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Strong invariance principles in Markov chain Monte Carlo are crucial to theoretically grounded output analysis. Using the wide-sense regenerative nature of the process, we obtain explicit bounds in the strong invariance converging rates for…
In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to…
The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…
Monte Carlo simulations are an important tool in statistical physics, complex systems science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
Monte Carlo algorithms simulate some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the…
Decision making for dynamic systems is challenging due to the scale and dynamicity of such systems, and it is comprised of decisions at strategic, tactical, and operational levels. One of the most important aspects of decision making is…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…