Proves Ω(√d) lower bound for PDMP samplers and presents a new adaptive PDMP achieving sub-√d empirical complexity O(d^α) (α∈[0.2,0.3]) for Gaussian-tailed targets.
Bou-Rabee, B
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce a novel and flexible framework for constructing locally adaptive Hamiltonian Monte Carlo (HMC) samplers by Gibbs sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For adaptively sampling path lengths, our Gibbs self-tuning (GIST) approach encompasses randomized HMC, multinomial HMC, the No-U-Turn Sampler (NUTS), and the Apogee-to-Apogee Path Sampler as special cases. We exemplify the GIST framework with a novel alternative to NUTS for locally adapting path lengths, evaluated with an exact Hamiltonian for a high-dimensional, ill-conditioned Gaussian measure and with the leapfrog integrator for a suite of diverse models.
representative citing papers
NUTS-mul and NUTS-BPS show nearly identical qualitative ergodicity behavior depending on target tails, with both mixing in O(d^{1/4}) time for Gaussians but smaller constants for NUTS-BPS.
ATune combines Gaussian theoretical analysis with burn-in simulation data to select system-specific splitting integrators and hyperparameter credible intervals for improved HMC stability and performance.
citing papers explorer
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Establishing an $\Omega(\sqrt{d})$ complexity lower bound for PDMP samplers and how to break it: a sub-$\sqrt{d}$ algorithm for Gaussian-tailed targets
Proves Ω(√d) lower bound for PDMP samplers and presents a new adaptive PDMP achieving sub-√d empirical complexity O(d^α) (α∈[0.2,0.3]) for Gaussian-tailed targets.
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A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets
NUTS-mul and NUTS-BPS show nearly identical qualitative ergodicity behavior depending on target tails, with both mixing in O(d^{1/4}) time for Gaussians but smaller constants for NUTS-BPS.