A neural network assisted Metropolis adjusted Langevin algorithm

Monte Carlo Methods and Applications, vol. 26, pp. 93–111

Abstract

Abstract In this paper, we derive a Markov chain Monte Carlo (MCMC) algorithm supported by a neural network. In particular, we use the neural network to substitute derivative calculations made during a Metropolis adjusted Langevin algorithm (MALA) step with inexpensive neural network evaluations. Using a complex, high-dimensional blood coagulation model and a set of measurements, we define a likelihood function on which we evaluate the new MCMC algorithm. The blood coagulation model is a dynamic model, where derivative calculations are expensive and hence limit the efficiency of derivative-based MCMC algorithms. The MALA adaptation greatly reduces the time per iteration, while only slightly affecting the sample quality. We also test the new algorithm on a 2-dimensional example with a non-convex shape, a case where the MALA algorithm has a clear advantage over other state of the art MCMC algorithms. To assess the impact of the new algorithm, we compare the results to previously generated results of the MALA and the random walk Metropolis Hastings (RWMH).

Authors 4

1. Christian Alexander Müller corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RwtH Aachen Joint Research Center for Computational Biomedicine , Aachen , Germany

2. Holger Diedam

   Bayer (Germany)

   Affiliation as printed

   Bayer AG , Applied Mathematics , Leverkusen , Germany

3. Thomas Mrziglod

   Bayer (Germany)

   Affiliation as printed

   Bayer AG , Applied Mathematics , Leverkusen , Germany

4. Andreas Schuppert Aachen

   RWTH Aachen University

   Affiliation as printed

   RwtH Aachen Joint Research Center for Computational Biomedicine , Aachen , Germany