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Hamiltonian Monte Carlo for Hierarchical Models

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If you have a question about this talk, please contact Robert Pinsler.

Hierarchical models provide a powerful framework for modelling and inference by defining second order and third order probability distributions over parameters at different levels of the generative model. Hamiltonian Monte Carlo (HMC) is one of the primary tools for inference in hierarchical models. While hierarchies provide modelling flexibility, they induce distinctive pathologies in the posterior that limit the efficiency of sampling algorithms like HMC . These pathologies can be best detected by visualising the joint posterior geometry through bivariate density plots and by HMC diagnostics. In this talk we will review HMC and its limitations in the context of posterior inference in hierarchical models. We will discuss some common techniques to simplify the posterior geometry through reparameterization that can significantly improve sampling efficiency. We will also briefly review advances like Riemann Manifold HMC that can address some of the weaknesses of Euclidean HMC in sampling from posterior geometries characterized by tight correlations and drastically changing curvature.

This talk is part of the Machine Learning Reading Group @ CUED series.

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