Conditioning Score-Based Generative Models by Neuro-Symbolic Constraints

Score-based and diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which requires training a noise-dependent classifier, even when the classifier for uncorrupted data is given. We propose an approach to sample from unconditional score-based generative models enforcing arbitrary logical constraints, without any additional training. Firstly, we show how to manipulate the learned score in order to sample from an un-normalized distribution conditional on a user-defined constraint. Then, we define a flexible and numerically stable neuro-symbolic framework for encoding soft logical constraints. Combining these two ingredients we obtain a general, but approximate, conditional sampling algorithm. We further developed effective heuristics aimed at improving the approximation. Finally, we show the effectiveness of our approach for various types of constraints and data: tabular data, images and time series.

Generating Realistic Synthetic Relational Data through Graph Variational Autoencoders

Synthetic data generation has recently gained widespread attention as a more reliable alternative to traditional data anonymization. The involved methods are originally developed for image synthesis. Hence, their application to the typically tabular and relational datasets from healthcare, finance and other industries is non-trivial. While substantial research has been devoted to the generation of realistic tabular datasets, the study of synthetic relational databases is still in its infancy. In this paper, we combine the variational autoencoder framework with graph neural networks to generate realistic synthetic relational databases. We then apply the obtained method to two publicly available databases in computational experiments. The results indicate that real databases' structures are accurately preserved in the resulting synthetic datasets, even for large datasets with advanced data types.