Transductive Conformal Inference for Full Ranking
This work addresses uncertainty quantification for ranking algorithms, which is important for applications like search engines and recommendation systems, but it is incremental as it builds on existing conformal prediction techniques.
The paper tackles the problem of quantifying uncertainty in full ranking algorithms when ground truth rankings are only partially known, by introducing a transductive conformal inference method that provides valid prediction sets for ranks and controls false coverage proportion, demonstrating efficiency on synthetic and real data with algorithms like RankNet and LambdaMart.
We introduce a method based on Conformal Prediction (CP) to quantify the uncertainty of full ranking algorithms. We focus on a specific scenario where $n+m$ items are to be ranked by some ``black box'' algorithm. It is assumed that the relative (ground truth) ranking of $n$ of them is known. The objective is then to quantify the error made by the algorithm on the ranks of the $m$ new items among the total $(n+m)$. In such a setting, the true ranks of the $n$ original items in the total $(n+m)$ depend on the (unknown) true ranks of the $m$ new ones. Consequently, we have no direct access to a calibration set to apply a classical CP method. To address this challenge, we propose to construct distribution-free bounds of the unknown conformity scores using recent results on the distribution of conformal p-values. Using these scores upper bounds, we provide valid prediction sets for the rank of any item. We also control the false coverage proportion, a crucial quantity when dealing with multiple prediction sets. Finally, we empirically show on both synthetic and real data the efficiency of our CP method for state-of-the-art algorithms such as RankNet or LambdaMart.