论文标题
统计推断是格林的功能
Statistical inference as Green's functions
论文作者
论文摘要
来自数据的统计推断是科学的基础任务。最近，它因其在数据科学和机器学习的主要兴趣推理系统中的核心作用而受到了越来越多的关注。但是，对统计推论的理解并不是那么坚实，而作为主观信念或常规程序曾经声称是客观的问题。我们在这里表明，对长序列可交换二进制随机变量的统计推断有一个客观描述，即理论和应用中的原型随机性。线性微分方程来自称为de Finetti的表示定理的身份，事实证明统计推断是由绿色的函数给出的。我们的发现是对科学规范问题的答案，该问题基于数据来追求客观性，其意义在大多数纯粹和应用领域中都将是深远的。
Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding of statistical inference is not that solid while remains as a matter of subjective belief or as the routine procedures once claimed objective. We here show that there is an objective description of statistical inference for long sequence of exchangeable binary random variables, the prototypal stochasticity in theories and applications. A linear differential equation is derived from the identity known as de Finetti's representation theorem, and it turns out that statistical inference is given by the Green's functions. Our finding is an answer to the normative issue of science that pursues the objectivity based on data, and its significance will be far-reaching in most pure and applied fields.
