2020/11/18 by David R. Burt, Sebastian W. Ober, Burt, David R. +5 · 3 citations
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2011.09421
openalex publication_date 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural networks, where we only need the former, and the latter is hard to represent. In this work, we highlight some advantages and limitations of employing the Kullback-Leibler divergence in this setting. For example, we show that minimizing the KL divergence between a wide class of parametric distributions and the posterior induced by a (non-degenerate) Gaussian process prior leads to an ill-defined objective function. Then, we propose (featurized) Bayesian linear regression as a benchmark for `function-space' inference methods that directly measures approximation quality. We apply this methodology to assess aspects of the objective function and inference scheme considered in Sun, Zhang, Shi, and Grosse (2018), emphasizing the quality of approximation to Bayesian inference as opposed to predictive performance.