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This paper introduces the Constrained Monte Carlo Tree Search (CMCTS) framework to enhance the mathematical reasoning capabilities of Large Language Models (LLM). By incorporating a constrained action space, Process Reward Model (PRM), and…

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…

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…

Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH) algorithm, are widely used for Bayesian inference. One of the most important issues for any MCMC method is the convergence of the Markov chain, which depends…

Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular…

The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of…

For UAV-aided wireless systems, online path planning attracts much attention recently. To better adapt to the real-time dynamic environment, we, for the first time, propose a Monte Carlo Tree Search (MCTS)-based path planning scheme. In…

To solve the problem of lateral and logitudinal joint decision-making of multi-vehicle cooperative driving for connected and automated vehicles (CAVs), this paper proposes a Monte Carlo tree search (MCTS) method with parallel update for…

Machine Learning (ML) algorithms are increasingly used as surrogate models to increase the efficiency of stochastic reliability analyses in geotechnical engineering. This paper presents a highly efficient ML aided reliability technique that…

Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the…

Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…

Sequential Monte Carlo has become a standard tool for Bayesian Inference of complex models. This approach can be computationally demanding, especially when initialized from the prior distribution. On the other hand, deter-ministic…

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…

Actor-critic methods, like Twin Delayed Deep Deterministic Policy Gradient (TD3), depend on basic noise-based exploration, which can result in less than optimal policy convergence. In this study, we introduce Monte Carlo Beam Search (MCBS),…

Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…

This paper develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation…

Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior…

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…

Bilinear Matrix Inequalities (BMIs) are fundamental to control system design but are notoriously difficult to solve due to their nonconvexity. This study addresses BMI-based control optimization problems by adapting and integrating advanced…

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…