querylikelihood

The query likelihood model is a probabilistic information retrieval approach that ranks documents by the likelihood that a document’s language model would generate the user’s query. In this framework, every document D is associated with a language model P(.|D) over terms, and the query Q is treated as data drawn from that model. Documents are ranked by P(Q|D), often computed as the product of term probabilities across the query: P(Q|D) = ∏_{w∈Q} P(w|D) or, equivalently, by summing the log probabilities of query terms.

Because a document’s language model is typically sparse, smoothing is used to combine the document-specific distribution with a background collection model P(w|C). Common smoothing methods include Dirichlet prior and Jelinek–Mercer smoothing. In Dirichlet smoothing, P(w|D) = (tf(w,D) + μ P(w|C)) / (|D| + μ), where tf(w,D) is the term frequency in the document, |D| is document length, μ is a parameter, and P(w|C) is the term’s probability in the collection. Jelinek–Mercer smoothing blends the document and collection models as P(w|D) = (1 − λ) P(w|D) + λ P(w|C). The collection model is typically estimated from the entire corpus.

Practical use involves computing P(w|D) for each term, assembling P(Q|D), and ranking documents by this likelihood (often using log probabilities for numerical stability). Strengths include good performance on short queries and robustness to unseen terms due to smoothing. The approach was introduced as a language-modeling method to information retrieval by Ponte and Croft, and has become a foundational technique in IR research and applications.