相关论文: Testing the criterion for correct convergence in t…
A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density…
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the…
There are problems in physics and particularly in field theory which are defined by complex valued weight functions $e^{-S}$ where $S$ is a polynomial action $S: R^n \rightarrow C $. The conditions under which a convergent complex Langevin…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence…
The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at…
At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care.…
In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of…
Effective Polyakov line models, derived from SU(3) gauge-matter systems at finite chemical potential, have a sign problem. In this article I solve two such models, derived from SU(3) gauge-Higgs and heavy quark theories by the relative…
We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves $\varepsilon$ error (in 2-Wasserstein…
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
Discretized Langevin diffusions are efficient Monte Carlo methods for sampling from high dimensional target densities that are log-Lipschitz-smooth and (strongly) log-concave. In particular, the Euclidean Langevin Monte Carlo sampling…
Efficient sampling from complex and high dimensional target distributions turns out to be a fundamental task in diverse disciplines such as scientific computing, statistics and machine learning. In this paper, we propose a new kind of…
The complex Langevin method is a general method to treat systems with complex action, such as QCD at nonzero density. The formal justification relies on the absence of certain boundary terms, both at infinity and at the unavoidable poles of…
Markov Chain Monte Carlo (MCMC) is a popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. An important consideration in using simulated…
In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the…
We study three possible ways to circumvent the sign problem in the O(3) nonlinear sigma model in 1+1 dimensions. We compare the results of the worm algorithm to complex Langevin and multiparameter reweighting. Using the worm algorithm, the…
Recently, structure learning of directed acyclic graphs (DAGs) has been formulated as a continuous optimization problem by leveraging an algebraic characterization of acyclicity. The constrained problem is solved using the augmented…
We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from…