Related papers: Large deviations principle for the Adaptive Multil…

Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…

We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…

In this work, arithmetic distribution matching (ADM) is presented. ADM invertibly transforms a discrete memoryless source (DMS) into a target DMS. ADM can be used for probabilistic shaping and for rate adaption. Opposed to existing…

In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…

This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…

The alternating direction method of multipliers (ADM or ADMM) breaks a complex optimization problem into much simpler subproblems. The ADM algorithms are typically short and easy to implement yet exhibit (nearly) state-of-the-art…

Artificial neural networks (ANNs) require tremendous amount of data to train on. However, in classification models, most data features are often similar which can lead to increase in training time without significant improvement in the…

Probabilistic models based on Restricted Boltzmann Machines (RBMs) imply the evaluation of normalized Boltzmann factors, which in turn require from the evaluation of the partition function Z. The exact evaluation of Z, though, becomes a…

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…

Adaptive importance sampling (AIS) algorithms are widely used to approximate expectations with respect to complicated target probability distributions. When the target has heavy tails, existing AIS algorithms can provide inconsistent…

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…

Large Language Models (LLMs) demonstrate impressive ability in handling reasoning tasks. However, unlike humans who can instinctively adapt their problem-solving strategies to the complexity of task, most LLM-based methods adopt a…

Parallel trajectory optimization via the Alternating Direction Method of Multipliers (ADMM) has emerged as a scalable approach to long-horizon motion planning. However, existing frameworks typically decompose the problem into parallel…

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…

In Bayesian statistics, exploring high-dimensional multimodal posterior distributions poses major challenges for existing MCMC approaches. This paper introduces the Annealed Leap-Point Sampler (ALPS), which augments the target distribution…