 1/4

P= (w|MS) =3D #(w,S) / |S|<= /div>
Sequence S

#(w,S) =3D number of times w occurs in S

|S| =3D length of S <= /div>

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Zero-Frequency Problem

&#= 8226;Suppose some event is not in our observation S

&= #8211;Model will assign zero probability to that event

M

• P (    ) =3D 1/2

• P (    ) =3D 1/4

• P (    ) =3D 1/4

Sequence S

• P (    )

•P (        = ;         ) =3D

=3D (1/2) ´ (1/4) ´ 0 ´ (1/4= ) =3D 0

• P (    )

´

• P (    )

´

• P (    )

´

!!

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Why is this a bad idea?

<= span class=3DBB style=3D'position:absolute;left:-3.96%'>•Modeling a document

<= span class=3DB1B style=3D'position:absolute;left:-3.03%'>–A word n= ot appearing doesn’t mean it’ll never appear…
<= span class=3DB1B style=3D'position:absolute;left:-3.4%'>–Safe to a= ssume that unseen words are rare, though

• <= /div>
<= span class=3DBB style=3D'position:absolute;left:-3.96%'>•Think of = the document model as a topic

<= span class=3DB1B style=3D'position:absolute;left:-3.01%'>–Many doc= uments that can be written about a single topic

<= span class=3DB1B style=3D'position:absolute;left:-2.99%'>–We try t= o guess the model is based on just one document

• <= /div>
<= span class=3DBB style=3D'position:absolute;left:-3.33%'>•Practical= effect: assigning zero probability to unseen words forces exact match=

------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/slide0225.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Text Retrieval Issues

Smoothing

P(w)

w

Maximum Likelihood Estimate

The solution: “smooth” the w= ord probabilities

Smoothed probability distribution

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Implementing Smoothing

<= span class=3DBB style=3D'position:absolute;left:-3.67%'>•Assign so= me small probability to unseen events

–But remem= ber to take away “probability mass” from other events

– <= /div>
<= span class=3DBB style=3D'position:absolute;left:-4.34%'>•Some tech= niques are easily understood

<= span class=3DB1B style=3D'position:absolute;left:-3.43%'>–Add one = to all the frequencies (including zero)

» <= /div>
<= span class=3DBB style=3D'position:absolute;left:-3.85%'>•More sophisticated methods improve ranking

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Recap: LM for IR

&#= 8226;Indexing-time:

&= #8211;Build a language model for every document

&#= 8226;Query-time Ranking

–Estimate the probability of generating the query = according to each model

= 211;Rank the documents according to these probabilities

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Language Model Advantages

<= span style=3D'mso-special-format:bullet;position:absolute;left:-4.26%'>•<= /span>Conceptually simple

•<= /span>

<= span style=3D'mso-special-format:bullet;position:absolute;left:-4.26%'>•<= /span>Explanatory value

•<= /span>

<= span style=3D'mso-special-format:bullet;position:absolute;left:-4.26%'>•<= /span>Exposes assumptions

•<= /span>

<= span style=3D'mso-special-format:bullet;position:absolute;left:-4.26%'>•<= /span>Minimizes reliance on heuristics

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Key Ideas

&#= 8226;Probabilistic methods formalize assumptions

&= #8211;Binary relevance

&= #8211;Document independence

&= #8211;Term independence

&= #8211;Uniform priors

&= #8211;Top-down scan

»
&#= 8226;Natural framework for combining evidence

&= #8211;e.g., non-uniform priors

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A Critique

&#= 8226;Most of the assumptions are not satisfied!

&= #8211;Searchers want utility, not relevance

&= #8211;Relevance is not binary

&= #8211;Terms are clearly not independent

&= #8211;Documents are often not independent

» <= /div>
&#= 8226;Smoothing techniques are somewhat ad hoc

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But It Works!

•Ranked retrieval parad= igm is powerful

–Well suited to human search strategies

»

•Probability theory has explanatory power

–At least we know where= the weak spots are

–Probabilities are good= for combining evidence

»

•Good implementations e= xist (e.g., Lemur)

–Effective, efficient, = and large-scale

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Comparison With Vector Space

&#= 8226;Similar in some ways

&= #8211;Term weights based on frequency

&= #8211;Terms often used as if they were independent

– <= /div>
&#= 8226;Different in others

&= #8211;Based on probability rather than similarity

&= #8211;Intuitions are probabilistic rather than geometric

–

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A Complete System

&#= 8226;Perform an initial Boolean query

&#= 8211;Balancing breadth with understandability

• <= /div>
&#= 8226;Rerank the results

&#= 8211;Using either Okapi or a language model

&#= 8211;Possibly also accounting for proximity, links, …

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One Minute Paper

•<= /span>Which assumption underlying the probabilistic retrieval model causes you the most concern, and why?

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Click to edit Master text styles

Second level

Third level

Fourth level

Fifth level

1

14

Start 2:00

18

Contrast this with Boolean retrieval

1) TF was always 1 or zero

2) Searchers mad to consider collection frequency

6

Start 1:20

Think of it this way. Out of 100,000 people, you expect= a thousandth to be doctors -- that’s 100 people. Out of those 100 people, you expect 85 to have brown eyes.= So you expect 85 of the original 100,000 to be brown-eyed doctors.<= /div>
You know 10/1000 are doctors, an= d more than your average number of them (2 out of 10) are likely to have a B.S. degree. If you assume they’re independent, the probability you get is very much an unde= restimate of the true probability.

Notice that in this example, the= prior probabilities reflect the likelihood of someone having a particular kind of job, ignoring any information about income. E.g. we’re supposing food services workers are estimated at 20% of the population. Thus the best guess about profess= ion prior to info about income would be food services worker.

Notion of “partly relevant= ” in vector space models has been replaced by yes-or-no -- document d is relevant or it’s not. = The focus is then on the probability of the event “document d is in fact relevant to query q”. Question: what are some counter-examples t= hat show the assumptions are too strong?
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gIsEndShow=3D0, NUM_VIS_SLDS=3D74, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0346.htm",1,-1,1),new hrefList("slide0084.htm",1,-1,1),new hrefList("= slide0088.htm",1,-1,1),new hrefList("slide0071.htm",1,-1,1),new hrefList("s= lide0345.htm",1,-1,1),new hrefList("slide0089.htm",1,-1,1),new hrefList("sl= ide0090.htm",1,-1,1),new hrefList("slide0091.htm",1,-1,1),new hrefList("sli= de0092.htm",1,-1,1),new hrefList("slide0093.htm",1,-1,1),new hrefList("slid= e0347.htm",1,-1,1),new hrefList("slide0149.htm",1,-1,1),new hrefList("slide= 0177.htm",1,-1,1),new hrefList("slide0094.htm",1,-1,1),new hrefList("slide0= 095.htm",1,-1,1),new hrefList("slide0096.htm",1,-1,1),new hrefList("slide00= 97.htm",1,-1,1),new hrefList("slide0178.htm",1,-1,1),new hrefList("slide009= 8.htm",1,-1,1),new hrefList("slide0349.htm",1,-1,1),new hrefList("slide0100= .htm",1,-1,1),new hrefList("slide0102.htm",1,-1,1),new hrefList("slide0099.= htm",1,-1,1),new hrefList("slide0103.htm",1,-1,1),new hrefList("slide0104.h= tm",1,-1,1),new hrefList("slide0105.htm",1,-1,1),new hrefList("slide0181.ht= m",1,-1,1),new hrefList("slide0106.htm",1,-1,1),new hrefList("slide0107.htm= ",1,-1,1),new hrefList("slide0108.htm",1,-1,1),new hrefList("slide0109.htm"= ,1,-1,1),new hrefList("slide0110.htm",1,-1,1),new hrefList("slide0348.htm",= 1,-1,1),new hrefList("slide0116.htm",1,-1,1),new hrefList("slide0216.htm",1= ,-1,1),new hrefList("slide0130.htm",1,-1,1),new hrefList("slide0202.htm",1,= -1,1),new hrefList("slide0203.htm",1,-1,1),new hrefList("slide0204.htm",1,-= 1,1),new hrefList("slide0205.htm",1,-1,1),new hrefList("slide0117.htm",1,-1= ,1),new hrefList("slide0118.htm",1,-1,1),new hrefList("slide0119.htm",1,-1,= 1),new hrefList("slide0120.htm",1,-1,1),new hrefList("slide0121.htm",1,-1,1= ),new hrefList("slide0122.htm",1,-1,1),new hrefList("slide0123.htm",1,-1,1)= ,new hrefList("slide0124.htm",1,-1,1),new hrefList("slide0125.htm",1,-1,1),= new hrefList("slide0126.htm",1,-1,1),new hrefList("slide0128.htm",1,-1,1),n= ew hrefList("slide0210.htm",1,-1,1),new hrefList("slide0212.htm",1,-1,1),ne= w hrefList("slide0213.htm",1,-1,1),new hrefList("slide0214.htm",1,-1,1),new= hrefList("slide0215.htm",1,-1,1),new hrefList("slide0218.htm",1,-1,1),new = hrefList("slide0219.htm",1,-1,1),new hrefList("slide0220.htm",1,-1,1),new h= refList("slide0221.htm",1,-1,1),new hrefList("slide0222.htm",1,-1,1),new hr= efList("slide0223.htm",1,-1,1),new hrefList("slide0224.htm",1,-1,1),new hre= fList("slide0225.htm",1,-1,1),new hrefList("slide0226.htm",1,-1,1),new href= List("slide0227.htm",1,-1,1),new hrefList("slide0228.htm",1,-1,1),new hrefL= ist("slide0137.htm",1,-1,1),new hrefList("slide0142.htm",1,-1,1),new hrefLi= st("slide0143.htm",1,-1,1),new hrefList("slide0144.htm",1,-1,1),new hrefLis= t("slide0350.htm",1,-1,1),new hrefList("slide0145.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('

' + ENDSHOW_MESG + '
') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="us-ascii" Text Retrieval Issues ------=_NextPart_01C7FE17.F134A2D0 Content-Location: file:///C:/B278E2C3/796f073c_files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

No= tes

Slide Show

Outline

1

Ranked Retrieval=

LBSC 796/INFM 718R

Session 3

September 24, 2007

2

Agenda

Ranked retrieval

Similarity-based ranking

Probability-based ranking

3

The Perfect Query Paradox

Every information need has a perfect result set

All the relevant documents, no others

Every result set has a (nearly) perfect query

AND every word to get a query for document 1

Use AND NOT for every other known word

Repeat for each document in the result set

OR them to get a query that retrieves the result set

4

Boolean Retrieva= l

Strong points

Accurate, if you know the right strategies

Efficient for the computer

Weaknesses

Often results in too many documents, or none

Users must learn Boolean logic

Sometimes finds relationships that don’t exist

Words can have many meanings

Choosing the right words is sometimes hard

5

Leveraging the U= ser

6

Where Ranked Ret= rieval Fits

7

Ranked Retrieval Paradigm

Perform a fairly general search

One designed to retrieve more than is needed

Rank the documents in “best-first” order

Where best means “most likely to be relevant”

Display as a list of easily skimmed “surrogates”

E.g., snippets of text that contain query terms

8

Advantages of Ra= nked Retrieval

Leverages human strengths, covers weaknesses

Formulating precise queries can be difficult

People are good at recognizing what they want

Moves decisions from query to selection time

Decide how far down the list to go as you read it

Best-first ranking is an understandable idea

9

Ranked Retrieval Challenges

“Best first” is easy to say but hard to do!

Computationally, we can only approximate it

Some details will be opaque to the user

Query reformulation requires more guesswork

More expensive than Boolean

Storing evidence for “best” requires more space

Query processing time increases with query length

10

Simple Example:=
Partial-Match Ranking

Form all possible result sets in this order:

AND all the terms to get the first set

AND all but the 1st term, all but the 2nd, …

AND all but the first two terms, …

And so on until every combination has been done

Remove duplicates from subsequent sets

Display the sets in the order they were made

Document rank within a set is arbitrary

11

Partial-Match R= anking Example

12

Agenda

Ranked retrieval

Similarity-based ranking

Probability-based ranking

13

What’s a = Model?

A construct to help understand a complex system

A particular way of “looking at things”

Models inevitably make simplifying assumptions

14

Similarity-Based Queries

Model relevance as “similarity”

Rank documents by their similarity to the query

Treat the query as if it were a document

Create a query bag-of-words

Find its similarity to each document

Rank order the documents by similarity

Surprisingly, this works pretty well!

15

Similarity-Based Queries

Treat the query as if it were a document

Create a query bag-of-words

Find the similarity of each document

Using the coordination measure, for example

Rank order the documents by similarity

Most similar to the query first

Surprisingly, this works pretty well!

Especially for very short queries

16

Document Simila= rity

How similar are two documents?

In particular, how similar is their bag of words?

17

The Coordination Measure

Count the number of terms in common

Based on Boolean bag-of-words

Documents 2 and 3 share two common terms

But documents 1 and 2 share no terms at all

Useful for “more like this” queries

“more like doc 2” would rank doc 3 ahead of doc 1

Where have you seen this before?

18

Coordination Me= asure Example

19

Vector Space Mo= del

20

Counting Terms<= /a>

Terms tell us about documents

If “rabbit” appears a lot, it may be about rabbits

Documents tell us about terms

“the” is in every document -- not discriminating

Documents are most likely described well by rare terms that occur in them frequently

Higher “term frequency” is stronger evidence

Low “document frequency” makes it stronger still

21

"McDonald'= s slims down spuds"

McDonald's slims down spuds

Fast-food chain to reduce certain types of fat in its french fries w= ith new cooking oil.

NEW YORK (CNN/Money) - McDonald's Corp. is cutting the amount of "bad" fat in its french fries nearly in half, the fast-food chain said Tuesday as it moves to make all its fried menu items healthier.

But does that mean the popular shoestring fries won't taste the same? The company says no. "It's a win-win for our customers because = they are getting the same great french-fry taste along with an even healt= hier nutrition profile," said Mike Roberts, president of McDonald's = USA.

But others are not so sure. McDonald's will not specifically discuss= the kind of oil it plans to use, but at least one nutrition expert says playing with the formula could mean a different taste.

Shares of Oak Brook, Ill.-based McDonald's (MCD: down $0.54 to $23.2= 2, Research, Estimates) were lower Tuesday afternoon. It was unclear Tuesday whether competitors Burger King and Wendy's International (W= EN: down $0.80 to $34.91, Research, Estimates) would follow suit. Neither company could immediately be reached for comment.

…

16 × said

14 × McDonalds

12 × fat

11 × fries

8 × new

6 × company, french, nutrition

5 × food, oil, percent, reduce,

      taste, Tuesday

…

22

A Partial Solut= ion: TF*IDF

High TF is evidence of meaning

Low DF is evidence of term importance

Equivalently high “IDF”

Multiply them to get a “term weight”

Add up the weights for each query term

23

TF*IDF Example<= /a>

24

The Document Le= ngth Effect

People want documents with useful parts

But scores are computed for the whole document

Document lengths vary in many collections

So frequency could yield inconsistent resutls

Two strategies

Adjust term frequencies for document length

Divide the documents into equal “passages”

25

Document Length Normalization

Long documents have an unfair advantage

They use a lot of terms

So they get more matches than short documents

And they use the same words repeatedly

So they have much higher term frequencies

Normalization seeks to remove these effects

Related somehow to maximum term frequency

26

“Cosine&#= 8221; Normalization

Compute the length of each document vector

Multiply each weight by itself

Add all the resulting values

Take the square root of that sum

Divide each weight by that length

27

Cosine Normaliz= ation Example

28

Formally …= ;

29

Why Call It “Cosine”?

30

Interpreting th= e Cosine Measure

Think of query and the document as vectors

Query normalization does not change the ranking

Square root does not change the ranking

Similarity is the angle between two vectors

Small angle =3D very similar

Large angle =3D little similarity

Passes some key sanity checks

Depends on pattern of word use but not on length

Every document is most similar to itself

31

“Okapi BM-25” Term Weights

32

Passage Retriev= al

Another approach to long-document problem

E.g., break it up into coherent units

Recognizing topic boundaries can be hard

Overlapping 300 word passages work well

Use best passage rank as the document’s rank

Passage ranking can also help focus examination

33

Summary

Goal: find documents most similar to the query

Compute normalized document term weights

Some combination of TF, DF, and Length

Sum the weights for each query term

In linear algebra, this is an “inner product” operation=

34

Agenda

Ranked retrieval

Similarity-based ranking

Probability-based ranking

35

The Key Idea

We ask “is this document relevant?”

Vector space: we answer “somewhat”

Probabilistic: we answer “probably”

The key is to know what “probably” means

First, we’ll formalize that notion

Then we’ll apply it to ranking

36

“Noisy-Ch= annel” Model of IR

37

Where do the probabilities fit?

38

Probabilistic I= nference

Suppose there’s a horrible, but very rare disease

But there’s a very accurate test for it

Unfortunately, you tested positive…

39

Bayes’ Th= eorem

You want to find

But you only know

How rare the disease is

How accurate the test is

Use Bayes’ Theorem (hence Bayesian Inference)

40

Applying Bayes&= #8217; Theorem

41

Another View

42

Probability=

Alternative definitions

Statistical: relative frequency as n ® ¥
Subjective: degree of belief<= /li>

Thinking statistically

Imagine a finite amount of “stuff”

Associate the number 1 with the total amount

Distribute that “mass” over the possible events

43

Statistical Independence

A and B are independent if and only if:

    P(A and = B) =3D P(A) ´ P(B)

Independence formalizes “unrelated”

P(“being brown eyed”) =3D 85/100

P(“being a doctor”) =3D 1/1000

P(“being a brown eyed doctor”) =3D 85/100,000

44

Dependent Event= s

Suppose”

P(“having a B.S. degree”) =3D 2/10

P(“being a doctor”) =3D 1/1000

Would you expect

P(“having a B.S. degree and being a doctor”)

   =3D 2/10,000<= span style=3D'mso-spacerun:yes'>   ???

Extreme example:

P(“being a doctor”) =3D 1/1000

P(“having studied anatomy”) =3D 12/1000

45

Conditional Pro= bability

P(A | B) º P(A and B) / P(B)

46

More on Conditi= onal Probability

Suppose

P(“having studied anatomy”) =3D 12/1000

P(“being a doctor and having studied anatomy”) =3D 1/10= 00

Consider

P(“being a doctor” | “having studied anatomy̶= 1;) =3D 1/12

But if you assume all doctors have studied anatomy

P(“having studied anatomy” | “being a doctor̶= 1;) =3D 1

47

Some Notation

Consider

A set of hypotheses:    H1, H2, H3

Some observable evidence &nb= sp; O

P(O|H1) =3D probability of O being observed

   if we knew H= 1 were true

P(O|H2) =3D probability of O being observed

   if we knew H= 2 were true

P(O|H3) =3D probability of O being observed

   if we knew H= 3 were true

48

An Example<= /font>

Let

O =3D “Joe earns more than $100,000/year”

H1 =3D “Joe is a doctor”

H2 =3D “Joe is a college professor”

H3 =3D “Joe works in food services”

Suppose we do a survey and we find out

P(O|H1) =3D 0.6

P(O|H2) =3D 0.07

P(O|H3) =3D 0.001

What should be our guess about Joe’s profession?

49

Bayes’ Ru= le

What’s P(H1|O)? P(H2|O)? P(H3|O= )?

Theorem:

50

Back to the Exa= mple

Suppose we also have good data about priors:

P(O|H1) =3D 0.6 P(H1) =3D 0.0001&n= bsp; doctor

P(O|H2) =3D 0.07 P(H2) =3D 0.001    prof

P(O|H3) =3D 0.001 P(H3) =3D 0.2      &nbs= p; food

We can calculate

P(H1|O) =3D 0.00006 / P(“earning > $100K/year”)

P(H2|O) =3D 0.0007 / P(“earning > $100K/year”)

P(H3|O) =3D 0.0002 / P(“earning > $100K/year”)

51

Key Ideas

Defining probability using frequency

Statistical independence

Conditional probability

Bayes’ rule

52

Probability Ran= king Principle

Assume binary relevance, document independence

Each document is either relevant or it is not

Relevance of one doc reveals nothing about another

Assume the searcher works down a ranked list

Seeking some number of relevant documents

Theorem (provable from assumptions):

Documents should be ranked in order of decreasing probability of relevance to the query,

P(d relevant-to q)

53

Language Models=

Probability distribution over strings of text

How likely is a string in a given “language”?

Probabilities depend on what language we’re modeling

54

Unigram Languag= e Model

Assume each word is generated independently

Obviously, this is not true…

But it seems to work well in practice!

The probability of a string, given a model:

55

A Physical Meta= phor

Colored balls are randomly drawn from an urn (with replacement)

56

An Example<= /font>

57

Comparing Langu= age Models

58

Retrieval w/ La= nguage Models

Build a model for every document

Rank document d based on P(M_D | q)

Expand using Bayes’ Theorem

Same as ranking by P(q | M_D)

59

Visually …= ;

60

Ranking Models?=

61

Building Docume= nt Models

How do we build a language model for a document?

62

A First Try=

Simply count the frequencies in the document =3D maximum likelihood estimate

63

Zero-Frequency = Problem

Suppose some event is not in our observation S

Model will assign zero probability to that event

64

Why is this a b= ad idea?

Modeling a document

A word not appearing doesn’t mean it’ll never appear= 230;

Safe to assume that unseen words are rare, though

Think of the document model as a topic

Many documents that can be written about a single topic

We try to guess the model is based on just one document

Practical effect: assigning zero probability to unseen words forces exact match

65

Smoothing

66

Implementing Sm= oothing

Assign some small probability to unseen events

But remember to take away “probability mass” from other events

Some techniques are easily understood

Add one to all the frequencies (including zero)

More sophisticated methods improve ranking

67

Recap: LM for I= R

Indexing-time:

Build a language model for every document

Query-time Ranking

Estimate the probability of generating the query according to each model

Rank the documents according to these probabilities

68

Language Model Advantages

Conceptually simple

Explanatory value

Exposes assumptions

Minimizes reliance on heuristics

69

Key Ideas

Probabilistic methods formalize assumptions

Binary relevance

Document independence

Term independence

Uniform priors

Top-down scan

Natural framework for combining evidence

e.g., non-uniform priors

70

A Critique<= /font>

Most of the assumptions are not satisfied!

Searchers want utility, not relevance

Relevance is not binary

Terms are clearly not independent

Documents are often not independent

Smoothing techniques are somewhat ad hoc

71

But It Works!

Ranked retrieval paradigm is powerful

Well suited to human search strategies

Probability theory has explanatory power

At least we know where the weak spots are

Probabilities are good for combining evidence

Good implementations exist (e.g., Lemur)

Effective, efficient, and large-scale

72

Comparison With= Vector Space

Similar in some ways

Term weights based on frequency

Terms often used as if they were independent

Different in others

Based on probability rather than similarity

Intuitions are probabilistic rather than geometric

73

A Complete Syst= em

Perform an initial Boolean query

Balancing breadth with understandability

Rerank the results

Using either Okapi or a language model

Possibly also accounting for proximity, links, …

74

One Minute Pape= r

Which assumption underlying the probabilistic retrieval model causes= you the most concern, and why?

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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	Contrast this with Boolean retrieval

	1) TF was always 1 or zero
	2) Searchers mad to consider collection frequency


	Think of it this way. Out of 100,000 people, you expect a thousandth to be doctors -- that’s 100 people.=
	Out of those 100 people, you expect 85 to have brown eyes. So you expect 85 of the original 100,000 to be brown-eyed doctors.


	You know 10/1000 are doctors, and more than your average number of them (2 out of = 10) are likely to have a B.S. degree. If you assume they’re independent, the probability you get is very much an underestimate of the true probability.


	Notice that in this example, the prior probabilities reflect the likelihood of someone having a particular kind of job, ignoring any information about income. E.g. we’= ;re supposing food services workers are estimated at 20% of the population. Thus the best guess about profes= sion prior to info about income would be food services worker.


	Notion of “partly relevant” in vector space models has been replaced= by yes-or-no -- document d is relevant or it’s not. The focus is then on the probabi= lity of the event “document d is in fact relevant to query q”.
	Question: what are some counter-examples that show the assumptions are too strong?<= /font>

1	Ranked Retrieval= LBSC 796/INFM 718R Session 3 September 24, 2007
2	Agenda Ranked retrieval Similarity-based ranking Probability-based ranking
3	The Perfect Query Paradox Every information need has a perfect result set All the relevant documents, no others Every result set has a (nearly) perfect query AND every word to get a query for document 1 Use AND NOT for every other known word Repeat for each document in the result set OR them to get a query that retrieves the result set
4	Boolean Retrieva= l Strong points Accurate, if you know the right strategies Efficient for the computer Weaknesses Often results in too many documents, or none Users must learn Boolean logic Sometimes finds relationships that don’t exist Words can have many meanings Choosing the right words is sometimes hard
5	Leveraging the U= ser
6	Where Ranked Ret= rieval Fits
7	Ranked Retrieval Paradigm Perform a fairly general search One designed to retrieve more than is needed Rank the documents in “best-first” order Where best means “most likely to be relevant” Display as a list of easily skimmed “surrogates” E.g., snippets of text that contain query terms
8	Advantages of Ra= nked Retrieval Leverages human strengths, covers weaknesses Formulating precise queries can be difficult People are good at recognizing what they want Moves decisions from query to selection time Decide how far down the list to go as you read it Best-first ranking is an understandable idea
9	Ranked Retrieval Challenges “Best first” is easy to say but hard to do! Computationally, we can only approximate it Some details will be opaque to the user Query reformulation requires more guesswork More expensive than Boolean Storing evidence for “best” requires more space Query processing time increases with query length
10	Simple Example:= Partial-Match Ranking Form all possible result sets in this order: AND all the terms to get the first set AND all but the 1st term, all but the 2nd, … AND all but the first two terms, … And so on until every combination has been done Remove duplicates from subsequent sets Display the sets in the order they were made Document rank within a set is arbitrary
11	Partial-Match R= anking Example
12	Agenda Ranked retrieval Similarity-based ranking Probability-based ranking
13	What’s a = Model? A construct to help understand a complex system A particular way of “looking at things” Models inevitably make simplifying assumptions
14	Similarity-Based Queries Model relevance as “similarity” Rank documents by their similarity to the query Treat the query as if it were a document Create a query bag-of-words Find its similarity to each document Rank order the documents by similarity Surprisingly, this works pretty well!
15	Similarity-Based Queries Treat the query as if it were a document Create a query bag-of-words Find the similarity of each document Using the coordination measure, for example Rank order the documents by similarity Most similar to the query first Surprisingly, this works pretty well! Especially for very short queries
16	Document Simila= rity How similar are two documents? In particular, how similar is their bag of words?
17	The Coordination Measure Count the number of terms in common Based on Boolean bag-of-words Documents 2 and 3 share two common terms But documents 1 and 2 share no terms at all Useful for “more like this” queries “more like doc 2” would rank doc 3 ahead of doc 1 Where have you seen this before?
18	Coordination Me= asure Example
19	Vector Space Mo= del
20	Counting Terms<= /a> Terms tell us about documents If “rabbit” appears a lot, it may be about rabbits Documents tell us about terms “the” is in every document -- not discriminating Documents are most likely described well by rare terms that occur in them frequently Higher “term frequency” is stronger evidence Low “document frequency” makes it stronger still
21	"McDonald'= s slims down spuds" McDonald's slims down spuds Fast-food chain to reduce certain types of fat in its french fries w= ith new cooking oil. NEW YORK (CNN/Money) - McDonald's Corp. is cutting the amount of "bad" fat in its french fries nearly in half, the fast-food chain said Tuesday as it moves to make all its fried menu items healthier. But does that mean the popular shoestring fries won't taste the same? The company says no. "It's a win-win for our customers because = they are getting the same great french-fry taste along with an even healt= hier nutrition profile," said Mike Roberts, president of McDonald's = USA. But others are not so sure. McDonald's will not specifically discuss= the kind of oil it plans to use, but at least one nutrition expert says playing with the formula could mean a different taste. Shares of Oak Brook, Ill.-based McDonald's (MCD: down $0.54 to $23.2= 2, Research, Estimates) were lower Tuesday afternoon. It was unclear Tuesday whether competitors Burger King and Wendy's International (W= EN: down $0.80 to $34.91, Research, Estimates) would follow suit. Neither company could immediately be reached for comment. … 16 × said 14 × McDonalds 12 × fat 11 × fries 8 × new 6 × company, french, nutrition 5 × food, oil, percent, reduce, taste, Tuesday …
22	A Partial Solut= ion: TF*IDF High TF is evidence of meaning Low DF is evidence of term importance Equivalently high “IDF” Multiply them to get a “term weight” Add up the weights for each query term
23	TF*IDF Example<= /a>
24	The Document Le= ngth Effect People want documents with useful parts But scores are computed for the whole document Document lengths vary in many collections So frequency could yield inconsistent resutls Two strategies Adjust term frequencies for document length Divide the documents into equal “passages”
25	Document Length Normalization Long documents have an unfair advantage They use a lot of terms So they get more matches than short documents And they use the same words repeatedly So they have much higher term frequencies Normalization seeks to remove these effects Related somehow to maximum term frequency
26	“Cosine&#= 8221; Normalization Compute the length of each document vector Multiply each weight by itself Add all the resulting values Take the square root of that sum Divide each weight by that length
27	Cosine Normaliz= ation Example
28	Formally …= ;
29	Why Call It “Cosine”?
30	Interpreting th= e Cosine Measure Think of query and the document as vectors Query normalization does not change the ranking Square root does not change the ranking Similarity is the angle between two vectors Small angle =3D very similar Large angle =3D little similarity Passes some key sanity checks Depends on pattern of word use but not on length Every document is most similar to itself
31	“Okapi BM-25” Term Weights
32	Passage Retriev= al Another approach to long-document problem E.g., break it up into coherent units Recognizing topic boundaries can be hard Overlapping 300 word passages work well Use best passage rank as the document’s rank Passage ranking can also help focus examination
33	Summary Goal: find documents most similar to the query Compute normalized document term weights Some combination of TF, DF, and Length Sum the weights for each query term In linear algebra, this is an “inner product” operation=
34	Agenda Ranked retrieval Similarity-based ranking Probability-based ranking
35	The Key Idea We ask “is this document relevant?” Vector space: we answer “somewhat” Probabilistic: we answer “probably” The key is to know what “probably” means First, we’ll formalize that notion Then we’ll apply it to ranking
36	“Noisy-Ch= annel” Model of IR
37	Where do the probabilities fit?
38	Probabilistic I= nference Suppose there’s a horrible, but very rare disease But there’s a very accurate test for it Unfortunately, you tested positive…
39	Bayes’ Th= eorem You want to find But you only know How rare the disease is How accurate the test is Use Bayes’ Theorem (hence Bayesian Inference)
40	Applying Bayes&= #8217; Theorem
41	Another View
42	Probability= Alternative definitions Statistical: relative frequency as n ® ¥ Subjective: degree of belief<= /li> Thinking statistically Imagine a finite amount of “stuff” Associate the number 1 with the total amount Distribute that “mass” over the possible events
43	Statistical Independence A and B are independent if and only if: P(A and = B) =3D P(A) ´ P(B) Independence formalizes “unrelated” P(“being brown eyed”) =3D 85/100 P(“being a doctor”) =3D 1/1000 P(“being a brown eyed doctor”) =3D 85/100,000
44	Dependent Event= s Suppose” P(“having a B.S. degree”) =3D 2/10 P(“being a doctor”) =3D 1/1000 Would you expect P(“having a B.S. degree and being a doctor”) =3D 2/10,000<= span style=3D'mso-spacerun:yes'> ??? Extreme example: P(“being a doctor”) =3D 1/1000 P(“having studied anatomy”) =3D 12/1000
45	Conditional Pro= bability P(A \| B) º P(A and B) / P(B)
46	More on Conditi= onal Probability Suppose P(“having studied anatomy”) =3D 12/1000 P(“being a doctor and having studied anatomy”) =3D 1/10= 00 Consider P(“being a doctor” \| “having studied anatomy̶= 1;) =3D 1/12 But if you assume all doctors have studied anatomy P(“having studied anatomy” \| “being a doctor̶= 1;) =3D 1
47	Some Notation Consider A set of hypotheses: H1, H2, H3 Some observable evidence &nb= sp; O P(O\|H1) =3D probability of O being observed if we knew H= 1 were true P(O\|H2) =3D probability of O being observed if we knew H= 2 were true P(O\|H3) =3D probability of O being observed if we knew H= 3 were true
48	An Example<= /font> Let O =3D “Joe earns more than $100,000/year” H1 =3D “Joe is a doctor” H2 =3D “Joe is a college professor” H3 =3D “Joe works in food services” Suppose we do a survey and we find out P(O\|H1) =3D 0.6 P(O\|H2) =3D 0.07 P(O\|H3) =3D 0.001 What should be our guess about Joe’s profession?
49	Bayes’ Ru= le What’s P(H1\|O)? P(H2\|O)? P(H3\|O= )? Theorem:
50	Back to the Exa= mple Suppose we also have good data about priors: P(O\|H1) =3D 0.6 P(H1) =3D 0.0001&n= bsp; doctor P(O\|H2) =3D 0.07 P(H2) =3D 0.001 prof P(O\|H3) =3D 0.001 P(H3) =3D 0.2 &nbs= p; food We can calculate P(H1\|O) =3D 0.00006 / P(“earning > $100K/year”) P(H2\|O) =3D 0.0007 / P(“earning > $100K/year”) P(H3\|O) =3D 0.0002 / P(“earning > $100K/year”)
51	Key Ideas Defining probability using frequency Statistical independence Conditional probability Bayes’ rule
52	Probability Ran= king Principle Assume binary relevance, document independence Each document is either relevant or it is not Relevance of one doc reveals nothing about another Assume the searcher works down a ranked list Seeking some number of relevant documents Theorem (provable from assumptions): Documents should be ranked in order of decreasing probability of relevance to the query, P(d relevant-to q)
53	Language Models= Probability distribution over strings of text How likely is a string in a given “language”? Probabilities depend on what language we’re modeling
54	Unigram Languag= e Model Assume each word is generated independently Obviously, this is not true… But it seems to work well in practice! The probability of a string, given a model:
55	A Physical Meta= phor Colored balls are randomly drawn from an urn (with replacement)
56	An Example<= /font>
57	Comparing Langu= age Models
58	Retrieval w/ La= nguage Models Build a model for every document Rank document d based on P(M_D \| q) Expand using Bayes’ Theorem Same as ranking by P(q \| M_D)
59	Visually …= ;
60	Ranking Models?=
61	Building Docume= nt Models How do we build a language model for a document?
62	A First Try= Simply count the frequencies in the document =3D maximum likelihood estimate
63	Zero-Frequency = Problem Suppose some event is not in our observation S Model will assign zero probability to that event
64	Why is this a b= ad idea? Modeling a document A word not appearing doesn’t mean it’ll never appear= 230; Safe to assume that unseen words are rare, though Think of the document model as a topic Many documents that can be written about a single topic We try to guess the model is based on just one document Practical effect: assigning zero probability to unseen words forces exact match
65	Smoothing
66	Implementing Sm= oothing Assign some small probability to unseen events But remember to take away “probability mass” from other events Some techniques are easily understood Add one to all the frequencies (including zero) More sophisticated methods improve ranking
67	Recap: LM for I= R Indexing-time: Build a language model for every document Query-time Ranking Estimate the probability of generating the query according to each model Rank the documents according to these probabilities
68	Language Model Advantages Conceptually simple Explanatory value Exposes assumptions Minimizes reliance on heuristics
69	Key Ideas Probabilistic methods formalize assumptions Binary relevance Document independence Term independence Uniform priors Top-down scan Natural framework for combining evidence e.g., non-uniform priors
70	A Critique<= /font> Most of the assumptions are not satisfied! Searchers want utility, not relevance Relevance is not binary Terms are clearly not independent Documents are often not independent Smoothing techniques are somewhat ad hoc
71	But It Works! Ranked retrieval paradigm is powerful Well suited to human search strategies Probability theory has explanatory power At least we know where the weak spots are Probabilities are good for combining evidence Good implementations exist (e.g., Lemur) Effective, efficient, and large-scale
72	Comparison With= Vector Space Similar in some ways Term weights based on frequency Terms often used as if they were independent Different in others Based on probability rather than similarity Intuitions are probabilistic rather than geometric
73	A Complete Syst= em Perform an initial Boolean query Balancing breadth with understandability Rerank the results Using either Okapi or a language model Possibly also accounting for proximity, links, …
74	One Minute Pape= r Which assumption underlying the probabilistic retrieval model causes= you the most concern, and why?