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]):

$$ \log \left(p\left(Rel|d,q\right)\right) \propto \sum_{t\in q} \log \dfrac{p\left(t|Rel\right)\cdotp p\left(\overline{t}|\overline{Rel}\right)}{p\left( t|\overline{Rel}\right) \cdotp p\left(\overline{t}|Rel\right)} $$

(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, \(...