Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter learning, often neglecting the potential of knowledge-intensive learning, a particular issue in data-scarce/knowledge-rich domains such as healthcare. To bridge this gap, we propose a novel unified framework that can systematically integrate diverse domain knowledge into the parameter learning process of PCs. Experiments on several benchmarks as well as real world datasets show that our proposed framework can both effectively and efficiently leverage domain knowledge to achieve superior performance compared to purely data-driven learning approaches.

Real-world machine-learning applications require robust models that generalize well to distribution shift settings, which is typical in real-world situations. Domain adaptation techniques aim to address this issue of distribution shift by minimizing the disparities between domains to ensure that the model trained on the source domain performs well on the target domain. Nevertheless, the existing domain adaptation methods are computationally very expensive. In this work, we aim to improve the efficiency of existing supervised domain adaptation (SDA) methods by using a subset of source data that is similar to target data for faster model training. Specifically, we propose ORIENT, a subset selection framework that uses the submodular mutual information (SMI) functions to select a source data subset similar to the target data for faster training. Additionally, we demonstrate how existing robust subset selection strategies, such as GLISTER, GRADMATCH, and CRAIG, when used with a held-out query set, fit within our proposed framework and demonstrate the connections with them. Finally, we empirically demonstrate that SDA approaches like d-SNE, CCSA, and standard Cross-entropy training, when employed together with ORIENT, achieve a) faster training and b) better performance on the target data.

While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed around personal health. Our empirical evaluation against competing methods from both generative and causal modelling demonstrates that interventional SPNs indeed are both expressive and causally adequate.