The paper proves a large deviation principle for Gibbs measures on Polish spaces and applies it to specific cases.
problem Large deviation principles for Gibbs measures on Polish spaces.
method General Laplace principle for non-normalized Gibbs measures, applied to conditional Gibbs measures, Coulomb gases, and Fekete points.
result The Laplace principle is proven and applied to specific cases, providing a deterministic version of Γ-convergence. Macrocanonical models generate textures matching input features.
problem Generating textures that match specific features.
method Use Gibbs measures and minimize a convex function for sampling.
result Macrocanonical models can be applied to real-valued images under certain conditions.
Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.
problem Improving the mixing time of Gibbs sampler under strong log-concavity.
method Analyzing Gibbs sampler contraction under strong log-concavity, providing sharp contraction rate.
result Gibbs sampler contracts entropy linearly with condition number and independent of dimension under strong log-concavity.
Asynchronous Gibbs sampling can accurately estimate expectations of functions of all variables under certain conditions.
problem Estimating expectations of functions of all variables in graphical models.
method Coupling synchronous and asynchronous Gibbs samplers to control expected Hamming distance, using concentration of measure results.
result The bias in estimating expectations of polynomial functions is smaller than the standard deviation of the function value in the true model.
Generalizes entropy-drift inequality for specific geometric spaces.
problem Entropy, drift, and critical exponent in Gibbs measures on geometrically finite manifolds.
method Generalization of Guivarc'h's inequality for CAT(-1) spaces, analysis of random walks.
result Equality in entropy-drift inequality achieved if and only if Gibbs density is equivalent to hitting measure.
Rapid mixing of Langevin dynamics on Riemannian manifolds
problem Mixing time of Langevin dynamics on Riemannian manifolds
method Relation between Langevin processes in domain and image
result Achievable polynomial mixing times
This paper solves mapping problems with a novel Gibbs sampling method.
problem Mapping problems with uncertainties in data associations and landmark cardinality.
method Derives a hybrid Poisson, multi-Bernoulli mixture distribution using a conjugate prior and Poisson process prior. Uses Gibbs sampling to sample from the posterior.
result The proposed method outperforms state-of-the-art methods on synthetic data.
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.
Study measures rigidity for random walks and flows via generalized u-Gibbs states.
problem Measure rigidity for stationary measures of random walks and flows.
method Factorization method applied to generalized u-Gibbs states.
result Established extra invariance of generalized u-Gibbs states.
A result about projections of Gibbs measures from a particular class arising in economic modeling is proved.
Decentralized learning achieves centralized performance via Gibbs measures.
problem Achieving centralized performance in decentralized machine learning.
method ERM-RER learning framework with Gibbs measures and relative-entropy regularization.
result Achieving centralized performance with Gibbs measures and specific scaling of regularization factors.
Paper develops a new generalization bound using PAC-Bayes theory and Gibbs distributions.
problem Limits of traditional generalization bounds due to complexity measures.
method Leverages PAC-Bayes bounds with Gibbs distributions to derive a flexible generalization bound.
result Derives a generalization bound that can adapt to both hypothesis class and task complexity.
New method uses Coulomb gases for Monte Carlo integration with reduced errors.
problem Reducing integration errors in numerical algorithms.
method Using Gibbs measures with a large deviations approach.
result Preserves large deviation principle for improved integration.
Study birth-death dynamics for sampling Gibbs measures with nonconvex potentials.
problem Sampling Gibbs measures with nonconvex potentials.
method Birth-death dynamics, Kullback-Leibler divergence, χ2 divergence, kernel-based approximations, Γ-convergence of gradient flows. result Probability density converges exponentially fast to Gibbs equilibrium measure with a universal rate.
The paper tackles sampling from Gibbs measures with constrained support, providing a sampling guarantee.
problem Sampling from Gibbs measures with constrained support, especially in the pre-asymptotic regime.
method Analyzing the spectral gap of Langevin dynamics to provide a non-asymptotic sampling guarantee.
result The low-temperature Gibbs distribution concentrates on a neighborhood of its mode in the pre-asymptotic regime.
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many exi…
Study convergence of simulated annealing in continuous and discrete settings.
problem Analyzing convergence rate of simulated annealing methods.
method Apply Eyring-Kramers law to prove polynomial decay of tail probabilities.
result Explicit rate of convergence for continuous and discrete simulated annealing.
Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univa…
Study on Metropolis-within-Gibbs schemes for high-dimensional Bayesian models.
problem Improving the scalability of MCMC methods for complex Bayesian models.
method Relating convergence properties to conditional conductance for non-conjugate hierarchical models.
result Established dimension-free convergence results for Metropolis-within-Gibbs schemes.
Gibbs sampler mixes quickly for certain smooth distributions.
problem Drawing samples from log-smooth log-concave distributions.
method Analyzes Gibbs sampler on log-smooth and strongly log-concave distributions.
result Gibbs sampler mixes in O⋆(κ2n7.5) steps. We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet process, corresponding to the Dirichlet process, and the stable (or three-param…
GADD accelerates uniform-rate discrete diffusion models by 2 orders of magnitude.
problem Slow sampling in uniform-rate discrete diffusion models.
method Gibbs-based corrector (GADD) that constructs Gibbs posterior likelihoods directly from the concrete score function.
result Achieves an overall sampling complexity of O(polylog(ε−1)). The paper improves Gibbs sampling for large graphs by minibatching.
problem High computational cost of single Gibbs sampling update step.
method Minibatching: subsampling factors to estimate their sum.
result Minibatched Gibbs can be made unbiased and converge faster.
New Gibbs sampling reduces GLMB filtering complexity to linear time.
problem NP-hard GLMB density computation in multi-object systems.
method Tempered Gibbs sampler exploiting GLMB structure.
result Linear complexity O(T(P+M)) for GLMB filtering. Improved Swendsen-Wang sampler speeds up learning attractive GMs.
problem Slow mixing in Gibbs sampler for attractive binary pairwise GMs.
method Introduced and analyzed Swendsen-Wang dynamics for stochastic partitioned graphs.
result Swendsen-Wang dynamics achieve O(log n) mixing time for attractive binary pairwise GMs.
Let M be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure mF associated to a potential F. We compute the Hausdorff dimension of the conditional measures of mF. We study the mF-almost sure asymptotic penetration behaviour of locally geodesic lines of…
Sharp large deviations and Gibbs conditioning for portfolio credit risk models.
problem Analyzing the risk of default in financial portfolios with dependent factors.
method Sharp large deviation estimates and conditional Bahadur-Rao estimates for threshold models with diverging latent factors.
result Conditioned on a large exceedance event, default indicators become asymptotically i.i.d., and loss-given-default is exponentially tilted.
The paper improves probabilistic herding methods using Gibbs distributions.
problem Improving integration accuracy over Monte Carlo quadrature in infinite-dimensional RKHS.
method Developed a Gibbs distribution over quadrature nodes to minimize MMD.
result The Gibbs distribution outperforms i.i.d. Monte Carlo in integration accuracy.
Derives stochastic and dissipative dynamics preserving Gibbs measure.
problem Understanding and deriving structure-preserving stochastic systems.
method Extension of Hamilton-Pontryagin principle, symmetry reduction, and inclusion of dissipation.
result New derivation of double-bracket dissipation.
Improved spectral gap for MwG with adaptive RWM proposals.
problem Improving mixing efficiency of MwG for log-concave distributions.
method Using adaptive RWM proposals tuned to match conditional variances of log-concave target distributions.
result Established a spectral gap lower bound of order O(1/κd) for MwG. Holomorphic vector fields and anti-canonical divisors on complex manifolds are studied.
problem Existence of non-trivial holomorphic vector fields on compact complex manifolds.
method Vanishing result for measure preserving holomorphic vector fields, Gibbs stability, and log terminal singularities.
result No non-trivial holomorphic vector fields on compact complex manifolds with big anti-canonical line bundle.
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
problem Inference on Levy density for financial models with jumps.
method Gibbs posterior framework using a loss function for intractable likelihood.
result Gibbs posterior achieves nearly optimal rate of convergence under certain conditions.
New Gibbs sampling method improves MCMC efficiency.
problem Improving efficiency of Gibbs sampling.
method Non-uniform random scan with selection probability optimization.
result Non-uniform scan improves mixing time of Markov chain.
A new Gibbs sampler method speeds up Bayesian inference.
problem Efficient sampling from complex posterior distributions.
method Recycling auxiliary samples within Gibbs estimators.
result Significant improvement in accuracy and computational efficiency.
New diagnostic tool for assessing approximate Bayesian inference.
problem Assessing the trustworthiness of approximate Bayesian inference.
method Reframe the problem in terms of incompatible conditional distributions and use Gibbs priors.
result The diagnostic tool can discover the inductive bias in various Bayesian models and approximations.
APG samplers use neural suff stats to improve deep model inference.
problem Efficient inference in deep generative models.
method Amortized population Gibbs, neural suff stats, KL divergence minimization.
result Significant improvement in inference accuracy.
Paper shows how meta-learning can reduce prior learning cost.
problem Learning the prior in meta-learning with fast rates.
method Examined Gibbs algorithm in meta-learning context.
result Bernstein's condition holds at meta level, reducing prior learning cost.
Proposes a new model for estimating financial volatility with jumps.
problem Estimating volatility from financial time series with jumps.
method Gibbs Sampler with exact posterior distributions.
result Model captures speculative movements and propagates jumps in volatility.
Bayesian inference over admissible histories leads to irreversible kinetics.
problem Modeling irreversible processes in systems with uncertain histories.
method A Gibbs-type measure weighted by energy-dissipation action and observation constraints, interpreted as a Bayesian posterior.
result The measure concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution.
We analyze Gibbs-based transfer learning algorithms using information theory.
problem Understanding the generalization error of transfer learning.
method Information-theoretic analysis focusing on α-weighted-ERM and two-stage-ERM. result Exact characterization of generalization behavior using conditional symmetrized KL information.
Proposes a link between randomness and compression in deep learning.
problem Improving efficiency in deep learning training.
method Introduces a novel tomographic compression framework called Dual Tomographic Compression (DTC).
result Demonstrates high correlation between learning performance and Gibbs entropy over compression ratios.
A new method improves uncertainty quantification in Bayesian inference.
problem Poor uncertainty quantification in traditional Gibbs posteriors.
method Sequential Gibbs posteriors with a Bernstein-von Mises theorem.
result Sequential Gibbs posteriors provide better frequentist coverage.
New sampler reduces MCMC complexity for Bayesian variable selection.
problem High-dimensional Bayesian variable selection with high computation complexity.
method Variable-complexity subset weighted-Tempered Gibbs Sampler (wTGS) with Rao-Blackwellized estimator.
result Variances of Rao-Blackwellized estimator are smaller than those of subset wTGS.
GDiff tackles blind denoising with Gibbs sampling and Monte Carlo inference.
problem Blind denoising of signals with unknown noise parameters.
method Gibbs Diffusion (GDiff) method that alternates sampling steps from a conditional diffusion model and a Monte Carlo sampler.
result GDiff achieves blind denoising of natural images and cosmic microwave background data.
In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a Gibbs posterior originating in statistical mechanics. The Gibbs posterior is con…
This paper improves conditional sampling for VAEs by overcoming structural issues.
problem Computational intractability of conditional sampling in VAEs.
method Proposes two methods to address pitfalls in Metropolis-within-Gibbs (MWG) for VAEs.
result Improved performance on sampling tasks.
Paper studies matching of samples from two distributions with a Gibbs probability weight.
problem Matching two independent i.i.d. samples from two distributions with a weighted cost.
method Uses chaos decomposition of polynomial functions of empirical distributions to derive asymptotics.
result Convergence of resulting random joint distribution to Schrödinger problem solution as N→∞.
Quantum methods speed up inference in Markov logic networks.
problem Efficient inference in Markov logic networks (MLNs).
method Analysis of graph structures and application of quantum protocols to Gibbs sampling.
result Exponential speedup in approximate probabilistic inference using quantum methods.