An efficient reduction of ranking to classification

This paper describes an efficient reduction of the learning problem of ranking to binary classification. As with a recent result of Balcan et al., the reduction guarantees an average pairwise misranking regret of at most $2r$ using a binary classifier with regret $r$. However, our reduction applies to a broader class of ranking loss functions, admits a simpler proof, and the expected running time complexity of our algorithm in terms of number of calls to a classifier or preference function is improved from $\Omega(n^2)$ to $O(n \log n)$. Furthermore, when the top $k$ ranked elements only are required ($k \ll n$), as in many applications in information extraction or search engines, the time complexity of our algorithm can be further reduced to $O(k \log k + n)$. Our reduction and algorithm are thus practical for realistic applications where the number of points to rank exceeds several thousands. Much of our results also extend beyond the bipartite case previously studied.