In computing and information science, the Binary Independence Model (BIM)[1][2] is a probabilistic information retrieval technique.
That is, only the presence or absence of terms in documents are recorded.
Terms are independently distributed in the set of relevant documents and they are also independently distributed in the set of irrelevant documents.
The representation is an ordered set of Boolean variables.
That is, the representation of a document or query is a vector with one Boolean element for each term under consideration.
Many documents can have the same vector representation with this simplification.
"Independence" signifies that terms in the document are considered independently from each other and no association between terms is modeled.
This assumption is very limiting, but it has been shown that it gives good enough results for many situations.
This independence is the "naive" assumption of a Naive Bayes classifier, where properties that imply each other are nonetheless treated as independent for the sake of simplicity.
This assumption allows the representation to be treated as an instance of a Vector space model by considering each term as a value of 0 or 1 along a dimension orthogonal to the dimensions used for the other terms.
are the probabilities of retrieving a relevant or nonrelevant document, respectively.
The exact probabilities can not be known beforehand, so estimates from statistics about the collection of documents must be used.
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.
Yu and Salton,[1] who first introduce BIM, propose that the weight of the ith term is an increasing function of
Robertson and Spärck Jones[2] later showed that if the ith term is assigned the weight of
, then optimal retrieval effectiveness is obtained under the Binary Independence Assumption.
The Binary Independence Model was introduced by Yu and Salton.
[1] The name Binary Independence Model was coined by Robertson and Spärck Jones[2] who used the log-odds probability of the probabilistic relevance model to derive
) by Luk,[3] obeying the probability ranking principle.