Alternative IR models

1. Alternative IR models Slides from Samer Hassan, Ian Ruthven

2. Technical Memo Example: Titles

3. Technical Memo Example: Terms and Documents

4. Alternative IR models

5. Probabilistic model Asks the question �what is probability that user will see relevant information if they read this document� P(rel|di) � probability of relevance after reading di How likely is the user to get relevance information from reading this document high probability means more likely to get relevant info.

6. Probabilistic model �if a reference retrieval system's response to each request is a ranking of the documents in the collection in order of decreasing probability of relevance ... the overall effectiveness of the system to its user will be the best that is obtainable��, Probability ranking principle Rank documents based on decreasing probability of relevance to user Calculate P(rel|di) for each document and rank Suggests mathematical approach to IR and matching Can predict (somewhat) good retrieval models based on their estimates of P(rel|di)

7. Example

8. Relevance Feedback What these systems are doing is Using examples of documents the user likes To detect which words are useful new query words query expansion To detect how useful these words are change weights of query words term reweighting Use new query for retrieval

9. Query Expansion Add useful terms to the query Terms that appear often in relevant documents Try to compensate for poor queries usually short, can be ambiguous, use too many common words add better terms to user�s query Try to emphasize recall

10. Term Weighting Reweight query terms Assign new weights according to importance in relevant documents Personalized searching Try to improve precision

11. Probabilistic Models Most probabilistic models based on combining probabilities of relevance and non-relevance of individual terms Probability that a term will appear in a relevant document Probability that the term will not appear in a non-relevant document These probabilities are estimated based on counting term appearances in document descriptions

12. Example Assume we have a collection of 100 documents N=100 20 of the documents contain the term sausage Searcher has read and marked 10 documents as relevant R=10 Of these relevant documents 5 contain the term sausage How important is the word sausage to the searcher?

13. Probability of Relevance from these four numbers we can estimate probability of sausage given relevance information i.e. how important term sausage is to relevant documents is number of relevant documents containing sausage (5) is number of relevant documents that do not contain sausage (5) Eq. (I) is higher if most relevant documents contain sausage lower if most relevant documents do not contain sausage high value means sausage is important term to user in our example (5/5=1)

14. Probability of Non-relevance Also we can estimate probability of sausage given non-relevance information i.e. how important term sausage is to non-relevant documents is number of non-relevant documents that contain term sausage (20-5)=15 is number of non-relevant documents that do not contain sausage (100-20-10+5)=75

15. F4 reweighting formula how important is sausage being present in relevant documents how important is sausage being absent from non-relevant documents from example on slide 10 weight of sausage is 5 (1/0.2)

16. F4 reweighting formula F4 gives new weights to all terms in collection (or just query) high weights to important terms Low weights to unimportant terms replaces idf, tf, or any other weights document score is based on sum of query terms in documents

17. Probabilistic model can also use to rank terms for addition to query rank terms in relevant documents by term reweighting formula i.e. by how good the terms are at retrieving relevant documents add all terms add some, e.g. top 5 in probabilistic formula query expansion and term reweighting done separately

18. Probabilistic model Advantages over vector-space Strong theoretical basis Based on probability theory (very well understood) Easy to extend Disadvantages Models are often complicated No term frequency weighting Which is better vector-space or probabilistic? Both are approximately as good as each other Depends on collection, query, and other factors

19. Explicit/Latent Semantic Analysis BOW Explicit Semantic Analysis Latent Semantic Anaylsis

20. Explicit/Latent Semantic Analysis Objective Replace indexes that use sets of index terms/docs by indexes that use concepts. Approach Map the term vector space into a lower dimensional space, using singular value decomposition. Each dimension in the new space corresponds to a explicit/latent concept in the original data.

21. Deficiencies with Conventional Automatic Indexing Synonymy: Various words and phrases refer to the same concept (lowers recall). Polysemy: Individual words have more than one meaning (lowers precision) Independence: No significance is given to two terms that frequently appear together Explict/Latent semantic indexing addresses the first of these (synonymy), and the third (dependence)

22. Technical Memo Example: Titles

23. Technical Memo Example: Terms and Documents

24. Technical Memo Example: Query Query: Find documents relevant to "human computer interaction� Simple Term Matching: Matches c1, c2, and c4 Misses c3 and c5

25. Mathematical concepts Define X as the term-document matrix, with t rows (number of index terms) and d columns (number of documents). Singular Value Decomposition For any matrix X, with t rows and d columns, there exist matrices T0, S0 and D0', such that: X = T0S0D0� T0 and D0 are the matrices of left and right singular vectors S0 is the diagonal matrix of singular values

26. Dimensions of matrices

27. Reduced Rank S0 can be chosen so that the diagonal elements are positive and decreasing in magnitude. Keep the first k and set the others to zero. Delete the zero rows and columns of S0 and the corresponding rows and columns of T0 and D0. This gives: X = TSD' Interpretation If value of k is selected well, expectation is that X retains the semantic information from X, but eliminates noise from synonymy and recognizes dependence.

28. Dimensionality Reduction

29. Recombination after Dimensionality Reduction

30. Mathematical Revision

31. Comparing a Query and a Document A query can be expressed as a vector in the term-document vector space xq. xqi = 1 if term i is in the query and 0 otherwise. (Ignore query terms that are not in the term vector space.) Let pqj be the inner product of the query xq with document dj in the term-document vector space.

32. Comparing a Query and a Document