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Structural Markov laws / Geometry and HMC

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This talk will focus on two particular aspects of my research:

Suppose that we wish to infer the structure of a graphical model: how should we choose a prior over the space of possible graphs? I’ll introduce the notion of a structural Markov property, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This characterises an exponential family that is conjugate under sampling from compatible Markov distributions.

In the second part, I will talk about various geometric aspects of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm. I will explain how HMC can be extended to manifolds, such as spheres and Stiefel manifolds (the manifold of orthogonal matrices). I will also describe how this geometric understanding can guide the optimal tuning of the algorithm.

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

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