personal search

44
Personal Search Retrieval Model and Evaluation Jinyoung Kim UMass Amherst CS646 Lecture 1

Upload: harry

Post on 24-Feb-2016

67 views

Category:

Documents


0 download

DESCRIPTION

UMass Amherst CS646 Lecture. Personal Search. Retrieval Model and Evaluation. Jinyoung Kim. Outline. Personal Search Overview Retrieval Models for Personal Search Evaluation Methods for Personal Search Associative Browsing Model for Personal Info. Experimental Results. (optional). - PowerPoint PPT Presentation

TRANSCRIPT

On Personal Search

Personal SearchRetrieval Model and EvaluationJinyoung KimUMass Amherst CS646 Lecture1 I just became 4th year student. Feel free to interrupt me for questions!1OutlinePersonal Search Overview

Retrieval Models for Personal Search

Evaluation Methods for Personal Search

Associative Browsing Model for Personal Info.

Experimental Results

2(optional)So, this is pretty much what Ive done so far in UMass.2Personal Search Overview3Personal SearchWhatSearching over users own personal informationDesktop search is most common form

WhyPersonal information has grown over the yearsIn terms of the amount and heterogeneitySearch can help users access their informationQ : Is it the only option? How about browsing?44Typical ScenariosI'm looking for an email about my last flight

I want to retrieve all I've read about Apple iPad

I need to find a slide I wrote for IR seminar

Q : Anything else?5Personal Search ExampleQuery : James Registration

6

B> User wants to get back to the previous document. (known-item search)Relevant email was not found at top, swamped by other file types6Personal Search ExampleUser-defined ranking for type-specific resultsCan't we do better than this?

7B> Lets see whats happening under the hood.7Characteristics & Related ProblemsPeople mostly do re-findingKnown-item search

Many document typesFederated Search (Distributed IR)

Unique metadata for each typeSemi-structured document retrieval8Example : title, content, path (URL) is common / calendar item has place / For multimedia items retrieval, metadata is critical8Research IssuesHow can we exploit the document structure (e.g. metadata) for retrieval?

How can we evaluate personal search algorithms overcoming privacy concerns?

What are other methods for personal information access?e.g. Associative Browsing Model9Retrieval Model for Personal Search10Time: 9:1010Design ConsiderationsEach type has different characteristicsHow can we exploit type-specific features?e.g. email has a thread structure

Knowing the document type the user is looking for will be usefulHow can we make this prediction?

Users want to see the combined resultHow would you present the result?

11E> How would you design a retrieval model? e.g. Throwing all documents into single indexProblem is that we cant specialize the ranking for each document type.11Retrieval-Merge StrategyType-specific Ranking Use most suitable algorithm for each typeType Prediction Predict which document type user is looking forCombine into the Final Result Rank list merging

12So, we take a different approach from Spotlight example, yet changing between them is trivial12Type-specific RankingDocument-based Retrieval ModelScore each document as a wholeField-based Retrieval ModelCombine evidences from each field

q1 q2 ... qmDocument-based ScoringField-based Scoringf1f2fn...q1 q2 ... qmf1f2fn...f1f2fn...w1w2wnw1w2wn13B> Assume queries with m words, documents with n fields.F> Why will this work?Terms from shorter fields are better representedEach field can be weighted differently13Type-specific RankingDocument-based MethodsDocument Query-likelihood (DQL)

Field-based MethodsMixture of Field Language Models (MFLM)

wj is trained to maximize retrieval performancee.g. : 1 / : 0.5 / ...

Recalling from lecture on LM, were using the document or field as the source of language.Now we can assign weights to each field14Type-specific RankingExampleQuery : james registrationDocument fields : Term distribution

DQL vs. MFLM15P(q|f)james.sregist.sjames.cregist.cjames.tregist.tD1 (R)0/101/101/1005/1001/20/2D2 (NR)0/100/105/10020/1000/20/2DQL1 : (1+1)/112 * (5+1)/112

DQL2 : 5/112 * 20/112

DQL1 (0.105) < DQL2 (0.877)MFLM1 : (1/100+1/2) * (1/10+5/100)

MFLM2 : 5/100 * 20/100

MFLM1 (0.077) > MFLM2 (0.01)1> Relevant document (D1) has a few terms in metadata fields, whereas non-relevant document (D2) have many terms in contents.2> Field-based model can effectively use the evidence from shorter fields15Type-specific RankingProbabilistic Retrieval Model for Semi-structured data (PRM-S)[KXC09]Basic IdeaUse the probabilistic mapping between query-words and document fields for weighting

q1 q2 ... qmf1f2fn...f1f2fn...P(F1|q1)P(F2|q1)P(Fn|q1)P(F1|qm)P(F2|qm)P(Fn|qm)16

Change from MFLM : we use different field weight for each query-term16Type-specific RankingPRM-S Model [KXC09]Estimate the implicit mapping of each query word to document fields

Combine field-level evidences based on mapping probabilities

17 Fj: field of collection fj: field of each documentPM : combine prior and likelihood of mapping, where likelihood is essentially a query-likelihood of collection field language model - Its like classifying each query word into one of document fields, using term distribution17Type-specific RankingMFLM vs. PRM-S

18q1 q2 ... qmf1f2fn...f1f2fn...w1w2wnw1w2wnq1 q2 ... qmf1f2fn...f1f2fn...P(F1|q1)P(F2|q1)P(Fn|q1)P(F1|qm)P(F2|qm)P(Fn|qm)18Type-specific RankingWhy does PRM-S work?Relevant document has query-terms in many different fieldsPRM-S boosts PQL(q|f) when query-term is found in correct field(s)

19

B> Remember that our goal is to rank relevant as high up as possible.1> Correct field means where relevant document has the query-term in that fieldNow, document should have terms in correct field, in addition to 19Type-specific RankingPRM-S Model [KXC09]Performance in TREC Email Search TaskW3C mailing list collection150 known-item queries

Q : Will it work for other document types?e.g. webpages and office documents

(Mean Reciprocal Rank)20Answer : it doesnt work as well when the term distribution for each fields are not as distinct from each other20Predicting Document TypeA look on Federated Search (aka Distributed IR)There are many information silos (resources)Users want to search over all of themThree major problemsResource representationResource selectionResult merging

21

Predicting Document TypeQuery-likelihood of Collection [Si02]Get query-likelihood score for each collection LMTreat each collection as a big bag of wordsBest performance in recent evaluation [Thomas09]

Q : Can we exploit the field structure here?

22Type prediction is like resource selection, where each document type comprise individual collection22Predicting Document TypeField-based collection Query-Likelihood [KC10]Calculate QL score for each field of a collectionCombine Field-level scores into a collection score

Why it works?Terms from shorter fields are better representede.g. James from , registration from Recall why MFLM worked better than DQL

2323Merging into Final Rank ListWhat we have for each collectionType-specific rankingType score

CORI Algorithm for Merging[Callan95] Use normalized collection and document score

240.4 is a constant that can be tuned for performance

24Evaluation Methods for Personal Search25Time : 9:3525Challenges in Personal Search EvaluationHard to create a test-collectionEach user has different documents and habits

Privacy concernsPeople will not donate their documents and queries for research

Q : Cant we just do some user study?26Problems with User StudiesIts costlyA working system should be implementedParticipants should be using it for a long timeBig barrier for academic researchers

Data is not reusable by third partiesThe findings cannot be repeated by others

Q : How can we perform a cheap & repeatable evaluation?27Pseudo-desktop Method [KC09]Collect documents of reasonable size and variety

Generate queries automatically Randomly select a target documentTake terms from the document

Validate generated queries with manual queriesCollected by showing each document and asking:What is the query you might use to find this one?2828DocTrack Game [KC10]Basic IdeaThe user is shown a target documentThe user is asked to find the documentScore is given based on users search result

29Actual Demo of DocTrack

29DocTrack Game [KC10]BenefitsParticipants are motivated to contribute the dataResulting queries and logs are reusableFree from privacy concernMuch cheaper than doing a traditional user study

LimitationsArtificial data & task

30Actual Demo of DocTrack

30Experimental Results31Time : 9:50

31Experimental SettingPseudo-desktop CollectionsCrawl of W3C mailing list & documentsAutomatically generated queries100 queries / average length 2

CS CollectionUMass CS department webpages & emails & etc.Human-formulated queries from DocTrack game984 queries / average length 3.97

Other detailsMean Reciprocal Rank was used for evaluation32Collection StatisticsPseudo-desktop Collections

CS Collection

33(#Docs (Length))Type Prediction PerformancePseudo-desktop Collections

CS Collection

FQL improves performance over CQLCombining features improves the performance further

34(% of queries with correct prediction)Feature-based model is becoming quite common for most of IR tasks (LTR)34Pseudo-desktop Collections

CS CollectionRetrieval Performance

(Mean Reciprocal Rank)35Best : use best type-specific retrieval methodOracle : predict correct type perfectlyType prediction seems to have more impact on retrieval performance35Associative Browsing Model for Personal Information 36Time : 10:05

36MotivationKeyword search doesnt always workSometimes you dont have good keyword

Browsing can help here, yetHierarchical folder structure is restrictiveYou cant tag all your documents

Associative browsing as a solutionOur mind seems to work by associationLets use a similar model for personal info!37Data Model38

Show screencast if you have time38Building the ModelConcepts are extracted from metadatae.g. senders and receivers of email

Concept occurrences are found in documentsThe link between concepts and documents

We still need to find the link between concepts and between documentsThere are many ways of doing thatLets build a feature-based model, where weights are adjusted by users click feedback39Time ; 10:1539Summary40Time : 10:1540SummaryRetrieval ModelRetrieval-merge strategy works for personal searchExploiting field structure is helpful both for retrieval and type prediction

Evaluation MethodEvaluation itself is a challenge for personal searchReasonable evaluation can be done by simulation or game-based user study

Associative Browsing ModelSearch can be combined with other interaction models to enable better information access41More LessonsResembling users mental process is the key for the design of a retrieval modelThe mapping assumption of PRM-S model

Language models are useful for many taskse.g. Document LM / Field LM / Collection LM / ...

Each domain requires specialized retrieval model and evaluation methodSearch is never a solved problem!

42Major References[KXC09] A Probabilistic Retrieval Model for Semi-structured Data Jinyoung Kim, Xiaobing Xue and W. Bruce Croft in ECIR'09

[KC09] Retrieval Experiments using Pseudo-Desktop Collections Jinyoung Kim and W. Bruce Croft in CIKM'09

[KC10] Ranking using Multiple Document Types in Desktop Search Jinyoung Kim and W. Bruce Croft in SIGIR'10

[KBSC10] Building a Semantic Representation for Personal Information Jinyoung Kim, Anton Bakalov, David A. Smith and W. Bruce Croft in CIKM'10

4343Further ReferencesMy webpagehttp://www.cs.umass.edu/~jykim

Chapter in [CMS]Retrieval Models (Ch7) / Evaluation (Ch8)

Chapter in [MRS]XML Retrieval (Ch10) / Language Model (Ch12)44

P (Q|d) =mi=1

PQL(qi|d)

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

P (Q|d) =mi=1

nj=1

wjPQL(qi|fj)

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

P (Q|d) =mi=1

nj=1

PM (Fj |qi)PQL(qi|fj)

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

PM (Fj |qi) = PM (qi|Fj)PM (Fj)P (qi)

PQL(qi|Fj)PM (Fj)

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

P (Q|d) =mi=1

nj=1

wjPQL(qi|fj)

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

P (Q|d) =mi=1

nj=1

PM (Fj |qi)PQL(qi|fj)

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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

fr.chachatelier.pierre.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