覆盖约束共形模型选择的序贯置信集

中文摘要 AI 辅助

现代共形预测系统通常维护多个自适应流水线，这些流水线在基础预测器、共形分数、校准窗口和更新规则方面各不相同。由于覆盖率是硬约束，而效率只能在可行流水线中优化，因此比较它们十分困难。我们将此问题表述为随机约束argmin的序贯推断问题。在每个时刻，目标是满足多个前缀平均条件误覆盖约束的最小成本流水线集合。我们引入了覆盖约束序贯模型置信集（CC-SMCS），它将可证明可行、可能可行和可能约束最优的流水线区分开来。利用同时鞅置信序列，CC-SMCS将矩形置信区域投影到约束argmin上，并允许精确的闭式规则。以至少$1-\delta$的概率，它同时包含所有时刻的每个约束最优流水线。这种有限样本保证不需要平稳性或混合假设，并且在数据依赖停止下仍然有效。我们还建立了覆盖边界处安全认证的不可能性结果，并将构造扩展到延迟多视野反馈和结果依赖的效率目标。

英文摘要

Modern conformal forecasting systems often maintain several adaptive pipelines that differ in base forecasters, conformity scores, calibration windows, and update rules. Comparing them is difficult because coverage is a hard constraint, whereas efficiency should be optimized only among feasible pipelines. We formulate this problem as sequential inference for a stochastic constrained argmin. At each time, the target is the set of minimum-cost pipelines satisfying multiple prefix-average conditional miscoverage constraints. We introduce Coverage-Constrained Sequential Model Confidence Sets (CC-SMCS), which separate certifiably feasible, possibly feasible, and possibly constrained-optimal pipelines. Using simultaneous martingale confidence sequences, CC-SMCS projects a rectangular confidence region onto the constrained argmin and admits an exact closed-form rule. With probability at least $1-δ$, it contains every constrained-optimal pipeline simultaneously over all times. This finite-sample guarantee requires no stationarity or mixing assumptions and remains valid under data-dependent stopping. We also establish an impossibility result for safe certification at the coverage boundary and extend the construction to delayed multi-horizon feedback and outcome-dependent efficiency objectives.

发表机构

• Jinan University（暨南大学）

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