Explaining the success of modern energy-based modelling with complexity theory

Energy-based probabilistic models are enjoying renewed popularity due to their state-of-the-art applications in language and image processing. This success is enabled by efficient methods for estimating and sampling these models. Many of these methods are improved versions of older ones, such as Noise-Contrastive Estimation and Score-Matching for estimation, and Langevin dynamics for sampling. Overwhelmingly, these improvements rely on a common technique called annealing, which introduces a sequence of intermediate distributions that start from a Gaussian and end with the data distribution. Given the success of annealing, it is important to understand when and why it enables efficient algorithms and how to implement them effectively. My current line of research provides a quantitative understanding of the limitations of older methods, conditions under which annealing improves them, and a principled approach for picking the intermediate distributions.