针对无遗憾对手的校准回归
Calibrated Regression Against An Adversary Without Regret
- Cornell University（康奈尔大学）
- Cornell Tech（康奈尔科技学院）
- Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对在线非概率分布数据流，提出一种事后重新校准的回归算法，保证预测校准性且相对基线模型具有低遗憾，并在贝叶斯优化中加速收敛。
AI中文摘要：
我们关注在线设置中的概率预测，其中数据不遵循概率分布。我们的工作旨在实现两个目标：（1）产生能够准确反映模型置信度的有效概率；以及（2）确保性能的传统概念（例如，高准确率）仍然成立。我们引入了在线算法，保证在任意数据点流上实现这些目标，包括由对手选择的数据。具体而言，我们的算法产生的预测是（1）校准的——即，80%的置信区间在80%的情况下包含真实结果——并且（2）相对于用户指定的基线模型具有低遗憾。我们实现了一种事后重新校准策略，在回归中可证明地实现了这些目标；以前的算法应用于分类或实现了（1）但没有实现（2）。在贝叶斯优化的背景下，这是一种数据分布随时间变化的在线基于模型的决策任务，我们的方法加速了向更优最优值的收敛。
英文摘要：
We are interested in probabilistic prediction in online settings in which data does not follow a probability distribution. Our work seeks to achieve two goals: (1) producing valid probabilities that accurately reflect model confidence; and (2) ensuring that traditional notions of performance (e.g., high accuracy) still hold. We introduce online algorithms guaranteed to achieve these goals on arbitrary streams of data points, including data chosen by an adversary. Specifically, our algorithms produce forecasts that are (1) calibrated -- i.e., an 80% confidence interval contains the true outcome 80% of the time -- and (2) have low regret relative to a user-specified baseline model. We implement a post-hoc recalibration strategy that provably achieves these goals in regression; previous algorithms applied to classification or achieved (1) but not (2). In the context of Bayesian optimization, an online model-based decision-making task in which the data distribution shifts over time, our method yields accelerated convergence to improved optima.
