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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