In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such improvements were measured were accurately capturing the intended goal, whether the numerical differences in the resulting values were significant, or whether uncertainty played a role in this study and if it should have been taken into account, was of secondary importance. Whereas probability theory, be it frequentist or Bayesian, used to be the gold standard in science before the advent of the supercomputer, it was quickly replaced in favor of black box models and sheer computing power because of their ability to handle large data sets. This evolution sadly happened at the expense of interpretability and trustworthiness. However, while people are still trying to improve the predictive power of their models, the community is starting to realize that for many applications it is not so much the exact prediction that is of importance, but rather the variability or uncertainty. The work in this dissertation tries to further the quest for a world where everyone is aware of uncertainty, of how important it is and how to embrace it instead of fearing it. A specific, though general, framework that allows anyone to obtain accurate uncertainty estimates is singled out and analysed. Certain aspects and applications of the framework -- dubbed `conformal prediction' -- are studied in detail. Whereas many approaches to uncertainty quantification make strong assumptions about the data, conformal prediction is, at the time of writing, the only framework that deserves the title `distribution-free'. No parametric assumptions have to be made and the nonparametric results also hold without having to resort to the law of large numbers in the asymptotic regime.

翻译：过去几十年间，数据分析和机器学习领域的研究主要聚焦于优化预测模型，以突破现有模型性能极限。但人们往往忽视以下问题：衡量改进效果的指标是否准确反映预期目标？数值差异是否具有统计学意义？不确定性在研究中的角色是否应被纳入考量？在超级计算机时代来临前，无论频率学派还是贝叶斯学派概率论都是科学界的黄金标准，然而当黑箱模型凭借处理大规模数据集的能力迅速取代传统方法时，这种演变遗憾地牺牲了模型的可解释性与可信度。尽管研究者仍在追求提升模型预测能力，但学界已逐渐认识到，许多应用场景中真正重要的并非精确预测值，而是变异性或不确定性。本论文致力于推动构建一个全民认知不确定性、理解其重要性并学会与之共处而非恐惧的世界。我们独选出一种普适性框架进行深入剖析——该框架能使任何人获得准确的不确定性估计，并对其特定应用场景展开详尽研究。相较于众多需要强数据假设的不确定性量化方法，共形预测在撰写本文时仍是唯一称得上"无分布假设"的框架：无需预设参数模型，其非参数结论在渐近状态下亦无需依赖大数定律即可成立。