1. Modeling Modern Information Retrieval
by R. Baeza-Yates and B. Ribeiro-Neto
Addison-Wesley, 1999.
(Chapter 2)

2. Introduction Ranking algorithms Taxonomy of IR Models
The central problem regarding IR systems is the issue of predicting which documents are relevant and which are not.
Taxonomy of IR Models
Boolean: set theoretic
Vector: algebraic
Probabilistic

3. Retrieval Ad hoc Filtering (Routing)
the documents in the collection remain relatively static while new queries are submitted to the system
Filtering (Routing)
the queries remain relatively static while new documents come into the system
construction of user profile

4. Basic Concepts In the classic models
each document is described by a set of representative keywords called index terms
index terms are mainly nouns
distinct index terms have varying relevance
index term weights are usually assumed to be mutually independent

5. Boolean Model Binary decision criterion Data retrieval model
A query is a Boolean expression which can be represented as a disjunction of conjunctive vectors
Advantage
clean formalism, simplicity
Disadvantage
exact matching may lead to retrieval of too few or too many documents

6. Vector Model (1/4) Index terms are assigned non-binary weights
Term weights are used to compute the degree of similarity between documents and the user query
Then, retrieved documents are sorted in decreasing order.
Definition For the vector model, the weight wi,j is associated with term ki and document dj

7. Vector Model (2/4)
Degree of similarity

8. Vector Model (3/4) Salton Definition IR vs. clustering
intra-clustering similarity: tf factor (term frequency)
inter-cluster dissimilarity: idf factor (inverse document frequency)
Definition
normalized frequency
inverse document fequency
term-weighting schemes
query-term weights

9. Vector Model (4/4) Advantages Disadvantage
its term-weighting scheme improves retrieval performance
its partial matching strategy allows retrieval of documents that approximate the query conditions
its cosine ranking formula sorts the documents according to their degree of similarity to the query
Disadvantage
The assumption of mutual independence between index terms

10. Probabilistic Model (1/7)
Introduced by Roberston and Sparck Jones, 1976
Also called binary independence retrieval (BIR) model
Idea: Given a user query q, and the ideal answer set of the relevant documents, the problem is to specify the properties for this set.
i.e.the probabilistic model tries to estimate the probability that the user will find the document dj relevant with ratio
P(dj relevant to q)/P(dj nonrelevant to q)

11. Probabilistic Model (2/7)
Definition
All index term weights are all binary i.e., wi,j  {0,1}
Let R be the set of documents know to be relevant to query q
Let be the complement of R
Let be the probability that the document dj is relevant to the query q
Let be the probability that the document dj is nonelevant to query q

12. Probabilistic Model (3/7)
The similarity sim(dj,q) of the document dj to the query q is defined as the ratio
Using Bayes’ rule,
P(R) stands for the probability that a document randomly selected from the entire collection is relevant
stands for the probability of randomly selecting the document dj from the set R of relevant documents

13. Probabilistic Model (4/7)
Assuming independence of index terms and given q=(d1, d2, …, dt),

14. Probabilistic Model (5/7)
Pr(ki |R) stands for the probability that the index term ki is present in a document randomly selected from the set R
stands for the probability that the index term ki is not present in a document randomly selected from the set R
let Pr(ki |R)=pi
di is either 0 or 1
0: di is absent from q
1: di is present in q

15. Probabilistic Model (6/7)

16. Probabilistic Model (7/7)
The retrieval value of each ki present in a document (i.e., di=1) is term relevance weight
pj = 0.5, qj = dfj / N

17. Estimation of Term Relevance