Variational Inference for GARCH-family Models

The Bayesian estimation of GARCH-family models has been typically addressed through Monte Carlo sampling. Variational Inference is gaining popularity and attention as a robust approach for Bayesian inference in complex machine learning models; however, its adoption in econometrics and finance is limited. This paper discusses the extent to which Variational Inference constitutes a reliable and feasible alternative to Monte Carlo sampling for Bayesian inference in GARCH-like models. Through a large-scale experiment involving the constituents of the S& P 500 index, several Variational Inference optimizers, a variety of volatility models, and a case study, we show that Variational Inference is an attractive, remarkably well-calibrated, and competitive method for Bayesian learning

Doubly Stochastic Variational Inference for Deep Gaussian Processes

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs, but inference in these models has proved challenging. Existing approaches to inference in DGP models assume approximate posteriors that force independence between the layers, and do not work well in practice. We present a doubly stochastic variational inference algorithm, which does not force independence between layers. With our method of inference we demonstrate that a DGP model can be used effectively on data ranging in size from hundreds to a billion points. We provide strong empirical evidence that our inference scheme for DGPs works well in practice in both classification and regression.Comment: NIPS 201