document: Estimating rates of rare events at multiple resolutions We consider the problem of estimating occurrence rates of rare eventsfor extremely sparse data , using pre-existing hierarchies to perform inference at multiple resolutions . In particular , we focus on the problem of estimating click rates for ( webpage , advertisement ) pairs ( called impressions ) where both the pages and the ads are classified into hierarchies that capture broad contextual information at different levels of granularity . Typically the click rates are low and the coverage of the hierarchies is sparse . To overcome these difficulties we devise a sampling method whereby we analyze aspecially chosen sample of pages in the training set , and then estimate click rates using a two-stage model . The first stage imputes the number of ( webpage , ad ) pairs at all resolutions of the hierarchy to adjust for the sampling bias . The second stage estimates clickrates at all resolutions after incorporating correlations among sibling nodes through a tree-structured Markov model . Both models are scalable and suited to large scale data mining applications . On a real-world dataset consisting of 1\/2 billion impressions , we demonstrate that even with 95 % negative ( non-clicked ) events in the training set , our method can effectively discriminate extremely rare events in terms of their click propensity .
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