Conditional Density Estimation with Bayesian Normalising Flows

Abstract

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.

References in corpus (6)

• Variational Inference with Normalizing Flows
• Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks
• Masked Autoregressive Flow for Density Estimation
• Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation
• A Deep and Tractable Density Estimator
• Overpruning in Variational Bayesian Neural Networks

Cited by in corpus (20)

• Normalizing Flows: An Introduction and Review of Current Methods
• Deep Structural Causal Models for Tractable Counterfactual Inference
• Algorithmic recourse under imperfect causal knowledge: a probabilistic approach
• Learning Likelihoods with Conditional Normalizing Flows
• Dynamical mass inference of galaxy clusters with neural flows
• On the representation and learning of monotone triangular transport maps
• Dim but not entirely dark: Extracting the Galactic Center Excess' source-count distribution with neural nets
• Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows
• Semi-Conditional Normalizing Flows for Semi-Supervised Learning
• VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments
• Towards a data-driven model of hadronization using normalizing flows
• Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics
• Noise Contrastive Meta-Learning for Conditional Density Estimation using Kernel Mean Embeddings
• Conditional Density Estimation, Latent Variable Discovery and Optimal Transport
• Structured Output Learning with Conditional Generative Flows
• Semi-supervised Learning with Missing Values Imputation
• Weakly Supervised Label Learning Flows
• Dirac Delta Regression: Conditional Density Estimation with Clinical Trials
• Viscos Flows: Variational Schur Conditional Sampling With Normalizing Flows
• Uncertainty estimation under model misspecification in neural network regression