Max-margin learning is a powerful approach to building classifiers and structured output predictors. Recent work on max-margin supervised topic models has successfully integrated it with Bayesian topic models to discover discriminative latent semantic structures and make accurate predictions for unseen testing data. Ho…
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48 results for “Gibbs classifiers”
In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error measure; this puts our contribution in the line of work aiming at dealing with perfo…
In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emp…
Paper extends PAC-Bayesian theory using shifted Rademacher processes.
problem Improving PAC-Bayesian bounds for fast rates.
method Using shifted Rademacher processes to match Catoni's bounds and derive new fast-rate bounds.
result New fast-rate PAC-Bayes bounds derived in terms of empirical risk surface flatness.
We show that Entropy-SGD (Chaudhari et al., 2017), when viewed as a learning algorithm, optimizes a PAC-Bayes bound on the risk of a Gibbs (posterior) classifier, i.e., a randomized classifier obtained by a risk-sensitive perturbation of the weights of a learned classifier. Entropy-SGD works by optimizing the bound's p…
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 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.
Combines MALA and Adam for efficient uncertainty quantification in deep learning.
problem Uncertainty estimation in deep neural networks.
method Integrates Metropolis Adjusted Langevin Algorithm (MALA) with momentum-based optimization (Adam) for efficient sampling from posterior distributions.
result The algorithm approximates the Gibbs posterior in total variation distance and efficiently quantifies epistemic uncertainty.
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various PAC-Bayesian approaches to derive such bounds. The bounds do not require additional hold…
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…
Gibbs versus non-Gibbs distributions in money dynamicscond-mat.stat-mech
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…
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.
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.
The notion of Berman-Gibbs stability was originally introduced by Robert Berman for -Fano varieties . We show that the pair is K-stable (resp. K-semistable) provided that 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.
Estimating Gibbs free energies via isobaric-isothermal flowsphysics.comp-ph
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.
Diffusive Gibbs Samplingstat.ML
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.
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 …
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 steps.
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.
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.
In this paper, we provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different target distribution. On the one hand, we propose an improvement of the previous approach proposed by Germain et al. (2…
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…
Improved particle Gibbs sampling by marginalizing parameters.
problem Bayesian inference in high-dimensional state-space models is challenging.
method Marginalized particle Gibbs sampling, combining MCMC and sequential Monte Carlo.
result Marginalization improves performance beyond the Gibbs sampler, scaling linearly.
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 for GLMB filtering.
Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inferencestat.ML
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…
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.
Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inferencemath.ST
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.
Characterizing and Understanding the Generalization Error of Transfer Learning with Gibbs Algorithmcs.LG
We analyze Gibbs-based transfer learning algorithms using information theory.
problem Understanding the generalization error of transfer learning.
method Information-theoretic analysis focusing on -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.