Probabilistic relevance feedback

Rather than reweighting the query in a vector space, if a user has told us some relevant and nonrelevant documents, then we can proceed to build a . One way of doing this is with a Naive Bayes probabilistic model. If $R$ is a Boolean indicator variable expressing the relevance of a document, then we can estimate $P(x_t=1\vert R)$, the probability of a term $t$ appearing in a document, depending on whether it is relevant or not, as:

$$\hat{P}(x_t=1\vert R=1) = \vert VR_{t}\vert/\vert VR\vert$$ (50)

$$\hat{P}(x_t=1\vert R=0) = (df_t - \vert VR_t\vert)/(N - \vert VR\vert)$$ (51)

where $N$ is the total number of documents, $df_t$ is the number that contain $t$, $VR$ is the set of known relevant documents, and $VR_{t}$ is the subset of this set containing $t$. Even though the set of known relevant documents is a perhaps small subset of the true set of relevant documents, if we assume that the set of relevant documents is a small subset of the set of all documents then the estimates given above will be reasonable. This gives a basis for another way of changing the query term weights. We will discuss such probabilistic approaches more in Chapters 11 13 , and in particular outline the application to relevance feedback in Section 11.3.4 (page ). For the moment, observe that using just Equation 50 as a basis for term-weighting is likely insufficient. The equations use only collection statistics and information about the term distribution within the documents judged relevant. They preserve no memory of the original query.