Examples Of Query Likening Model In IR

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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
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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

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