UC Irvine

Probabilistic graphical models provide a general framework for generative modeling and inference of structured data. Alternatively, the more modern approach of neural networks can flexibly fit complex and high-dimensional data but lacks the interpretability and adaptability of graphical models. In this work, we provide novel algorithms that combine the strengths of both approaches. We focus on time series data, which are defined by structured relationships between measurements at neighboring time steps. First, we focus on a scientific setting where data is low-dimensional and contains sparse, sometimes irregular observations of dynamic processes. In this setting, some of the underlying structure of the model is known to scientists, but we seek to uncover a small number of interpretable underlying parameters such as the reaction rate of a chemical in a system or the reproduction rate of an animal species. We propose a novel algorithm that deploys neural networks to speed up variational inference in Gauss-Markov models, allowing fast recovery of these global parameters of interest. Second, we show how graphical models can be integrated into deep generative models to fit high-dimensional data. Our adaptations to the Structured Variational Autoencoder (SVAE) solve its substantial optimization challenges. We propose novel algorithms for learning SVAEs, and are the first to demonstrate the SVAE's ability to handle multimodal uncertainty when data is missing by incorporating discrete latent variables. Our experimental results on human motion and audio spectrogram data show the clear performance advantages of this approach while also constructing interpretable segmentations of time series. Finally, we turn our attention to learning objectives other than maximum likelihood. In particular, we show how anti-discrimination constraints can be scaled to deep learning settings like models of images and text. Looking forward, we believe these ideas can be combined to enforce ethical and hand-crafted objectives on high-dimensional data via graphical model specifications. Applications for this neural network-graphical model synthesis include climate data analysis and text-conditioned modeling of human motion.