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精确的系统:关于前金系统的连贯概率和对线性子空间的连贯预测
Rabanus Derr1, Robert C Williamson2
1Department of Computer Science, University of Tübingen, 72076 Tübingen, Germany.
Entropy (Basel, Switzerland)
|September 28, 2023
概括
不准确的概率在特定事件集上是精确的,称为精度系统. 这些系统形成 (前) 丁金系统,将不精确的概率与量子理论和机器学习等不同领域联系起来.
科学领域:
- 可能性理论概率理论.
- 决策理论 决策理论
- 量子概率 量子概率是指量子的概率.
- 机器学习 机器学习
背景情况:
- 不准确的概率理论往往忽视了不准确的概率可以在特定事件集上准确.
- 这些集合,称为精度系统,是基本的,但未被充分探索.
- 在不同领域的现有研究暗中使用类似的结构.
研究的目的:
- 在不精确的概率中正式引入和分析"精度系统".
- 建立精密系统和 (前) 丁金系统之间的连接.
- 探索将这些系统嵌入到集合代数中的含义及其与连贯性的关系.
主要方法:
- 较低和较高概率的数学分析.
- 在轻微假设下证明 (先) 丁金系统的形成.
- 对嵌入系统到集代数中的可扩展性条件的研究.
- 准确和信任集系统之间的格子二元性的探索.
- 概括到预期类型的不精确概率和部分预期.
主要成果:
- 对于较低和较高概率的精度系统形成 (先) 丁金系统.
- 可扩展性条件等同于不精确概率中的连贯性.
- 建立了一个格子二元性,将精度系统与信誉集联系起来.
- 该框架将部分预期概括为部分预期,连贯性和可扩展性保持同等.
结论:
- 精度系统在各种概率学和决策理论领域提供了一个统一的结构.
- 可扩展性和连贯性的等价性简化了理论分析.
- 开发的格子二元性为不精确的概率和信任集提供了新的视角.
- 将对部分预期的概括扩大了框架的适用性.
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