Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale

Wu, Changye; Stoehr, Julien; Robert, Christian P.

doi:10.48550/arxiv.1810.04449

Cited by 4 publications

(6 citation statements)

References 8 publications

(9 reference statements)

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“…We see that manually-optimized Hamiltonian zigzag delivers substantial increases in ess compared to Zigzag-Nuts. Such efficiency gains are also observed by the authors who proposed alternative methods for tuning hmc (Wang et al, 2013;Wu et al, 2018). The results here indicate that their tuning approaches may be worthy alternatives to Zigzag-Nuts and may further increase Hamiltonian zigzag's overall advantage over Markovian zigzag.…”

Section: Simulation Set-up and Efficiency Metricssupporting

confidence: 78%

Hamiltonian zigzag sampler got more momentum than its Markovian counterpart: Equivalence of two zigzags under a momentum refreshment limit

Nishimura¹,

Zhang²,

Suchard³

2021

Preprint

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Zigzag and other piecewise deterministic Markov process samplers have attracted significant interest for their non-reversibility and other appealing properties for Bayesian posterior computation. Hamiltonian Monte Carlo is another state-of-the-art sampler, exploiting fictitious momentum to guide Markov chains through complex target distributions. In this article, we uncover a remarkable connection between the zigzag sampler and a variant of Hamiltonian Monte Carlo exploiting Laplace-distributed momentum. The position and velocity component of the corresponding Hamiltonian dynamics travels along a zigzag path paralleling the Markovian zigzag process; however, the dynamics is non-Markovian as the momentum component encodes non-immediate pasts. This information is partially lost during a momentum refreshment step, in which we preserve its direction but re-sample magnitude. In the limit of increasingly frequent momentum refreshments, we prove that this Hamiltonian zigzag converges to its Markovian counterpart. This theoretical insight suggests that, by retaining full momentum information, Hamiltonian zigzag can better explore target distributions with highly correlated parameters. We corroborate this intuition by comparing performance of the two zigzag cousins on high-dimensional truncated multivariate Gaussians, including a 11,235-dimensional target arising from a Bayesian phylogenetic multivariate probit model applied to HIV virus data.

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Section: Simulation Set-up and Efficiency Metricssupporting

confidence: 78%

Hamiltonian zigzag sampler got more momentum than its Markovian counterpart: Equivalence of two zigzags under a momentum refreshment limit

Nishimura¹,

Zhang²,

Suchard³

2021

Preprint

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“…A popular approach suggested in [32] tunes L based on the ESJD by doubling L until the path makes a U-turn and retraces back towards the starting point, that is by stopping to increase L when the distance to the proposed state reaches a stationary point [4]; see also [57] for a variation and [48] for a version using sequential proposals. Modern probabilistic programming languages such as Stan [12], PyMC3 [51], Turing [23,58] or TFP [39] furthermore allow for an adaptation of a diagonal or dense mass-matrix within NUTS based on the sample covariance matrix.…”

Section: Related Workmentioning

confidence: 99%

“…We consider a stochastic volatility model [36,34] that has been used with minor variations for adapting HMC [25,32,57]. Assume that the latent log-volatilities follow an autoregressive AR(1) process so that h 1 ∼ N (0, σ 2 /(1 − φ 2 )) and for t ∈ {1, .…”

Section: Stochastic Volatility Modelmentioning

confidence: 99%

Entropy-based adaptive Hamiltonian Monte Carlo

Hirt¹,

Titsias²,

Δελλαπόρτας³

2021

Preprint

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Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be sensitive to the choice of mass matrix used therein. We develop a gradient-based algorithm that allows for the adaptation of the mass matrix by encouraging the leapfrog integrator to have high acceptance rates while also exploring all dimensions jointly. In contrast to previous work that adapt the hyperparameters of HMC using some form of expected squared jumping distance, the adaptation strategy suggested here aims to increase sampling efficiency by maximizing an approximation of the proposal entropy. We illustrate that using multiple gradients in the HMC proposal can be beneficial compared to a single gradientstep in Metropolis-adjusted Langevin proposals. Empirical evidence suggests that the adaptation method can outperform different versions of HMC schemes by adjusting the mass matrix to the geometry of the target distribution and by providing some control on the integration time.35th Conference on Neural Information Processing Systems (NeurIPS 2021).

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“…Therefore, NUTS does not require tuning for T during the warm-up phase. Following (Wu et al, 2018), we choose time of integration T to be the 90th percentile of the trajectories followed by NUTS. 10…”

Section: Choice Of Parametersmentioning

confidence: 99%

Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions

Modi¹,

Barnett²,

Carpenter³

2021

Preprint

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The efficiency of Hamiltonian Monte Carlo (HMC) can suffer when sampling a distribution with a wide range of length scales, because the small step sizes needed for stability in high-curvature regions are inefficient elsewhere. To address this we present a delayed rejection variant: if an initial HMC trajectory is rejected, we make one or more subsequent proposals each using a step size geometrically smaller than the last. We extend the standard delayed rejection framework by allowing the probability of a retry to depend on the probability of accepting the previous proposal. We test the scheme in several sampling tasks, including multiscale model distributions such as Neal's funnel, and statistical applications. Delayed rejection enables up to five-fold performance gains over optimally-tuned HMC, as measured by effective sample size per gradient evaluation. Even for simpler distributions, delayed rejection provides increased robustness to step size misspecification. Along the way, we provide an accessible but rigorous review of detailed balance for HMC.

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Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale

Cited by 4 publications

References 8 publications

Hamiltonian zigzag sampler got more momentum than its Markovian counterpart: Equivalence of two zigzags under a momentum refreshment limit

Hamiltonian zigzag sampler got more momentum than its Markovian counterpart: Equivalence of two zigzags under a momentum refreshment limit

Entropy-based adaptive Hamiltonian Monte Carlo

Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions

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