When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for probabilistic reasoning in order to determine the confidence (or epistemic uncertainty) in the probabilities in light of the training data. We propose an approach to overcome the independence assumption behind most of the approaches dealing with a large class of probabilistic reasoning that includes Bayesian networks as well as several instances of probabilistic logic. We provide an algorithm for Bayesian learning from sparse, albeit complete, observations, and for deriving inferences and their confidences keeping track of the dependencies between variables when they are manipulated within the unifying computational formalism provided by probabilistic circuits. Each leaf of such circuits is labelled with a beta-distributed random variable that provides us with an elegant framework for representing uncertain probabilities. We achieve better estimation of epistemic uncertainty than state-of-the-art approaches, including highly engineered ones, while being able to handle general circuits and with just a modest increase in the computational effort compared to using point probabilities.

中文翻译：

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处理概率回路中的认知和运动不确定性

与AI系统协作时，我们需要评估何时信任其建议。如果我们在可能会出错的区域错误地信任它，则可能会发生灾难性故障，因此需要贝叶斯方法进行概率推理，以便根据训练数据确定概率的置信度（或认知不确定性）。我们提出了一种克服大多数方法背后的独立性假设的方法，这些方法处理的是包括贝叶斯网络以及概率逻辑的多个实例在内的一大类概率推理。我们提供了一种算法，用于从稀疏，完整，观察到的贝叶斯学习，当推论和它们的置信度在概率电路提供的统一计算形式中被操纵时，跟踪变量之间的依赖关系。这样的电路的每一片叶子都标有一个beta分布的随机变量，为我们提供了一个优雅的框架来表示不确定的概率。与最先进的方法（包括高度工程化的方法）相比，我们可以更好地估计认知不确定性，同时能够处理通用电路，并且与使用点概率相比，计算量仅会适度增加。