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In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…

Monte-Carlo Tree Search (MCTS) is one of the most-widely used methods for planning, and has powered many recent advances in artificial intelligence. In MCTS, one typically performs computations (i.e., simulations) to collect statistics…

The Job Shop Scheduling Problem (JSSP) is a well-known optimization problem in manufacturing, where the goal is to determine the optimal sequence of jobs across different machines to minimize a given objective. In this work, we focus on…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…

An efficient, joint transmission delay and channel parameter estimation algorithm is proposed for uplink asynchronous direct-sequence code-division multiple access (DS-CDMA) systems based on the space-alternating generalized expectation…

We propose SYNCE (synchronized step correlation enhancement), a new algorithm for coupling Markov chains within multilevel Markov chain Monte Carlo (ML-MCMC) estimators. We apply this algorithm to solve Bayesian inverse problems using…

Physics-based simulations and learning-based models are vital for complex robotics tasks like deformable object manipulation and liquid handling. However, these models often struggle with accuracy due to epistemic uncertainty or the…

We examine a type of modified Monte Carlo Tree Search (MCTS) for strategising in combinatorial games. The modifications are derived by analysing simplified strategies and simplified versions of the underlying game and then using the results…

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…

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…

Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly…

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…

Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…

Recent advancements in large language models (LLMs) have shown remarkable potential in automating machine learning tasks. However, existing LLM-based agents often struggle with low-diversity and suboptimal code generation. While recent work…

Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

Dynamic resource allocation (DRA) problems are an important class of dynamic stochastic optimization problems that arise in a variety of important real-world applications. DRA problems are notoriously difficult to solve to optimality since…

This paper introduces the MCTS algorithm to the financial world and focuses on solving significant multi-period financial planning models by combining a Monte Carlo Tree Search algorithm with a deep neural network. The MCTS provides an…