通用离散概率计算框架
A framework for general discrete probability calculations
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中文总结 AI 辅助
研究如何正确描述离散概率系统，提出通过对概率值做一般性陈述及熵最大化补充信息来计算概率，该方法有广泛应用，其理论框架是软件实现基础，且易扩展，仅需常用Python库。
中文摘要 AI 辅助
概率遵循一套简单明了的规则。然而在实际中，概率推理可能极不直观，即便简单问题也可能误算。我们提出一种方法来正确描述离散概率支配的系统。本文所述方法能对概率值做一般性陈述，用于计算相关概率。若陈述不足无法得出唯一答案，就用熵最大化补充缺失信息。该方法在从实验物理到自然语言分析等领域有广泛潜在应用。这里描述的理论框架也是一个软件实现的基础，该软件易于扩展，仅需numpy、torch、sympy和scipy等常用Python库。
英文摘要
Probability follows a simple and concise set of rules. In practice, however, reason- ing about probability may be highly unintuitive and this leads to the possibility of miscalculations even for simple problems. We present an approach to facilitate the correct description of systems governed by discrete probability. The methods described in this paper allow making general statements about the values of prob- ability. This information can next be used to calculate any probability related to the system described by the statements. In case there are too few statements to provide a unique answer, entropy maximization is used to fill in the miss- ing information. The approach has wide potential applications that range from experimental physics to natural language analysis. The theoretical framework described here is also the basis of a software implementation that is designed to be straightforward to extend and requires only popular python libraries, numpy, torch, sympy, and scipy.
