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Order Effects of Measurements in Multi-Agent Hypothesis Testing
arXiv - CS - Multiagent Systems Pub Date : 2020-03-26 , DOI: arxiv-2003.11693
Aneesh Raghavan and John S. Baras

In multi-agent systems, agents observe data, and use them to make inferences and take actions. As a result sensing and control naturally interfere, more so from a real-time perspective. A natural consequence is that in multi-agent systems there are propositions based on the set of observed events that might not be simultaneously verifiable, which leads to the need for probability structures that allow such \textit{incompatible events}. We revisit the structure of events in a multi-agent system and we introduce the necessary new models that incorporate such incompatible events in the formalism. These models are essential for building non-commutative probability models, which are different than the classical models based on the Kolmogorov construction. From this perspective, we revisit the concepts of \textit{event-state-operation structure} and the needed \textit{relationship of incompatibility} from the literature and use them as a tool to study the needed new algebraic structure of the set of events. We present an example from multi-agent hypothesis testing where the set of events does not form a Boolean algebra, but forms an ortholattice. A possible construction of a `noncommutative probability space', accounting for \textit{incompatible events} is discussed. We formulate and solve the binary hypothesis testing problem in the noncommutative probability space. We illustrate the occurrence of `order effects' in the multi-agent hypothesis testing problem by computing the minimum probability of error that can be achieved with different orders of measurements.

中文翻译:

多智能体假设检验中测量的顺序效应

在多代理系统中,代理观察数据,并使用它们进行推理和采取行动。因此,传感和控制自然会相互干扰,从实时角度来看更是如此。一个自然的结果是,在多智能体系统中,存在基于观察事件集的命题,这些命题可能无法同时验证,这导致需要允许此类 \textit{不兼容事件} 的概率结构。我们重新审视了多代理系统中事件的结构,并引入了必要的新模型,这些模型将这些不兼容的事件纳入了形式主义。这些模型对于构建与基于 Kolmogorov 构造的经典模型不同的非交换概率模型至关重要。从这个角度来说,我们从文献中重新审视了 \textit{event-state-operation structure} 和所需的 \textit{relationship of incompatibility} 的概念,并将它们用作研究事件集所需的新代数结构的工具。我们提供了一个来自多智能体假设检验的例子,其中事件集不形成布尔代数,而是形成正交。讨论了“非交换概率空间”的可能构造,解释了 \textit{不兼容事件}。我们在非交换概率空间中制定并解决二元假设检验问题。我们通过计算不同测量顺序可以实现的最小错误概率来说明多智能体假设检验问题中“顺序效应”的发生。我们提供了一个来自多智能体假设检验的例子,其中事件集不形成布尔代数,而是形成正交。讨论了“非交换概率空间”的可能构造,解释了 \textit{不兼容事件}。我们在非交换概率空间中制定并解决二元假设检验问题。我们通过计算不同测量顺序可以实现的最小错误概率来说明多智能体假设检验问题中“顺序效应”的发生。我们提供了一个来自多智能体假设检验的例子,其中事件集不形成布尔代数,而是形成正交。讨论了“非交换概率空间”的可能构造,解释了 \textit{不兼容事件}。我们在非交换概率空间中制定并解决二元假设检验问题。我们通过计算不同测量顺序可以实现的最小错误概率来说明多智能体假设检验问题中“顺序效应”的发生。我们在非交换概率空间中制定并解决二元假设检验问题。我们通过计算不同测量顺序可以实现的最小错误概率来说明多智能体假设检验问题中“顺序效应”的发生。我们在非交换概率空间中制定并解决二元假设检验问题。我们通过计算不同测量顺序可以实现的最小错误概率来说明多智能体假设检验问题中“顺序效应”的发生。
更新日期:2020-11-13
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