1,661 research outputs found
Hamiltonian ABC
Approximate Bayesian computation (ABC) is a powerful and elegant framework
for performing inference in simulation-based models. However, due to the
difficulty in scaling likelihood estimates, ABC remains useful for relatively
low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of
likelihood-free algorithms that apply recent advances in scaling Bayesian
learning using Hamiltonian Monte Carlo (HMC) and stochastic gradients. We find
that a small number forward simulations can effectively approximate the ABC
gradient, allowing Hamiltonian dynamics to efficiently traverse parameter
spaces. We also describe a new simple yet general approach of incorporating
random seeds into the state of the Markov chain, further reducing the random
walk behavior of HABC. We demonstrate HABC on several typical ABC problems, and
show that HABC samples comparably to regular Bayesian inference using true
gradients on a high-dimensional problem from machine learning.Comment: Submission to UAI 201
A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
We propose a new sensitivity analysis methodology for complex stochastic
dynamics based on the Relative Entropy Rate. The method becomes computationally
feasible at the stationary regime of the process and involves the calculation
of suitable observables in path space for the Relative Entropy Rate and the
corresponding Fisher Information Matrix. The stationary regime is crucial for
stochastic dynamics and here allows us to address the sensitivity analysis of
complex systems, including examples of processes with complex landscapes that
exhibit metastability, non-reversible systems from a statistical mechanics
perspective, and high-dimensional, spatially distributed models. All these
systems exhibit, typically non-gaussian stationary probability distributions,
while in the case of high-dimensionality, histograms are impossible to
construct directly. Our proposed methods bypass these challenges relying on the
direct Monte Carlo simulation of rigorously derived observables for the
Relative Entropy Rate and Fisher Information in path space rather than on the
stationary probability distribution itself. We demonstrate the capabilities of
the proposed methodology by focusing here on two classes of problems: (a)
Langevin particle systems with either reversible (gradient) or non-reversible
(non-gradient) forcing, highlighting the ability of the method to carry out
sensitivity analysis in non-equilibrium systems; and, (b) spatially extended
Kinetic Monte Carlo models, showing that the method can handle high-dimensional
problems
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