Conditional Density Estimation with Bayesian Normalising Flows
This addresses the challenge of conditional density estimation for applications like spatial modeling, though it appears incremental as it builds on existing normalising flow methods with a Bayesian approach.
The paper tackles the problem of modeling complex conditional distributions by developing a Bayesian framework that uses normalising flows as flexible likelihood models, achieving state-of-the-art performance on some benchmark regression datasets and applying it to large-scale spatial density modeling tasks with over 1 million datapoints.
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice. This paper employs normalising flows as a flexible likelihood model and presents an efficient method for fitting them to complex densities. These estimators must trade-off between modeling distributional complexity, functional complexity and heteroscedasticity without overfitting. We recognize these trade-offs as modeling decisions and develop a Bayesian framework for placing priors over these conditional density estimators using variational Bayesian neural networks. We evaluate this method on several small benchmark regression datasets, on some of which it obtains state of the art performance. Finally, we apply the method to two spatial density modeling tasks with over 1 million datapoints using the New York City yellow taxi dataset and the Chicago crime dataset.