Examples Of Query Likening Model In IR

The first basic language modelling approach in IR is the Query Likelihood Model (QLM) to estimate the probability of generating the query terms as a random sample from the document. In particular, the probability $P(d/q)$ of a document $d$ conditioning on query $q$ as likelihood relevant represent the QLM models citep{ponte1998sigir}. Applying Baye 's rule on $P(d/q)$ to get:
egin{equation}
label{BayesQLM}
P(d/q) = frac{P(q/d)P(d)}{P(q)} end{equation} where $P(q)$ could be ignored as it is equivalent across all documents. Also, the document prior $P(d)$ could be ignored as it is uniformly the same across all documents. The document prior $P(d)$ could be the probability of estimated over other documents ' characteristics such as page rank …show more content…
In comparison with the previous likelihood models, unified likelihood model shows more effective results citep{Lafferty:2001} and also is represented as the current state-of-the-art method in language modelling for IR citep{zhai2008ftir}. subsubsection{Term-based Language Model Estimation}
The main component in language model approaches is how to estimate the probability of generating query terms from a specific language model (i.e, $P(t/LM_{text})$) as a language model process. The simplest and commonly used method is the Maximum Likelihood Estimation (MLE; citep{fisher1922rsta}); defined as:

egin{equation} label{MLE} LM_{text} = P_{MLE} = frac{tf_{t,text}}{L_{text}} end{equation} where $tf_{t,text}$ is the term frequency of term $t$ in a sample $text$ (i.e, query or document), $L_{text}$ is the number of tokens the $text$ has. As an example, using MLE method overall query terms in unigram language modelling framework gives the following