A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new algorithm for sampling from complex distributions.
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
Introduces HMC method for sampling Gibbs densities.
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…
New Gibbs sampling reduces GLMB filtering complexity to linear time.
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.
Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.
Gibbs-ERM learning is a natural idealized model of learning with stochastic optimization algorithms (such as Stochastic Gradient Langevin Dynamics and ---to some extent--- Stochastic Gradient Descent), while it also arises in other contexts, including PAC-Bayesian theory, and sampling mechanisms. In this work we study …
Paper introduces a Gibbs sampler for Bayesian inversion of ill-posed problems.
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…
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…
The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To address this non-conjugacy concern, we propose the application of Pólygamma data a…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent Pólya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gi…
Study birth-death dynamics for sampling Gibbs measures with nonconvex potentials.
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.
Bayesian model predicts circular data with fast Gibbs sampling.
Study detects P-type bifurcations in single system realizations using unreliable kernel density estimates.
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.
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. …
Generative Bayesian Filtering improves inference in complex models without explicit density evaluations.
New mixture models for clustering and density estimation of unknown distributions.
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
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…
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…
HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.
Bayesian neural networks with nonparametric noise models for system identification.
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.
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.
New model estimates Gibbs free energies using machine learning and isobaric-isothermal flows.
Modified Gibbs-Helmholtz equation geometric models for thermodynamics.
Study on Metropolis-within-Gibbs schemes for high-dimensional Bayesian models.
New method improves uncertainty quantification in latent variable models.
DiGS improves sampling from multi-modal distributions.
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.
This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.
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…