Towards Human-AI Complementarity with Prediction Sets

TL;DR

This paper investigates the limitations of conformal prediction sets in decision support systems, proves the NP-hardness of finding optimal sets, and introduces an efficient greedy algorithm that outperforms conformal prediction in practice.

Contribution

It demonstrates the NP-hardness of optimizing prediction sets for human accuracy and proposes a simple greedy algorithm that improves over conformal prediction methods.

Findings

Greedy algorithm achieves higher average accuracy than conformal prediction.

Optimal prediction set problem is NP-hard and hard to approximate.

The proposed method performs near-optimally in synthetic and real data simulations.

Abstract

Decision support systems based on prediction sets have proven to be effective at helping human experts solve classification tasks. Rather than providing single-label predictions, these systems provide sets of label predictions constructed using conformal prediction, namely prediction sets, and ask human experts to predict label values from these sets. In this paper, we first show that the prediction sets constructed using conformal prediction are, in general, suboptimal in terms of average accuracy. Then, we show that the problem of finding the optimal prediction sets under which the human experts achieve the highest average accuracy is NP-hard. More strongly, unless P = NP, we show that the problem is hard to approximate to any factor less than the size of the label set. However, we introduce a simple and efficient greedy algorithm that, for a large class of expert models and non-conformity scores, is guaranteed to find prediction sets that provably offer equal or greater performance than those constructed using conformal prediction. Further, using a simulation study with both synthetic and real expert predictions, we demonstrate that, in practice, our greedy algorithm finds near-optimal prediction sets offering greater performance than conformal prediction.