2015

The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling

Betancourt, M. J.

Understand

Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte Carlo produces computationally efficient Monte Carlo estimators, even with respect to complex and high-dimensional target distributions.

  • When confronted with data-intensive applications, however, the algorithm may be too expensive to implement, leaving us to consider the utility of approximations such as data subsampling.
  • In this paper I demonstrate how data subsampling fundamentally compromises the efficient exploration of Hamiltonian flow and hence the scalable performance of Hamiltonian Monte Carlo itself.

Built on

  • Hybrid Monte Carlo

    Duane, Simon, Kennedy, A.D., Pendleton, Brian J., and Roweth, Duncan · 1987

    Earlier work this paper cites.

  • Simulating Hamiltonian Dynamics

    Leimkuhler, B. and Reich, S · 2004

    Earlier work this paper cites.

  • Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations

    Hairer, E., Lubich, C., and Wanner, G · 2006

    Earlier work this paper cites.

  • Riemann Manifold Langevin and Hamiltonian Monte Carlo methods

    Girolami, Mark and Calderhead, Ben · 2011

    Earlier work this paper cites.

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Then

  • Stochastic gradient Hamiltonian Monte Carlo

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