Query likelihood model
Encyclopedia
The query likelihood model is a language model
used in Information Retrieval
. A language model is constructed for each document in the collection. It is then possible to rank each document by the probability of specific documents given a query. This is interpreted as being the likelihood
of a document being relevant given a query.
, the probability of a document, given a query can be written as follows:
Since the probability of the query P(q) is the same for all documents, this can be ignored. Further, it is typical to assume that the probability of documents is uniform. Thus, P(d) is also ignored.
Documents are then ranked by the probability that a query is observed as a random sample from the document model. The multinomial unigram language model is commonly used to achieve this. We have:
,where the multinomial coefficient is 
for query .
Language model
A statistical language model assigns a probability to a sequence of m words P by means of a probability distribution.Language modeling is used in many natural language processing applications such as speech recognition, machine translation, part-of-speech tagging, parsing and information...
used in Information Retrieval
Information retrieval
Information retrieval is the area of study concerned with searching for documents, for information within documents, and for metadata about documents, as well as that of searching structured storage, relational databases, and the World Wide Web...
. A language model is constructed for each document in the collection. It is then possible to rank each document by the probability of specific documents given a query. This is interpreted as being the likelihood
Likelihood function
In statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values...
of a document being relevant given a query.
Calculating the likelihood
Using Bayes' ruleBayes' theorem
In probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....
, the probability of a document, given a query can be written as follows:
Since the probability of the query P(q) is the same for all documents, this can be ignored. Further, it is typical to assume that the probability of documents is uniform. Thus, P(d) is also ignored.
Documents are then ranked by the probability that a query is observed as a random sample from the document model. The multinomial unigram language model is commonly used to achieve this. We have:
,where the multinomial coefficient is for query .