论文标题
关于可牵引概率模型中的约束性可确定性
On Constraint Definability in Tractable Probabilistic Models
论文作者
论文摘要
纳入约束是概率机器学习的主要问题。各种各样的问题都需要将预测与关于约束的推理集成在一起，从地图上的建模路线到批准贷款预测。在前者中，我们可能需要预测模型来尊重地图上节点之间的物理路径的存在，而在后者中，我们可能要求预测模型尊重公平性约束，以确保结果不会受到偏见。从广义上讲，约束可能是概率，逻辑或因果关系，但总体挑战是确定是否以及如何学习模型来处理所有声明的约束。据我们所知，这在很大程度上是一个开放的问题。在本文中，我们考虑了关于在合并约束时如何实现可处理概率模型的学习（例如总计网络）的数学询问。
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions. In the former, we may require the prediction model to respect the presence of physical paths between the nodes on the map, and in the latter, we may require that the prediction model respect fairness constraints that ensure that outcomes are not subject to bias. Broadly speaking, constraints may be probabilistic, logical or causal, but the overarching challenge is to determine if and how a model can be learnt that handles all the declared constraints. To the best of our knowledge, this is largely an open problem. In this paper, we consider a mathematical inquiry on how the learning of tractable probabilistic models, such as sum-product networks, is possible while incorporating constraints.
