Binary independence model

In computing and information science, the binary independence model (BIM) is a probabilistic information retrieval technique. The model makes some simple assumptions to make the estimation of document/query similarity probable and feasible.

In computing and information science, the binary independence model (BIM) is a probabilistic information retrieval technique. The model makes some simple assumptions to make the estimation of document/query similarity probable and feasible. P(R|x,q) = \frac{P(x|R,q)*P(R|q)}{P(x|q)} where P(x|R=1,q) and P(x|R=0,q) are the probabilities of retrieving a relevant or nonrelevant document, respectively. If so, then that document's representation is x. The exact probabilities can not be known beforehand, so estimates from statistics about the collection of documents must be used. P(R=1|q) and P(R=0|q) indicate the previous probability of retrieving a relevant or nonrelevant document respectively for a query q. If, for instance, we knew the percentage of relevant documents in the collection, then we could use it to estimate these probabilities. Since a document is either relevant or nonrelevant to a query we have that: P(R=1|x,q) + P(R=0|x,q) = 1 terms in the query such that the retrieval effectiveness will be high. Let p_i and q_i be the probability that a relevant document and an irrelevant document has the term respectively. Yu and Salton, who first introduce BIM, propose that the weight of the term is an increasing function of Y_i = \frac{p_i *(1-q_i)}{(1-p_i)*q_i} . Thus, if Y_i is higher than Y_j , the weight of term will be higher than that of term . Yu and Salton showed that such a weight assignment to query terms yields better retrieval effectiveness than if query terms are equally weighted. Robertson and Spärck Jones later showed that if the term is assigned the weight of \log Y_i , then optimal retrieval effectiveness is obtained under the binary independence assumption. The binary independence model was introduced by Yu and Salton. The term binary independence model was coined by Robertson and Spärck Jones who used the log-odds probability of the probabilistic relevance model to derive \log Y_i where the log-odds probability is shown to be rank equivalent to the probability of relevance (i.e., P(R|d,q) ) by Luk, obeying the probability ranking principle.

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