Conformal prediction can be used to construct prediction sets that cover the true outcome with a desired probability, but can sometimes lead to large prediction sets that are costly in practice. The most useful outcome is a singleton prediction-an unambiguous decision-yet existing efficiency-oriented methods primarily optimize average set size. Motivated by this, we propose a new nonconformity score that aims to minimize the probability of producing non-singleton sets. Starting from a non-convex constrained optimization problem as a motivation, we provide a geometric reformulation and associated algorithm for computing the nonconformity score and associated split conformal prediction sets in O(K) time for K-class problems. Using this score in split conformal prediction leads to our proposed Singleton-Optimized Conformal Prediction (SOCOP) method. We evaluate our method in experiments on image classification and LLM multiple-choice question-answering, comparing with standard nonconformity scores such as the (negative) label probability estimates and their cumulative distribution function; both of which are motivated by optimizing length. The results show that SOCOP increases singleton frequency (sometimes by over 20%) compared to the above scores, with minimal impact on average set size.

翻译：一致性预测可用于构建以期望概率覆盖真实结果的预测集，但有时会导致预测集过大，在实践中代价高昂。最有用的结果是单例预测——一个明确的决策——然而现有的效率导向方法主要优化平均集大小。受此启发，我们提出了一种新的非一致性评分，旨在最小化产生非单例集的概率。从一个非凸约束优化问题出发作为动机，我们提供了几何重构及相关算法，用于在K类问题中以O(K)时间复杂度计算非一致性评分及相关的拆分一致性预测集。在拆分一致性预测中使用该评分即得到我们提出的单例优化一致性预测方法。我们在图像分类和大型语言模型多项选择问答实验中评估了我们的方法，并与标准的非一致性评分（如（负）标签概率估计及其累积分布函数）进行比较；这两种评分均以优化长度为动机。结果表明，与上述评分相比，SOCOP提高了单例频率（有时超过20%），同时对平均集大小的影响最小。