论文标题
正式化独立性的推定
Formalizing the presumption of independence
论文作者
论文摘要
数学证明旨在提供自信的结论，但是可以使用非常相似的推论过程来使不确定的估计值开放。这种推理的关键因素是使用$ \ mathbb {e} [xy] = \ mathbb {e} [x] [x] \ Mathbb {e} [y] $的“默认”估计值，而在没有$ x $和$ y $之间的任何特定信息的情况下，我们致电 *$ x $和$ y $之间的相关性，我们致电 *独立性 *。基于这种启发式的推理是司空见惯的，直观地吸引人的，而且通常很成功 - 但完全非正式。 在本文中，我们介绍了启发式估计量的概念，以此作为这种不稳定推理的潜在形式化。我们为启发式估计器引入了一套直觉上可取的连贯性能，这些估计器不满意任何现有候选者。然后，我们提出了我们的主要开放问题：是否存在启发式估计器，可以正式地将独立推定的直观有效应用正式化，而又不接受虚假论点？
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of $\mathbb{E}[XY] = \mathbb{E}[X] \mathbb{E}[Y]$ in the absence of any specific information about the correlation between $X$ and $Y$, which we call *the presumption of independence*. Reasoning based on this heuristic is commonplace, intuitively compelling, and often quite successful -- but completely informal. In this paper we introduce the concept of a heuristic estimator as a potential formalization of this type of defeasible reasoning. We introduce a set of intuitively desirable coherence properties for heuristic estimators that are not satisfied by any existing candidates. Then we present our main open problem: is there a heuristic estimator that formalizes intuitively valid applications of the presumption of independence without also accepting spurious arguments?
