Probability Ranking Principle

Synonyms

PRP

Definition

The probability ranking principle asserts that relevance has a probabilistic interpretation. According to this principle documents are ranked by a probability p(Rel|d, q), where Rel denotes the event of a document d being relevant to a query q. Robertson called this principle the probability ranking principle [1].

Key Points

By assuming independence between query terms, Robertson and Sparck-Jones proposed for the probability p(Rel|d,q) the following model (the RSJ model [2]):

$$\log (p(Rel\vert d,q)) \propto {\mathop{\sum }\limits _{t\in q}\log {p(t\vert Rel) \cdot p(\overline{t}\vert \overline{Rel})\over p(t\vert \overline{Rel}) \cdot p(\overline{t}\vert Rel)}}$$

((1))

where $\overline{Rel}$ indicates the event of non-relevance; t and $\overline{t}$ indicate the events that the term t occurs in document d or does not, respectively. For each query term t, the probability p(Rel|d,t) is given by the sum of two log-odds, \(\log {p(t\vert Rel)\over p(t\vert...