Lecture 9: Probabilistic Retrieval

1. Prof. Ray Larson University of California, Berkeley School of Information Lecture 9: Probabilistic Retrieval Principles of Information Retrieval

2. Mini-TREC • Need to make groups • Today – Give me a note with group members (names and login names) • 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://cheshire3.sourceforge.org • Zprise (Older search system from NIST) • http://www.itl.nist.gov/iaui/894.02/works/zp2/zp2.html • IRF (new Java-based IR framework from NIST) • http://www.itl.nist.gov/iaui/894.02/projects/irf/irf.html • Lemur • http://www-2.cs.cmu.edu/~lemur • Lucene (Java-based Text search engine) • http://jakarta.apache.org/lucene/docs/index.html • Galago (Also Java-based) • http://www.galagosearch.org • Others?? (See http://searchtools.com )

3. Mini-TREC • Proposed Schedule • February 16 – Database and previous Queries • March 2 – report on system acquisition and setup • March 9, New Queries for testing… • April 20, Results due • April 27, Results and system rankings • May 6 Group reports and discussion

4. Review: IR Models • Set Theoretic Models • Boolean • Fuzzy • Extended Boolean • Vector Models (Algebraic) • Probabilistic Models (probabilistic)

5. Similarity Measures Simple matching (coordination level match) Dice’s Coefficient Jaccard’s Coefficient Cosine Coefficient Overlap Coefficient

6. Documents in Vector Space t3 D1 D9 D11 D5 D3 D10 D4 D2 t1 D7 D6 D8 t2

7. Vector Space Visualization

8. Vector Space with Term Weights and Cosine Matching Di=(di1,wdi1;di2, wdi2;…;dit, wdit) Q =(qi1,wqi1;qi2, wqi2;…;qit, wqit) Term B 1.0 Q = (0.4,0.8) D1=(0.8,0.3) D2=(0.2,0.7) Q D2 0.8 0.6 0.4 D1 0.2 0 0.2 0.4 0.6 0.8 1.0 Term A

9. Document/Document Matrix

10. Hierarchical Methods 2 .4 3 .4 .2 4 .3 .3 .3 5 .1 .4 .4 .1 1 2 3 4 Single Link Dissimilarity Matrix Hierarchical methods: Polythetic, Usually Exclusive, Ordered Clusters are order-independent

11. Threshold = .1 2 .4 3 .4 .2 4 .3 .3 .3 5 .1 .4 .4 .1 1 2 3 4 2 0 3 0 0 4 0 0 0 5 1 0 0 1 1 2 3 4 1 2 5 3 4 Single Link Dissimilarity Matrix

12. Threshold = .2 2 .4 3 .4 .2 4 .3 .3 .3 5 .1 .4 .4 .1 1 2 3 4 2 0 3 0 1 4 0 0 0 5 1 0 0 1 1 2 3 4 1 2 5 3 4

13. Threshold = .3 2 .4 3 .4 .2 4 .3 .3 .3 5 .1 .4 .4 .1 1 2 3 4 2 0 3 0 1 4 1 1 1 5 1 0 0 1 1 2 3 4 1 2 5 3 4

14. K-means & Rocchio Clustering Doc Doc Doc Doc Doc Doc Doc Doc Agglomerative methods: Polythetic, Exclusive or Overlapping, Unordered clusters are order-dependent. 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)

15. 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?

16. Automatic Class Assignment Doc Doc Doc Doc Search Engine Doc 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 Automatic Class Assignment: Polythetic, Exclusive or Overlapping, usually ordered clusters are order-independent, usually based on an intellectually derived scheme

17. 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…

18. 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 pseudo-documents. (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.

19. 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.

20. 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

21. 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”

22. 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

23. 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

24. 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?

25. Bayes’ Formula • Bayesian statistical inference used in both models…

26. Bayes’ theorem For example: A: disease B: symptom

27. 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? Box2 Box1 p(box1) = .5 P(red ball | box1) = .4 P(blue ball | box1) = .6 p(box2) = .5 P(red ball | box2) = .5 P(blue ball | box2) = .5

28. 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

29. Bayes’ Theorem: Application in IR If documents are represented by binary vectors, then Steven & Sparck Jones term weighting

30. Bayes Theorem: Application in IR

31. 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.

32. 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

33. 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

34. 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

35. Model 2 – Robertson & Sparck Jones Given a term t and a query q Document Relevance + - + r n-r n - R-r N-n-R+r N-n R N-R N Document indexing

36. Robertson-Spark Jones Weights • Retrospective formulation --

37. Robertson-Sparck Jones Weights • Predictive formulation

38. 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:

39. 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

40. Probabilistic Models Q D y Qj x Di

41. 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

42. 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 query-document 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

43. 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) • P(A,B|R) = K P(A|R) P(B|R) • When K=1 this is the same as binary independence

44. 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:

45. Probabilistic Models: Logistic Regression • Estimates for relevance based on log-linear 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:

46. Logistic Regression 100 - 90 - 80 - 70 - 60 - 50 - 40 - 30 - 20 - 10 - 0 - Relevance 0 10 20 30 40 50 60 Term Frequency in Document

47. Probabilistic Models: Logistic Regression attributes Average Absolute Query Frequency Query Length Average Absolute Document Frequency Document Length Average Inverse Document Frequency Inverse Document Frequency Number of Terms in common between query and document -- logged

48. 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

49. 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 (?)

50. 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…