Using the calculations in Exercise 12.7 (below) as inspiration or as examples where appropriate, write one sentence each describing the treatment that the model in Equation (12.10) gives to each of the following quantities. Include whether it is present in the model or not and whether the effect is raw or scaled.

Equation (12.10)

a. Term frequency in a document b. Collection frequency of a term c. Document frequency of a term d. Length normalization of a term

Exercise 12.7: Suppose we have a collection that consists of the 4 documents given in the below table.

docID Document text 1 click go the shears boys click click click 2 click click 3 metal here 4 metal shears click here

Build a query likelihood language model for this document collection. Assume a mixturemodel between the documents and the collection, with both weighted at 0.5. Maximum likelihood estimation (mle) is used to estimate both as unigram models. Work out the model probabilities of the queries click, shears, and hence click shears for each document, and use those probabilities to rank the documents returned by each query. Fill in these probabilities in the below table:

Query Doc 1 Doc 2 Doc 3 Doc 4 click shears click shears

What is the final ranking of the documents for the query click shears?

12.7 ANSWERS