1,585 research outputs found

    Hamiltonian ABC

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    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

    Implicit Langevin Algorithms for Sampling From Log-concave Densities

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    For sampling from a log-concave density, we study implicit integrators resulting from θ\theta-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for θ∈[0,1] \theta \in [0,1] and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for θ≥1/2\theta\ge1/2, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We show that obtaining subsequent samples amounts to solving a strongly-convex optimization problem, which is readily achievable using one of numerous existing methods. Numerical examples supporting our theoretical analysis are also presented
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