arXiv:2501.11413cs.LGcs.AI2025-01被引 7

提出可预测预测集效率的理论框架,解决数据分布变化时模型可靠性与精度的权衡问题。

Generalization and Informativeness of Weighted Conformal Risk Control Under Covariate Shift

  • 基于训练时可获取的指标,推导出加权置信风险控制的效率上界
  • 揭示预测集信息量、分布偏移程度与校准/训练集规模的关系
  • 适用于需要高可靠性且分布可能漂移的场景,如定位系统

预测模型常需在与训练数据统计条件不匹配的情况下仍保持可靠。一种常见情况是协变量偏移:输入特征的边际分布发生变化,但给定输入下目标变量的条件分布保持不变。加权置信风险控制(W-CRC)利用训练阶段的数据,将点预测转化为测试时仍具有效风险保证的预测集,即使存在协变量偏移。然而,尽管W-CRC提供统计可靠性,其效率(以预测集大小衡量)仅能在测试时评估。本文将基础预测器的泛化性能与W-CRC在协变量偏移下的效率联系起来,推导出一个依赖于算法超参数和训练时可得的任务相关量的效率上界。该上界揭示了预测集信息量、协变量偏移程度以及校准集与训练集规模之间的关系。指纹定位实验验证了理论结果。

原文摘要 · Abstract (English)

Predictive models are often required to produce reliable predictions under statistical conditions that are not matched to the training data. A common type of training-testing mismatch is covariate shift, where the conditional distribution of the target variable given the input features remains fixed, while the marginal distribution of the inputs changes. Weighted conformal risk control (W-CRC) uses data collected during the training phase to convert point predictions into prediction sets with valid risk guarantees at test time despite the presence of a covariate shift. However, while W-CRC provides statistical reliability, its efficiency -- measured by the size of the prediction sets -- can only be assessed at test time. In this work, we relate the generalization properties of the base predictor to the efficiency of W-CRC under covariate shifts. Specifically, we derive a bound on the inefficiency of the W-CRC predictor that depends on algorithmic hyperparameters and task-specific quantities available at training time. This bound offers insights on relationships between the informativeness of the prediction sets, the extent of the covariate shift, and the size of the calibration and training sets. Experiments on fingerprinting-based localization validate the theoretical results.

置信预测协变量偏移可靠性分析泛化性

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