Natural Language Processing · free preview

Sparse Retrieval with tf-idf

The vector space model, term frequency and inverse document frequency, cosine scoring, BM25, and the inverted index that makes ranking fast.

1. Sparse Retrieval with tf-idf

2. Inverse document frequency

A collection has $N = 4$ documents and a term occurs in $\text{df} = 1$ of them. Compute $\text{idf} = \log_{10}(N/\text{df})$ , rounding to three decimals.

3. Damped term frequency

A term appears 1 times in a document. Compute its tf as $1 + \log_{10}(\text{count})$ , rounding to three decimals.

4. A perfect cosine

A one-word document contains exactly the query's single term, with everything else zero. What cosine does the tf-idf scoring assign, and why?

5. What the postings list holds

A user queries two terms. How does the inverted index make scoring efficient?

6. The two knobs of BM25

In BM25, what do the parameters $k$ and $b$ control, and what happens at the extremes?

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