Is Top-k Sufficient for Ranking?

Recently, 'top-k learning to rank' has attracted much attention in the community of information retrieval. The motivation comes from the difficulty in obtaining a full-order ranking list for training, when employing reliable pairwise preference judgment. Inspired by the observation that users mainly care about top ranked search result, top-k learning to rank proposes to utilize top-k ground-truth for training, where only the total order of top k items are provided, instead of a full-order ranking list. However, it is not clear whether the underlying assumption holds, i.e. top-k ground-truth is sufficient for training. In this paper, we propose to study this problem from both empirical and theoretical aspects. Empirically, our experimental results on benchmark datasets LETOR4.0 show that the test performances of both pairwise and list-wise ranking algorithms will quickly increase to a stable value, with the growth of k in the top-k ground-truth. Theoretically, we prove that the losses of these typical ranking algorithms in top-k setting are tighter upper bounds of (1-NDCG@k), compared with that in full-order setting. Therefore, our studies reveal that learning on top-k ground-truth is surely sufficient for ranking, which lay a foundation for the new learning to rank framework.