发表机构
Chinese University of Hong Kong（香港中文大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对已校准预测器的优化问题，将其建模为信号方案，明确了可构造性的线性信息表征，得出确定性输出预测器双边优化的多项式算法、多输入优化的NP难性，以及随机化输出预测器优化的多项式算法。
AI 中文摘要
预测聚合旨在将多个预测器的信息整合为一个更具信息量的预测器。我们在已校准预测器的框架下研究该问题，其中每个预测必须等于给定预测器信号下被预测量的条件期望。给定若干已校准的输入预测器和特征分布，但未知潜在贝叶斯概率，我们探究何时可构建优化后的已校准预测器，使其保留原始预测器的信息且无法利用现有信息进一步优化。我们将已校准预测器建模为信号方案，并通过与特征无关的加扰定义优化：若一个预测器的信号可模拟另一个的信号，则前者优化后者。可构造性通过可观测线性信息表征：每个信号对应特征空间上的一个向量，当新信号的向量位于输入信号向量的线性张成空间中时，该新信号可精确构造。在此框架下，我们建立了清晰的算法图景：对于确定性输出预测器，双边优化存在基于两个输入信号划分间二分图的多项式时间算法；而对于任意数量输入预测器的优化问题，其为NP难问题。相反，当允许随机化输出预测器时，我们通过将可构造信号向量分解为关联多面体锥的极射线，给出了适用于任意数量输入预测器的多项式时间算法。
英文摘要
Prediction aggregation aims to combine information from multiple predictors into a more informative one. We study this question in the setting of calibrated predictors, where each prediction must equal the conditional expectation of the quantity being predicted given the predictor's signal. Given several calibrated input predictors and the feature distribution, but not the underlying Bayes probabilities, we ask when one can construct refined calibrated predictors that preserve the information in the original predictors and cannot be further refined using the available information. We formulate calibrated predictors as signaling schemes and define refinement through feature-independent garblings: a predictor refines another if its signal can simulate the other's signal. Constructibility is characterized through observable linear information: each signal corresponds to a vector over the feature space, and a new signal is constructible exactly when its vector lies in the linear span of the input signal vectors. Under this formulation, we establish a sharp algorithmic picture. For deterministic output predictors, bilateral refinement admits a polynomial-time algorithm based on a bipartite graph between the two input signal partitions, while refinement with an arbitrary number of input predictors is $\mathsf{NP}$-hard. In contrast, when randomized output predictors are allowed, we give a polynomial-time algorithm for any number of input predictors by decomposing constructible signal vectors into extreme rays of the associated polyhedral cone.
CommentsA more compact version of the paper has been accepted by NeurIPS 2026
