PhD Thesis Defense: Abhinav Agrawal, Towards Reliable Black-Box Variational Inference
Content
Speaker
Abstract
Probabilistic models are essential for understanding complex systems across various scientific fields. Inferring the posterior distribution over the unknown quantities is central to generating insights from these models, but the posterior is often analytically intractable and must be approximated. Black-box variational inference (BBVI) is a leading approximate inference framework that uses optimization to find a tractable posterior approximation. BBVI methods apply to a wide variety of models and offer practitioners a faster alternative to expensive Markov chain Monte Carlo methods. While BBVI is promising, it suffers from several issues that hinder its widespread adoption. We identify four such challenges: robustness, scalability, evaluation, and accuracy, and address them in this thesis to make BBVI a reliable inference tool.
The first chapter addresses the issue of robustness. Naive BBVI approaches are often not robust enough to work out of the box and fail to converge without model-specific tuning. We improve this by integrating key algorithmic components like initialization strategies, gradient estimators, variational objectives, and advanced variational families. Extensive empirical studies demonstrate that our proposed scheme outperforms competing baselines without requiring model-specific tuning.
The second chapter improves scalability. When models are large, BBVI methods fail to scale and suffer from slow convergence. We address this by proposing a structured and amortized BBVI scheme that maintains accuracy while offering faster and more scalable inference than existing approaches.
The third chapter improves evaluation. The posterior predictive evaluation can sometimes be noisy, making it hard to predict accurately. We identify the conditions under which the simple Monte Carlo estimator of the PPD can exhibit an extremely low signal-to-noise ratio. Based on this analysis, we introduce an adaptive importance sampling approach that significantly improves the evaluation accuracy.
The fourth chapter improves accuracy. Normalizing flow-based variational inference (flow VI) is a promising class of BBVI methods, but its performance is mixed, with some works reporting success and others reporting optimization challenges. We conduct an empirical analysis to disentangle the impact of various factors like representational capacity, objectives, gradient estimators, batch sizes, and step sizes. Our analysis leads to practical recommendations for each factor, culminating in a flow VI approach that matches or surpasses leading turnkey Hamiltonian Monte Carlo methods on a wide variety of targets.
Collectively, the advances in this thesis make BBVI a reliable inference method.
Advisor
Justin Domke