用函数型随机理论重新阐释置信预测，让其更贴近实际应用。
Randomness, exchangeability, and conformal prediction
- 用函数型随机理论替代算法随机性理论，消除未指定常数问题。
- 证明所有满足IID的置信预测器可转化为高效置信预测器。
- 适合关注机器学习基础与预测可靠性研究者阅读。
本文主张更广泛地使用函数型随机理论——一种去除未指定加性常数的算法随机理论改良版。该理论有助于理解独立同分布（IID）与数据交换性的关系。尽管机器学习中普遍假设数据为IID，但置信预测依赖于数据交换性。Nouretdinov、V'yugin和Gammerman曾基于算法随机理论证明：在IID假设下，置信预测是通用方法。本文（为Alex Gammerman纪念文集所作）将回顾交换性与IID的关系、置信预测的早期历史、作者与Alex及其他人士的交往经历，并将Nouretdinov等人的结果转化为函数型随机理论语言，使理论更接近实践。转化表明：每个对IID数据有效的置信预测器，皆可转化为不损失太多预测效率的置信预测器。
原文摘要 · Abstract (English)
This paper argues for a wider use of the functional theory of randomness, a modification of the algorithmic theory of randomness getting rid of unspecified additive constants. Both theories are useful for understanding relationships between the assumptions of IID data and data exchangeability. While the assumption of IID data is standard in machine learning, conformal prediction relies on data exchangeability. Nouretdinov, V'yugin, and Gammerman showed, using the language of the algorithmic theory of randomness, that conformal prediction is a universal method under the assumption of IID data. In this paper (written for the Alex Gammerman Festschrift) I will selectively review connections between exchangeability and the property of being IID, early history of conformal prediction, my encounters and collaboration with Alex and other interesting people, and a translation of Nouretdinov et al.'s results into the language of the functional theory of randomness, which moves it closer to practice. Namely, the translation says that every confidence predictor that is valid for IID data can be transformed to a conformal predictor without losing much in predictive efficiency.
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