论归纳推理的原则

统一归纳逻辑：从形式学习到统计推断再到监督学习

Unified Inductive Logic: From Formal Learning to Statistical Inference to Supervised Learning

本文提出皮尔士式归纳逻辑，统一形式学习、统计推断与监督学习，并用统一原则证明各领域评估非演绎推理标准的合理性。

Simpson's Paradox: A Singularity of Statistical and Inductive Inference

The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and probability theory. The first contribution is to provide a schematic analysis of SP in $2\times 2$ contingency tables and present new results, detailed proofs of previous results and a unifying view of the important examples of SP that have been reported in the literature. The second contribution of the paper suggests a new perspective on the surprise element of SP, r…

The Inductive Bias of Restricted f-GANs

Generative adversarial networks are a novel method for statistical inference that have achieved much empirical success; however, the factors contributing to this success remain ill-understood. In this work, we attempt to analyze generative adversarial learning -- that is, statistical inference as the result of a game between a generator and a discriminator -- with the view of understanding how it differs from classical statistical inference solutions such as maximum likelihood inference and the method of moments. Specifically, we provide a theoretical characterization of the distribution infer…

Introduction to minimum message length inference

The aim of this manuscript is to introduce the Bayesian minimum message length principle of inductive inference to a general statistical audience that may not be familiar with information theoretic statistics. We describe two key minimum message length inference approaches and demonstrate how the principle can be used to develop a new Bayesian alternative to the frequentist $t$-test as well as new approaches to hypothesis testing for the correlation coefficient. Lastly, we compare the minimum message length approach to the closely related minimum description length principle and discuss simila…

超越保形预测器：基于置信预测器的自适应保形推断

Beyond Conformal Predictors: Adaptive Conformal Inference with Confidence Predictors

本研究证明自适应保形推断的覆盖保证适用于更广泛的非保形置信预测器，在非可交换数据下提供计算优势并提升预测效率。

作为归纳推理理论的频率统计学

Frequentist statistics as a theory of inductive inference

在对哲学和统计思想之间的相互关系进行了一些一般性的评论之后，讨论主要集中在显着性检验上。这些被定义为$p$值的计算，而不是“接受”和"拒绝“的正式程序。一些类型的原假设的描述和证据解释的原则规定的影响，$p$ -值在每个应用程序的具体情况下，与长期的解释。各种更复杂的情况进行了讨论，其中修改简单的$p$值可能是必要的。