Elise Walker ^1* Jonas A. Actor ¹ Carianne Martinez ^1,2 Nathaniel Trask ³

• ¹ Sandia National Laboratories, Albuquerque, United States
• ² Arizona State University, Tempe, Arizona, United States
• ³ University of Pennsylvania, Philadelphia, Pennsylvania, United States

Representation learning algorithms are often used to extract essential features from highdimensional datasets. These algorithms commonly assume that such features are independent.However, multimodal datasets containing complementary information often have causally related features. Consequently, there is a need to discover features purporting conditional independencies. Bayesian Networks (BN) are probabilistic graphical models which use directed acyclic graphs (DAGs) to encode the conditional independencies of a joint distribution. To discover features and their conditional independence structure, we develop pimaDAG -a variational autoencoder framework which learns features from multimodal datasets, possibly with known physics constraints, and a BN describing the feature distribution. Our algorithm introduces a new DAG parameterization, which we use to learn a BN simultaneously with a latent space of a variational autoencoder in an end-to-end differentiable framework via a single, tractable evidence lower bound loss function. We place a Gaussian mixture prior on the latent space and identify each of the Gaussians with an outcome of the DAG nodes; this identification enables feature discovery with conditional independence relationships obeying the Markov factorization property.Tested against a synthetic and a scientific dataset, our results demonstrate the capability of learning a BN on simultaneously discovered key features in a fully unsupervised setting.