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Hessian-based Markov-Chain Monte Carlo Algorithms

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Hessian-based Markov-Chain Monte Carlo Algorithms Tom Minka Microsoft Research Cambridge —— I will talk about how to make Markov-chain Monte Carlo run more efficiently in high-dimensional, continuous spaces. The idea is to shape the Markov transition density according to the local Hessian of the probability density function. This leads to a Hessian-based Metropolis-Hastings algorithm that we call HMH . A naive implementation of this idea would be quite expensive however, requiring the Hessian to be recomputed at each sample. Instead I will describe how to incrementally update the Hessian, and how to get many samples from the same Hessian (using the multiple-try Metropolis algorithm). The upshot is that, given any function where you can do efficient Hessian-based optimization, you can also do efficient sampling.

Joint work with Yuan (Alan) Qi.

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