Lecture 9 Probabilistic Retrieval Principles of Information Retrieval

Lecture 9: Probabilistic Retrieval Principles of Information Retrieval Prof. Ray Larson University of California, Berkeley School of Information Tuesday and Thursday 10: 30 am - 12: 00 pm Spring 2007 http: //courses. ischool. berkeley. edu/i 240/s 07 IS 240 – Spring 2007. 02. 13 - SLIDE 1

Mini-TREC • Need to make groups – Today • Systems – SMART (not recommended…) • ftp: //ftp. cs. cornell. edu/pub/smart – MG (We have a special version if interested) • http: //www. mds. rmit. edu. au/mg/welcome. html – Cheshire II & 3 • II = ftp: //cheshire. berkeley. edu/pub/cheshire & http: //cheshire. berkeley. edu • 3 = http: //cheshire 3. sourceforge. org – Zprise (Older search system from NIST) • http: //www. itl. nist. gov/iaui/894. 02/works/zp 2. html – IRF (new Java-based IR framework from NIST) • http: //www. itl. nist. gov/iaui/894. 02/projects/irf. html – Lemur • http: //www-2. cs. cmu. edu/~lemur – Lucene (Java-based Text search engine) • http: //jakarta. apache. org/lucene/docs/index. html – Others? ? (See http: //searchtools. com ) IS 240 – Spring 2007. 02. 13 - SLIDE 2

Mini-TREC • Proposed Schedule – February 15 – Database and previous Queries – February 27 – report on system acquisition and setup – March 8, New Queries for testing… – April 19, Results due – April 24 or 26, Results and system rankings – May 8 Group reports and discussion IS 240 – Spring 2007. 02. 13 - SLIDE 3

Review: IR Models • Set Theoretic Models – Boolean – Fuzzy – Extended Boolean • Vector Models (Algebraic) • Probabilistic Models (probabilistic) IS 240 – Spring 2007. 02. 13 - SLIDE 4

Similarity Measures Simple matching (coordination level match) Dice’s Coefficient Jaccard’s Coefficient Cosine Coefficient Overlap Coefficient IS 240 – Spring 2007. 02. 13 - SLIDE 5

Documents in Vector Space t 3 D 1 D 9 D 11 D 5 D 3 D 10 D 4 D 2 t 1 t 2 IS 240 – Spring 2007 D 8 D 6 2007. 02. 13 - SLIDE 6

Vector Space Visualization IS 240 – Spring 2007. 02. 13 - SLIDE 7

Vector Space with Term Weights and Cosine Matching Term B 1. 0 0. 8 D 2 Q Q = (0. 4, 0. 8) D 1=(0. 8, 0. 3) D 2=(0. 2, 0. 7) Di=(di 1, wdi 1; di 2, wdi 2; …; dit, wdit) Q =(qi 1, wqi 1; qi 2, wqi 2; …; qit, wqit) 0. 6 0. 4 D 1 0. 2 0. 4 0. 6 Term A IS 240 – Spring 2007 0. 8 1. 0 2007. 02. 13 - SLIDE 8

Document/Document Matrix IS 240 – Spring 2007. 02. 13 - SLIDE 9

Hierarchical Methods Single Link Dissimilarity Matrix 2 3 4 5 . 4. 4. 3. 1 1 . 2. 3. 4 2 . 3. 4 3 . 1 4 Hierarchical methods: Polythetic, Usually Exclusive, Ordered Clusters are order-independent IS 240 – Spring 2007. 02. 13 - SLIDE 10

Threshold =. 1 Single Link Dissimilarity Matrix 2 3 4 5 . 4. 4. 3. 1 1 . 2. 3. 4 2 . 3. 4 3 2 3 4 5 . 1 4 0 0 0 1 1 0 0 0 2 0 0 3 1 4 1 2 5 3 4 IS 240 – Spring 2007. 02. 13 - SLIDE 11

Threshold =. 2 2 3 4 5 . 4. 4. 3. 1 1 . 2. 3. 4 2 . 3. 4 3 2 3 4 5 . 1 4 0 0 0 1 1 1 0 0 2 0 0 3 1 4 1 2 5 3 4 IS 240 – Spring 2007. 02. 13 - SLIDE 12

Threshold =. 3 2 3 4 5 . 4. 4. 3. 1 1 . 2. 3. 4 2 . 3. 4 3 2 3 4 5 . 1 4 0 0 1 1 1 0 2 1 0 3 1 4 1 2 5 3 4 IS 240 – Spring 2007. 02. 13 - SLIDE 13

K-means & Rocchio Clustering Agglomerative methods: Polythetic, Exclusive or Overlapping, Unordered clusters are order-dependent. Doc Doc Rocchio’s method 1. Select initial centers (I. e. seed the space) 2. Assign docs to highest matching centers and compute centroids 3. Reassign all documents to centroid(s) IS 240 – Spring 2007. 02. 13 - SLIDE 14

Clustering • Advantages: – See some main themes • Disadvantage: – Many ways documents could group together are hidden • Thinking point: what is the relationship to classification systems and facets? IS 240 – Spring 2007. 02. 13 - SLIDE 15

Automatic Class Assignment: Polythetic, Exclusive or Overlapping, usually ordered clusters are order-independent, usually based on an intellectually derived scheme Search Engine Doc Doc 1. Create pseudo-documents representing intellectually derived classes. 2. Search using document contents 3. Obtain ranked list 4. Assign document to N categories ranked over threshold. OR assign to top-ranked category IS 240 – Spring 2007. 02. 13 - SLIDE 16

Automatic Categorization in Cheshire II • Cheshire supports a method we call “classification clustering” that relies on having a set of records that have been indexed using some controlled vocabulary. • Classification clustering has the following steps… IS 240 – Spring 2007. 02. 13 - SLIDE 17

Cheshire II - Cluster Generation • Define basis for clustering records. – Select field (I. e. , the contolled vocabulary terms) to form the basis of the cluster. – Evidence Fields to use as contents of the pseudodocuments. (E. g. the titles or other topical parts) • During indexing cluster keys are generated with basis and evidence from each record. • Cluster keys are sorted and merged on basis and pseudo-documents created for each unique basis element containing all evidence fields. • Pseudo-Documents (Class clusters) are indexed on combined evidence fields. IS 240 – Spring 2007. 02. 13 - SLIDE 18

Cheshire II - Two-Stage Retrieval • Using the LC Classification System – Pseudo-Document created for each LC class containing terms derived from “content-rich” portions of documents in that class (e. g. , subject headings, titles, etc. ) – Permits searching by any term in the class – Ranked Probabilistic retrieval techniques attempt to present the “Best Matches” to a query first. – User selects classes to feed back for the “second stage” search of documents. • Can be used with any classified/Indexed collection. IS 240 – Spring 2007. 02. 13 - SLIDE 19

Problems with Vector Space • There is no real theoretical basis for the assumption of a term space – it is more for visualization than having any real basis – most similarity measures work about the same regardless of model • Terms are not really orthogonal dimensions – Terms are not independent of all other terms IS 240 – Spring 2007. 02. 13 - SLIDE 20

Today • Probabilistic Models – Probabilistic Indexing (Model 1) – Probabilistic Retrieval (Model 2) – Unified Model (Model 3) – Model 0 and real-world IR – Regression Models – The “Okapi Weighting Formula” IS 240 – Spring 2007. 02. 13 - SLIDE 21

Probabilistic Models • Rigorous formal model attempts to predict the probability that a given document will be relevant to a given query • Ranks retrieved documents according to this probability of relevance (Probability Ranking Principle) • Rely on accurate estimates of probabilities IS 240 – Spring 2007. 02. 13 - SLIDE 22

Probability Ranking Principle • If a reference retrieval system’s response to each request is a ranking of the documents in the collections in the order of decreasing probability of usefulness to the user who submitted the request, where the probabilities are estimated as accurately as possible on the basis of whatever data has been made available to the system for this purpose, then the overall effectiveness of the system to its users will be the best that is obtainable on the basis of that data. Stephen E. Robertson, J. Documentation 1977 IS 240 – Spring 2007. 02. 13 - SLIDE 23

Model 1 – Maron and Kuhns • Concerned with estimating probabilities of relevance at the point of indexing: – If a patron came with a request using term ti, what is the probability that she/he would be satisfied with document Dj ? IS 240 – Spring 2007. 02. 13 - SLIDE 24

Bayes’ Formula • Bayesian statistical inference used in both models… IS 240 – Spring 2007. 02. 13 - SLIDE 25

Bayes’ theorem For example: A: disease B: symptom IS 240 – Spring 2007. 02. 13 - SLIDE 26

Bayes’ Theorem: Application Toss a fair coin. If it lands head up, draw a ball from box 1; otherwise, draw a ball from box 2. If the ball is blue, what is the probability that it is drawn from box 2? Box 1 p(box 1) =. 5 P(red ball | box 1) =. 4 P(blue ball | box 1) =. 6 IS 240 – Spring 2007 Box 2 p(box 2) =. 5 P(red ball | box 2) =. 5 P(blue ball | box 2) =. 5 2007. 02. 13 - SLIDE 27

Bayes’ Theorem: Application in IR Goal: want to estimate the probability that a document D is relevant to a given query. It is easier to estimate log odds of probability of relevance IS 240 – Spring 2007. 02. 13 - SLIDE 28

Bayes’ Theorem: Application in IR If documents are represented by binary vectors, then Steven & Sparck Jones term weighting IS 240 – Spring 2007. 02. 13 - SLIDE 29

Bayes Theorem: Application in IR IS 240 – Spring 2007. 02. 13 - SLIDE 30

Bayes’ Theorem: Application in IR Log odds of relevance: The task of estimating probability of relevance reduces to estimate the class-conditional probability density functions. IS 240 – Spring 2007. 02. 13 - SLIDE 31

Model 1 • A patron submits a query (call it Q) consisting of some specification of her/his information need. Different patrons submitting the same stated query may differ as to whether or not they judge a specific document to be relevant. The function of the retrieval system is to compute for each individual document the probability that it will be judged relevant by a patron who has submitted query Q. Robertson, Maron & Cooper, 1982 IS 240 – Spring 2007. 02. 13 - SLIDE 32

Model 1 Bayes • A is the class of events of using the system • Di is the class of events of Document i being judged relevant • Ij is the class of queries consisting of the single term Ij • P(Di|A, Ij) = probability that if a query is submitted to the system then a relevant document is retrieved IS 240 – Spring 2007. 02. 13 - SLIDE 33

Model 2 • Documents have many different properties; some documents have all the properties that the patron asked for, and other documents have only some or none of the properties. If the inquiring patron were to examine all of the documents in the collection she/he might find that some having all the sought after properties were relevant, but others (with the same properties) were not relevant. And conversely, he/she might find that some of the documents having none (or only a few) of the sought after properties were relevant, others not. The function of a document retrieval system is to compute the probability that a document is relevant, given that it has one (or a set) of specified properties. Robertson, Maron & Cooper, 1982 IS 240 – Spring 2007. 02. 13 - SLIDE 34

Model 2 – Robertson & Sparck Jones Given a term t and a query q Document indexing Document Relevance + - + r n-r n - R-r N-n-R+r N-n N-R N R IS 240 – Spring 2007. 02. 13 - SLIDE 35

Robertson-Spark Jones Weights • Retrospective formulation -- IS 240 – Spring 2007. 02. 13 - SLIDE 36

Robertson-Sparck Jones Weights • Predictive formulation IS 240 – Spring 2007. 02. 13 - SLIDE 37

Probabilistic Models: Some Unifying Notation • • • D = All present and future documents Q = All present and future queries (Di, Qj) = A document query pair x = class of similar documents, y = class of similar queries, Relevance is a relation: IS 240 – Spring 2007. 02. 13 - SLIDE 38

Probabilistic Models • Model 1 -- Probabilistic Indexing, P(R|y, Di) • Model 2 -- Probabilistic Querying, P(R|Qj, x) • Model 3 -- Merged Model, P(R| Qj, Di) • Model 0 -- P(R|y, x) • Probabilities are estimated based on prior usage or relevance estimation IS 240 – Spring 2007. 02. 13 - SLIDE 39

Probabilistic Models D Qj y Q x Di IS 240 – Spring 2007. 02. 13 - SLIDE 40

Logistic Regression • Based on work by William Cooper, Fred Gey and Daniel Dabney. • Builds a regression model for relevance prediction based on a set of training data • Uses less restrictive independence assumptions than Model 2 – Linked Dependence IS 240 – Spring 2007. 02. 13 - SLIDE 41

Dependence assumptions • In Model 2 term independence was assumed – P(R|A, B) = P(R|A)P(R|B) – This is not very realistic as we have discussed before • Cooper, Gey, and Dabney proposed linked dependence: – If two or more retrieval clues are statistically dependent in the set of all relevance-related querydocument pairs then they are statistically dependent to a corresponding degree in the set of all nonrelevance-related pairs. – Thus dependency in the relevant and nonrelevant documents is linked IS 240 – Spring 2007. 02. 13 - SLIDE 42

Linked Dependence • Linked Dependence Assumption: there exists a positive real number K such that the following two conditions hold: – P(A, B|R) = K P(A|R) P(B|R) – When K=1 this is the same as binary independence IS 240 – Spring 2007. 02. 13 - SLIDE 43

Linked Dependence • The Odds of an event E : O(E) = P(E)/P(E) • (See paper for details) • Multiplying by O(R) and taking logs we get: IS 240 – Spring 2007. 02. 13 - SLIDE 44

Probabilistic Models: Logistic Regression • Estimates for relevance based on loglinear model with various statistical measures of document content as independent variables. Log odds of relevance is a linear function of attributes: Term contributions summed: Probability of Relevance is inverse of log odds: IS 240 – Spring 2007. 02. 13 - SLIDE 45

Relevance Logistic Regression IS 240 – Spring 2007 100 90 80 70 60 50 40 30 20 10 0 - 0 10 20 30 40 50 60 Term Frequency in Document 2007. 02. 13 - SLIDE 46

Probabilistic Models: Logistic Regression attributes Average Absolute Query Frequency Query Length Average Absolute Document Frequency Document Length Average Inverse Document Frequency Number of Terms in common between query and document -- logged IS 240 – Spring 2007. 02. 13 - SLIDE 47

Probabilistic Models: Logistic Regression Probability of relevance is based on Logistic regression from a sample set of documents to determine values of the coefficients. At retrieval the probability estimate is obtained by: For the 6 X attribute measures shown previously IS 240 – Spring 2007. 02. 13 - SLIDE 48

Logistic Regression and Cheshire II • The Cheshire II system uses Logistic Regression equations estimated from TREC full-text data • In addition, an implementation of the Okapi BM-25 algorithm has been included also • Demo (? ) IS 240 – Spring 2007. 02. 13 - SLIDE 49

Current use of Probabilistic Models • Most of the major systems in TREC now use the “Okapi BM-25 formula” (or Language Models -- more on those later) which incorporates the Robertson-Sparck Jones weights… IS 240 – Spring 2007. 02. 13 - SLIDE 50

Okapi BM-25 • • • Where: Q is a query containing terms T K is k 1((1 -b) + b. dl/avdl) k 1, b and k 3 are parameters , usually 1. 2, 0. 75 and 7 -1000 tf is the frequency of the term in a specific document qtf is the frequency of the term in a topic from which Q was derived • dl and avdl are the document length and the average document length measured in some convenient unit (e. g. bytes) • w(1) is the Robertson-Sparck Jones weight. IS 240 – Spring 2007. 02. 13 - SLIDE 51

Probabilistic Models Advantages • Strong theoretical basis • In principle should supply the best predictions of relevance given available information • Can be implemented similarly to Vector IS 240 – Spring 2007 Disadvantages • Relevance information is required -- or is “guestimated” • Important indicators of relevance may not be term -- though terms only are usually used • Optimally requires ongoing collection of relevance information 2007. 02. 13 - SLIDE 52

Vector and Probabilistic Models • • • Support “natural language” queries Treat documents and queries the same Support relevance feedback searching Support ranked retrieval Differ primarily in theoretical basis and in how the ranking is calculated – Vector assumes relevance – Probabilistic relies on relevance judgments or estimates IS 240 – Spring 2007. 02. 13 - SLIDE 53