Advancing and Leveraging Tractable Likelihood Models

Abstract

The past decade has seen a remarkable improvement in a variety of machine learning applications thanks to numerous advances in deep neural networks (DNN). These models are now the de facto standard in fields ranging from image/speech recognition to driverless cars and have begun to permeate aspects of modern science and everyday life. The deep learning revolution has also resulted in highly effective generative models such as score matching models, diffusion models, VAEs, GANs, and tractable likelihood models. These models are best known for their ability to create novel samples of impressive quality but are usually limited to highly structured data modalities. Expanding the capabilities and applications of likelihood models beyond conventional data formats and generative applications can increase functionality, interpretability, and intuition compared to conventional methods. This dissertation addresses shortcomings in likelihood models over less structured data and explores methods to exploit a learned density as part of a larger application. We begin by advancing the performance of likelihood models outside the standard, ordered data regime by developing methods that are applicable to sets, e.g., point clouds. Many data sources contain instances that are a collection of unordered points, such as points on the surface of scans from human organs, sets of images from a web page, or LiDAR observations commonly used in driverless cars or (hyper-spectral) aerial surveys.We then explore several applications of density models. First, we consider generative process over neural networks themselves and show that training over ensembles of these sampled models can lead to improved robustness to adversarial attacks. Next, we demonstrate how to use the transformative portion of a normalizing flow as a feature extractor in conjunction with a downstream task to estimate expectations over model performance in local and global regions.Finally, we propose a learnable, continuous parameterization of mixture models directly on the input space to improve model interpretability while simultaneously allowing for arbitrary marginalization or conditioning without the need to train new models or develop complex masking mechanisms.Doctor of Philosoph