A new algorithm for sampling from complex distributions.
problem Sampling from high-dimensional multivariate probability densities.
method Combines kernel herding and Gibbs sampling for deterministic sampling.
result Significantly lower computation time compared to kernel herding.
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.
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.
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.
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. 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…
A new method avoids partition function computation for Gibbs density estimation.
problem Estimating Gibbs density functions without partition function computation.
method Maximum Recovery MAP (MR-MAP) and least-action type potential.
result MR-MAP estimators solve optimization problem quickly using neural network.
Efficiently infers Gaussian process density models with Gibbs sampling and variational methods.
problem Density estimation for complex, nonparametric models.
method Augmented likelihood with latent variables, Gibbs sampling, and variational mean field approximations.
result Efficient inference for Gaussian process density models with up to thousands of data points.
New method maps high-dimensional image spaces using MCMC to reveal patterns.
problem Characterizing complex probability densities in high-dimensional image spaces.
method Attraction-Diffusion (AD) MCMC tool to map metastable regions.
result AD efficiently maps highly non-convex probability densities.
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.
Study on Gibbs-ERM learning, focusing on excess risk bounds and effective dimension.
problem Understanding the interplay between data distribution and learning in large hypothesis spaces.
method Distribution-dependent analysis of Gibbs-ERM, focusing on excess risk and effective dimension.
result Distribution-dependent upper bounds on excess risk, showing effective dimension controls risk.
Proposes PG-DA for Bayesian MMNL estimation to handle non-conjugacy.
problem Non-conjugacy in the Bayesian estimation of MMNL models.
method Pólygamma data augmentation technique applied to MMNL estimation.
result Similar posterior estimates for binary choice scenarios, but empirical identification issues for J≥3 alternatives. Paper introduces a Gibbs sampler for Bayesian inversion of ill-posed problems.
problem Bayesian inversion of ill-posed problems with linear transformation and additive noise.
method Gibbs algorithm based on prior diffusion model.
result Gibbs algorithm offers a guarantee of convergence in a specific situation.
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.
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to …
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the suc…
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.
We apply a new numerical method, the singular Fourier-Padé (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in Lévy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecew…
The paper extends entropy maximization to multiscale settings and applies it to neural networks.
problem Achieving optimal risk bounds in neural networks using multiscale entropy.
method Generalizing maximum entropy to multiscale settings and applying it to neural networks.
result The multiscale Gibbs posterior can achieve a smaller excess risk than the single-scale Gibbs posterior in a teacher-student scenario.
Bayesian model predicts circular data with fast Gibbs sampling.
problem Predicting circular data in scientific fields.
method Expressive von Mises quasi-processes with Stratonovich augmentation for posterior inference.
result Fast Gibbs sampling for posterior inference.
Study detects P-type bifurcations in single system realizations using unreliable kernel density estimates.
problem Detecting P-type bifurcations in signals with unreliable kernel density estimates.
method Create persistence diagrams from single system realization, statistically analyze resulting set, compare point process modeling methods.
result Subsampling outperforms other point process modeling methods in predicting P-type bifurcations.
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of observations to capture the underlying density function. Thus it is not suitable for …
Accelerates sampling from Gibbs distributions using ARWP method.
problem Sampling from Gibbs distributions efficiently.
method ARWP method, combining Nesterov acceleration and regularized Wasserstein proximal.
result ARWP exhibits higher contraction rate and faster tail exploration.
Generative Bayesian Filtering improves inference in complex models without explicit density evaluations.
problem Performing posterior inference in complex nonlinear and non-Gaussian state-space models.
method Generative Bayesian Filtering (GBF) extends GBC to dynamic settings using deep neural networks for recursive posterior inference. Generative-Gibbs sampler bypasses density evaluations for parameter learning.
result GBF significantly outperforms likelihood-free approaches in accuracy and robustness for intractable state-space models.
New mixture models for clustering and density estimation of unknown distributions.
problem Clustering and density estimation of data with unknown distributions.
method Two fitting methods: EM algorithm and Bayesian non-parametric method using Gibbs sampler.
result Effective clustering and density estimation of data with unknown distributions.
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
problem Limited storage capacity and retrieval methods for non-vector pattern representations.
method Introduces a log-sum-exp energy function over Gaussian distributions, using optimal transport maps for retrieval dynamics.
result Proves exponential storage capacity and provides quantitative retrieval guarantees.
The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs has an O(1/T) convergence rate for models with independent variables and for ful…
New method speeds up Gibbs sampling for large graphs.
problem Efficiently sampling from large graphical models.
method Poisson-minibatching Gibbs sampling.
result Theoretical convergence rate guarantees for Poisson-minibatching Gibbs.
Adaptive scan Gibbs sampler improves large-scale inference performance.
problem Efficiently updating large-scale online inference problems.
method Derives an adaptive scan Gibbs sampler that optimizes mini-batch size selection.
result Demonstrates superior performance compared to collapsed Gibbs sampler.
Develops an efficient approximation for collapsed Gibbs sampling in complex models.
problem Intractability of integrating out variables in collapsed Gibbs sampling for complex models.
method Uses expectation propagation to approximate collapsed Gibbs integrals.
result Approximate sampler enables a runtime-accuracy tradeoff in sampling complex models.
HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.
problem Modeling noisy, sparse, and heterogeneous relational data.
method Hierarchical Chinese restaurant process and Dirichlet process mixture for clustering and modeling relation values.
result HIRM generalizes standard models and discovers relational structure in real-world datasets.
DoGS improves Gibbs sampling quality with variable selection orders and bounds.
problem Improving Gibbs sampler scan quality.
method Using Dobrushin influence to optimize Gibbs sampling.
result DoGS delivers higher-quality inferences with smaller sampling budgets.
Bayesian neural networks with nonparametric noise models for system identification.
problem Estimating parameters and noise processes in stochastic dynamic systems.
method Bayesian nonparametric approach using neural networks and Gibbs sampler.
result The method converges to full nonparametric Bayesian regression model.
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.
We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We consider three main applications: Conditional Gibbs measures on compact spaces, …
Improved Gibbs sampling yields higher likelihood solutions.
problem Gibbs sampling often returns suboptimal solutions due to bottlenecks.
method Interdependent Gibbs Samplers combining multiple samplers with coupling.
result High likelihood solutions significantly more often than regular Gibbs sampler.
We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity, and non-Gibbs distributions otherwise. While the exact solution in the case of zero saving propensity is already known to be give…
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.
Improved Gibbs sampler for crossed random effects models scales better with data.
problem Complexity issues in Gibbs samplers for crossed random effects models.
method Proposed a collapsed Gibbs sampler that is provably scalable.
result The collapsed Gibbs sampler outperforms alternative algorithms significantly.
Developed a Particle-Gibbs sampler for Bayesian feature allocation models.
problem Intractable exact inference in Bayesian feature allocation models.
method Particle-Gibbs sampler for feature allocation matrix updates.
result PG sampler improves performance of feature allocation models.
Souriau studies Gibbs states for symplectic manifolds with group actions.
problem Understanding Gibbs states for symplectic manifolds with symmetries.
method Adaptation of cross product for pseudo-Euclidean spaces, detailed proofs, examples of Gibbs states.
result Presentation of Gibbs states and associated thermodynamic functions for various symplectic manifolds.
The notion of Berman-Gibbs stability was originally introduced by Robert Berman for Q-Fano varieties X. We show that the pair (X,−KX) is K-stable (resp. K-semistable) provided that X is Berman-Gibbs stable (resp. semistable).
New model estimates Gibbs free energies using machine learning and isobaric-isothermal flows.
problem Estimating Gibbs free energies for complex systems.
method Normalizing flows trained to sample isobaric-isothermal ensemble.
result Excellent agreement with established baselines for water phases.
Modified Gibbs-Helmholtz equation geometric models for thermodynamics.
problem Geometric interpretation of Gibbs-Helmholtz equation in thermodynamics.
method Developed new holonomic and non-holonomic geometric models associated to Gibbs-Helmholtz equation.
result Characterized equivalence between Gibbs-Helmholtz entropy and other entropies.
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.
We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it al…
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algori…
New method improves uncertainty quantification in latent variable models.
problem Uncertainty quantification in latent variable models with SGLD-Gibbs.
method Statistical scaling limit theory for SGLD-Gibbs, proposing hyperparameter tuning.
result Explicit guidance on hyperparameter tuning for SGLD-Gibbs ensures meaningful uncertainty quantification.