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SUMMARY:On the robustness of gradient-based MCMC algorithms - Sam Livingst
 one — University College London
DTSTART:20191011T130000Z
DTEND:20191011T140000Z
UID:TALK130063@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We analyse the tension between robustness and efficiency for M
 arkov chain Monte Carlo (MCMC) sampling algorithms. In particular\, we foc
 us on robustness of MCMC algorithms with respect to heterogeneity in the t
 arget and their sensitivity to tuning\, an issue of great practical releva
 nce but still understudied theoretically. We show that the spectral gap of
  the Markov chains induced by classical gradient-based MCMC schemes (e.g. 
 Langevin and Hamiltonian Monte Carlo) decays exponentially fast in the deg
 ree of mismatch between the scales of the proposal and target distribution
 s\, while for the random walk Metropolis (RWM) the decay is linear. This r
 esult provides theoretical support to the notion that gradient-based MCMC 
 schemes are less robust to heterogeneity and more sensitive to tuning. Mot
 ivated by these considerations\, we propose a novel and simple to implemen
 t gradient-based MCMC algorithm\, inspired by the classical Barker accept-
 reject rule\, with improved robustness properties. Extensive theoretical r
 esults\, dealing with robustness to heterogeneity\, geometric ergodicity a
 nd scaling with dimensionality\, show that the novel scheme combines the r
 obustness of RWM with the efficiency of classical gradient-based schemes. 
 We illustrate with simulation studies how this type of robustness is parti
 cularly beneficial in the context of adaptive MCMC\, giving examples in wh
 ich the new scheme gives orders of magnitude improvements in performance o
 ver state-of-the-art alternatives. \n\n \nThis is joint work with Giacomo 
 Zanella\, see the preprint here: https://arxiv.org/abs/1908.11812
LOCATION:MR12
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