Extended Q-learning stability and convergence analysis.
problem Stability and convergence of Q-learning with linear function approximation.
method Analysis of (ε,κ)-tamed Gibbs policy, and other Q-learning variants. result Far more structure is required for convergence of Q-learning.
Study risk-sensitive market making with entropy regularization for better quote control.
problem Risk-sensitive market making with exponential utility and penalties.
method Entropy-regularized certainty-equivalent Bellman policies for discrete-time market dynamics.
result Proves convergence and performance bounds for entropy-regularized policies.
Develops a Bayesian framework for portfolio choice with a new posterior distribution.
problem Estimation risk in parametric portfolio policies.
method Generalized Bayesian framework with Gibbs posterior, utility maximization, and KNEEDLE algorithm.
result Optimal scaling parameter λ controls the balance between prior and data. New algorithm improves efficiency of Bayesian Causal Forest for subgroup analysis.
problem Estimating heterogeneous effects in subgroup analysis.
method Developed a novel algorithm for fitting Bayesian Causal Forest (BCF) model, more efficient than Gibbs sampler.
result New algorithm improves posterior exploration and coverage of interval estimates.
EB-GFN models discrete data with amortized MCMC sampling.
problem Probabilistic modeling of high-dimensional discrete data.
method EB-GFN combines GFlowNets with energy-based models for efficient sampling.
result EB-GFN effectively models various discrete data tasks.
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…
Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale to large graphical models by reducing its computational cost. In this paper, we p…
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, …
We develop a framework for approximating collapsed Gibbs sampling in generative latent variable cluster models. Collapsed Gibbs is a popular MCMC method, which integrates out variables in the posterior to improve mixing. Unfortunately for many complex models, integrating out these variables is either analytically or co…
The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently improve the quality of a discrete Gibbs sampler. Our Dobrushin-optimized Gibbs samp…
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…
For large scale on-line inference problems the update strategy is critical for performance. We derive an adaptive scan Gibbs sampler that optimizes the update frequency by selecting an optimum mini-batch size. We demonstrate performance of our adaptive batch-size Gibbs sampler by comparing it against the collapsed Gibb…
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.
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential moment, we show that the equality is achieved if and only if the Gibbs density is…
Continuous-time Q-learning theory developed for reinforcement learning.
problem Continuous-time reinforcement learning challenges.
method Entropy-regularized, exploratory diffusion process formulation; first-order approximation of Q-function; martingale conditions.
result Developed a q-learning theory independent of time discretization.
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.
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).
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.
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.
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.
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.
DiGS improves sampling from multi-modal distributions.
problem Inadequate mixing in MCMC methods for multi-modal distributions.
method Integrates diffusion models and Gibbs sampling to create an auxiliary noisy distribution.
result DiGS exhibits better mixing for multi-modal distributions than state-of-the-art methods.
The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Mark…
Improved MALA method for neural networks uncertainty quantification.
problem Uncertainty quantification in Bayesian neural networks.
method Corrected Stochastic MALA (csMALA) with a simplified correction term.
result Improved surrogate posterior for quantifying uncertainties in neural networks.
This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.
problem Analyzing convergence properties of Gibbs samplers for Bayesian hierarchical models.
method Using Bayesian asymptotics and total variation mixing times, the study provides dimension-free convergence results.
result Dimension-free convergence results for Gibbs samplers targeting hierarchical models under random data-generating assumptions.
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.
DABS uses a policy network to select experiments in high-dimensional design spaces.
problem Adaptive factorial screening in high-dimensional discrete design spaces.
method DABS learns a policy network offline to sequentially select experiments, incorporating sparsity and interactions via a spike-and-slab prior.
result DABS achieves superior accuracy and scalability over classical and Bayesian baselines under tight experimental budgets.
Gibbs sampling is the de facto Markov chain Monte Carlo method used for inference and learning on large scale graphical models. For complicated factor graphs with lots of factors, the performance of Gibbs sampling can be limited by the computational cost of executing a single update step of the Markov chain. This cost …
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.
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. Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
problem Sampling from Gibbs distributions with dissipative potentials.
method Langevin-type algorithms based on Liptser--Shiryaev theory and Poincaré inequalities.
result Upper bound on 2-Wasserstein distance for accurate approximation.
The Gibbs algorithm's generalization error is bounded, improving with prior volume in low temperatures.
problem Bounding the generalization error of the Gibbs algorithm in low temperature regimes.
method Analyzes the Gibbs algorithm's performance, extending known high-temperature bounds to low-temperature scenarios.
result With high probability, the generalization error decreases with the total prior volume of similar hypotheses.
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…
Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have bottlenecks, sometimes termed "local maxima", and thus samplers often return suboptima…
New bounds tighten the generalization error of Gibbs algorithm.
problem Bounding the generalization error of Gibbs algorithm.
method Characterization of generalization error in terms of symmetrized KL information.
result Exact characterization of Gibbs algorithm's expected generalization error.
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. 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.
A fundamental task in machine learning and related fields is to perform inference on Bayesian networks. Since exact inference takes exponential time in general, a variety of approximate methods are used. Gibbs sampling is one of the most accurate approaches and provides unbiased samples from the posterior but it has hi…
Algorithm learns interference network and optimizes treatment allocation for unknown network effects.
problem Adaptive experimentation under unknown network interference.
method Thompson sampling algorithm with Gibbs sampler for joint learning of interference network and treatment allocation.
result Proves a Bayesian regret bound and achieves sublinear regret in real-world applications.
New method transfers instances between domains using Gibbs Sampling and RBM.
problem Transfer Learning between domains with limited target data.
method Gibbs Sampling and RBM for instance transition.
result Significant improvement in target classification.
A result about projections of Gibbs measures from a particular class arising in economic modeling is proved.
Bayesian feature allocation models are a popular tool for modelling data with a combinatorial latent structure. Exact inference in these models is generally intractable and so practitioners typically apply Markov Chain Monte Carlo (MCMC) methods for posterior inference. The most widely used MCMC strategies rely on an e…
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.
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.
Gibbs pruning optimizes neural networks by combining physics and regularization.
problem Large neural networks are impractical for many applications.
method Combines statistical physics and stochastic regularization to train and prune networks simultaneously.
result Gibbs pruning achieves state-of-the-art performance on ResNet-56.
The paper proposes a Gibbs sampler for neural network posterior sampling.
problem Sampling from the posterior of neural networks.
method Adding noise to activations and using a Gibbs sampler.
result The Gibbs sampler achieves similar performance to MCMC methods on real and synthetic data.