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This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions. We develop novel connections between such Monte Carlo algorithms, the theory of Wasserstein gradient flow, and the…
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
A novel method for simulating the statistical mechanics of molecular systems in which both nuclear and electronic degrees of freedom are treated quantum mechanically is presented. The scheme combines a path integral description of the…
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Large deviations for additive path functionals of stochastic dynamics and related numerical approaches have attracted significant recent research interest. We focus on the question of convergence properties for cloning algorithms in…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
This paper faces a central theme in applied statistics and information science, which is the assessment of the stochastic structure of rank-size laws in text analysis. We consider the words in a corpus by ranking them on the basis of their…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
Many biochemical systems appearing in applications have a multiscale structure so that they converge to piecewise deterministic Markov processes in a thermodynamic limit. The statistics of the piecewise deterministic process can be obtained…
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-histogram, a new efficient algorithm for clustering categorical data. The k-histogram algorithm extends…
Given a convex function $f\colon\mathbb{R}^{d}\to\mathbb{R}$, the problem of sampling from a distribution $\propto e^{-f(x)}$ is called log-concave sampling. This task has wide applications in machine learning, physics, statistics, etc. In…
Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously…