We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical anal…
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48 results for “Hamiltonian slice sampling”
Gradient-guided nested sampling improves posterior inference efficiency.
problem Efficiently sampling from complex posterior distributions.
method Gradient-guided nested sampling combining differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization.
result Significantly faster mode discovery and more accurate partition function estimates.
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the Hamiltonian slice theorem of Marle, Guillemin and Sternberg. The result applies to a…
Novel method for model selection in Bayesian autoencoders.
problem Model selection for Bayesian autoencoders.
method Prior hyper-parameter optimization using distributional sliced-Wasserstein distance.
result State-of-the-art results in small-data regimes.
We consider a connected symplectic manifold acted on properly and in a Hamiltonian fashion by a connected Lie group . Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of Hamiltonian actions. The dimension of the moduli space of the Lagrangian orbits is giv…
Efficiently implements polar slice sampling for high-dimensional distributions.
problem Sampling from difficult-to-implement distributions in high dimensions.
method Separates directional and radial components for efficient implementation.
result Outperforms related methods in various settings.
Nested Slice Sampling accelerates Nested Sampling for GPU acceleration.
problem Challenging inference for complex, multimodal targets.
method Vectorized Nested Slice Sampling using Hit-and-Run Slice Sampling.
result NSS maintains accurate evidence estimates and high-quality posterior samples, robust on multimodal problems.
A new slicing method speeds up sliced Wasserstein estimation.
problem Efficiently estimating sliced Wasserstein distance.
method Random-Path Projecting Direction (RPD) for fast sampling.
result RPSW and IWRPSW show favorable performance in training generative models.
ESS improves MCMC efficiency for correlated & multimodal distributions.
problem Slice Sampling's sensitivity to initial length scale and difficulty with correlated distributions.
method Adaptive tuning and parallel walkers for efficient sampling.
result ESS improves efficiency by more than an order of magnitude on correlated distributions.
Extended elliptical slice sampling for infinite-dimensional spaces, proving reversibility.
problem Proving reversibility of elliptical slice sampling in infinite-dimensional spaces.
method Extended elliptical slice sampling to infinite-dimensional separable Hilbert spaces, providing an alternative proof of reversibility.
result The approach yields a positive semi-definite Markov operator, proving reversibility.
Elliptical slice sampling converges geometrically, providing reliable sampling for Bayesian learning.
problem Sampling from posterior distributions in Bayesian learning.
method Elliptical slice sampling, geometric ergodicity.
result Elliptical slice sampling yields geometric convergence guarantees under weak regularity assumptions.
We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minko…
A new slicing method reduces computational cost for cross-domain alignment.
problem High computational cost in solving Gromov-Wasserstein distance.
method Relation-Aware Projecting Direction (RAPD) and Relation-Aware Slicing Distribution (RASD).
result RASGW distance reduces computational cost and improves alignment accuracy.
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.
A new algorithm speeds up elliptical slice sampling for truncated multivariate normals.
problem Efficiently sampling from truncated multivariate normal distributions with linear constraints.
method Adapting elliptical slice sampling to linearly truncated multivariate normals, with an algorithm for ellipse-polytope intersection in O(m log m) time.
result The algorithm enhances numerical stability, speeds up running time, and is easy to parallelize.
This work investigates the properties of Gaussian-smoothed sliced divergences for comparing distributions.
problem Comparing probability distributions while preserving privacy.
method Investigates the theoretical properties of Gaussian-smoothed sliced Wasserstein distance and generalized versions.
result Gaussian smoothed sliced Wasserstein distance converges with a rate of \(O(n^{-1/2})\).
Introduces HMC method for sampling Gibbs densities.
problem Sampling from Gibbs densities efficiently.
method Hamiltonian Monte Carlo (HMC) method based on Hamiltonian dynamics.
result Idealized HMC preserves the target distribution and converges under certain conditions.
We propose an exact slice sampler for Hierarchical Dirichlet process (HDP) and its associated mixture models (Teh et al., 2006). Although there are existing MCMC algorithms for sampling from the HDP, a slice sampler has been missing from the literature. Slice sampling is well-known for its desirable properties includin…
A new method for comparing image probability measures using convolution operators.
problem Efficiently comparing images using conventional sliced Wasserstein methods.
method Proposed convolution sliced Wasserstein (CSW) methods with stride, dilation, and non-linear activation.
result CSW demonstrates favorable performance over conventional sliced Wasserstein in image comparison and deep generative modeling.
The paper explores statistical and topological properties of sliced probability divergences.
problem Understanding the topological, statistical, and computational consequences of slicing divergences.
method Deriving theoretical properties of sliced probability divergences, including metric axioms preservation and weak continuity.
result Sliced divergences share similar topological properties and have stable sample complexity.
Proposes a new distance metric for multi-marginal optimal transport.
problem Computational scalability in multi-marginal optimal transport.
method Random one-dimensional projections to construct sliced multi-marginal Wasserstein distance.
result Sliced multi-marginal Wasserstein distance is a metric with dimension-free sample complexity.
Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures …
A symplectic slice theoremmath.SG
We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries that have an associated momentum map. In these papers the momentum map played a cru…
Study efficient iterative method for distribution matching using sliced optimal transport.
problem Efficiently match distributions using sliced optimal transport.
method Slice-matching scheme based on sliced optimal transport, with quantitative non-asymptotic rates derived.
result Derive quantitative non-asymptotic rates for convergence to target distribution.
Proposes an energy-based sliced Wasserstein distance for improved probability measure comparison.
problem Inefficiencies and limitations in existing sliced Wasserstein distance approaches.
method Introduces an energy-based slicing distribution for better performance and stability.
result Demonstrates superior performance of the EBSW distance in various applications.
CB-SLICE identifies concept-based error slices in deep learning models.
problem Systematic errors in deep learning models on specific groups.
method Concept Bottleneck Models (CBMs) and concept representations.
result CB-SLICE outperforms state-of-the-art methods in error slice identification.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
New method improves performance of Hamiltonian MCMC for log Z estimation.
problem Estimating tight bounds on log Z for unnormalized distributions.
method Uncorrected Hamiltonian Annealing (UHA) using reparameterization gradients.
result Better performance and easier parameter tuning compared to existing methods.
Sampling Algorithms, from Survey Sampling to Monte Carlo Methods: Tutorial and Literature Reviewstat.ME
This paper reviews various sampling methods from statistics and machine learning.
problem Addressing sampling methods in statistics and machine learning.
method Explains and reviews simple random sampling, bootstrapping, stratified sampling, cluster sampling, multistage sampling, network sampling, snowball sampling, and sampling from cumulative distribution function.
result Summarizes characteristics, pros, and cons of different sampling methods.
New Hamiltonian Monte Carlo method for non-canonical dynamics.
problem Incompatibility of canonical symplectic structure with non-canonical dynamics.
method Developed a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures with implicit integration.
result Non-canonical Hamiltonian Monte Carlo provides sampling advantages.
A new approach simplifies Sliced-Wasserstein distances to improve learning performance.
problem The concentration of measure phenomenon makes random projections uninformative in high dimensions.
method Propose rescaling the 1D Wasserstein distance to make all slices equally informative.
result The classical Sliced-Wasserstein, properly configured, can match or surpass complex variants.
A new method for estimating SW from streaming data.
problem Estimating Wasserstein distance from sample streams.
method Introducing a streaming estimator of the 1DW and applying it to all projections.
result Stream-SW achieves more accurate approximation of SW than random subsampling.
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of challenges especially when analyzing high-dimensional data sets in which the numb…
CHMC improves HMC efficiency for multimodal distributions.
problem Slow convergence of HMC in multimodal distributions.
method Integrates a counterdiabatic term to optimize Hamiltonian changes.
result CHMC achieves efficient sampling from challenging distributions.
New method improves sampling from complex, multi-peaked distributions.
problem Sampling from high-dimensional, multimodal distributions using HMC.
method Combines tempered HMC with automatic tuning strategies.
result Demonstrates more effective scaling with dimension than adaptive methods.
To address three important issues involved in latent variable models (LVMs), including capturing infrequent patterns, achieving small-sized but expressive models and alleviating overfitting, several studies have been devoted to "diversifying" LVMs, which aim at encouraging the components in LVMs to be diverse. Most exi…
Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densitiesstat.CO
New method samples from piecewise smooth distributions using Hamiltonian Monte Carlo.
problem Sampling from distributions with discontinuous gradients.
method Generalized Randomized Hamiltonian Monte Carlo (GRHMC) for piecewise smooth targets.
result GRHMC processes sample from piecewise smooth target distributions with the desired distribution as the invariant distribution.
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible explanations for the data when maki…
Empower efficient representation of distributions through moment-preserving methods.
problem Representing high-dimensional probability measures efficiently and accurately.
method Empower efficient representation of distributions through moment-preserving methods.
result Empowers efficient and accurate representation of high-dimensional probability measures.
QHMC improves HMC for sampling from complex distributions.
problem Inefficiency of HMC in sampling from spiky and multimodal distributions.
method Proposes QHMC, a quantum-inspired version of HMC with a random mass matrix.
result QHMC and QSGNHT achieve more stable and accurate sampling results.
Reliability Analysis of Complex Systems using Subset Simulations with Hamiltonian Neural Networksstat.ML
New method combines neural networks with Monte Carlo for complex system reliability.
problem Estimating small failure probabilities in complex systems.
method Subset Simulation with Hamiltonian Neural Networks.
result High acceptance rates and computational efficiency in low-probability regions.
A permutation-based SW test achieves minimax-optimal power for two-sample testing.
problem Nonparametric two-sample testing using the sliced Wasserstein distance.
method Proposes a permutation-based SW test and analyzes its performance.
result Achieves minimax separation rate over multinomial and bounded-support alternatives.
Magnetic manifold HMC improves sampling on constrained manifolds.
problem Sampling from distributions restricted to embedded manifolds.
method Introduces magnetic manifold HMC, a generalization of HMC for constrained manifolds.
result Magnetic manifold HMC outperforms canonical manifold-constrained HMC.
HMC improves Gaussian sampling efficiency with long, random steps.
problem Efficiently sampling from high-dimensional Gaussian distributions.
method Hamiltonian Monte Carlo with long and random integration times.
result HMC achieves -closeness in total variation distance with gradient queries.
Introduces Lax-Kirchhoff moduli spaces for quivers and Lie groups.
problem Constructing moduli spaces for quivers and Lie groups.
method Introduces Lax equations and Kirchhoff conditions, constructs slices, and uses Marsden-Weinstein reduction.
result Proves is a finite-dimensional smooth symplectic manifold with a Hamiltonian action of .
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.
problem Estimating the expected max-sliced Wasserstein distance between a probability measure and its empirical distribution.
method Banach space version and operator norm approach for upper bounds.
result Upper bounds for max-sliced Wasserstein distances are essentially matching and sharp up to a log factor.
GIST adapts HMC by tuning parameters based on position and momentum.
problem Locally adaptive sampling in Hamiltonian Monte Carlo.
method GIST uses Gibbs sampling to adaptively tune HMC parameters.
result GIST improves sampling efficiency for high-dimensional models.