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A neural network assisted Metropolis adjusted Langevin algorithm

Author

Listed:
  • Müller Christian

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

  • Diedam Holger

    (Bayer AG, Applied Mathematics, Leverkusen, Germany)

  • Mrziglod Thomas

    (Bayer AG, Applied Mathematics, Leverkusen, Germany)

  • Schuppert Andreas

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

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).

Suggested Citation

  • Müller Christian & Diedam Holger & Mrziglod Thomas & Schuppert Andreas, 2020. "A neural network assisted Metropolis adjusted Langevin algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 93-111, June.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:2:p:93-111:n:2
    DOI: 10.1515/mcma-2020-2060
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