On Constraint Definability in Tractable Probabilistic Models
This addresses the challenge of integrating constraints into probabilistic machine learning for applications like route modeling or fairness in predictions, but it is incremental as it builds on existing models without new breakthroughs.
The paper tackles the problem of learning tractable probabilistic models, like sum-product networks, while incorporating constraints such as probabilistic, logical, or causal ones, and finds that this is largely an open problem with no concrete results or numbers provided.
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.