Before using Equation 1, we must estimate a unigram model from d: that is, an assignment of probabilities Pr(w | d) for all w ∈ V. One way to do this is to use a maximum likelihood estimate (MLE) -an assignment of Pr(w | d) for all w which maximizes the probability of generating d. The MLE is given by the equation is the number of occurrences of w in d, and |d| is the total number of words in d. However, using this formula means we will get a value of zero for Pr(q | d) if even a single query word q i is not found in d. To overcome this problem, we smooth the model by assigning some probability mass to such unseen words.
we adopt a two-stage smoothing method (Zhai and Lafferty, 2004): Here, U denotes a background language model, and µ > 0 and λ ∈ (0, 1) are parameters to the smoothing procedure.