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Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…
Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…
We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite size scaling…
Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…
The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular…
Slow relaxation and glassiness have been the focus of extensive research attention, along with popular and technological interest, for many decades. While much understanding has been attained through mean-field and mode-coupling models,…
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the…
Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin…
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
We present approximate algorithms for performing smoothing in a class of high-dimensional state-space models via sequential Monte Carlo methods ("particle filters"). In high dimensions, a prohibitively large number of Monte Carlo samples…
While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the…
We review Sweeny's algorithm for Monte Carlo simulations of the random cluster model. Straightforward implementations suffer from the problem of computational critical slowing down, where the computational effort per edge operation scales…
Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…
The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean-field theory (DMFT). In the strongly-correlated regime, the method of choice for solving the impurity model is the…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
The asymmetric simple exclusion process (ASEP) with periodic boundary conditions is investigated for shuffled dynamics. In this type of update, in each discrete timestep the particles are updated in a random sequence. Such an update is…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction…