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Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…
Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for Autonomous Aircraft. If the design is safe, as it is supposed to be, accident…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…
In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles…
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…
In image segmentation, there is often more than one plausible solution for a given input. In medical imaging, for example, experts will often disagree about the exact location of object boundaries. Estimating this inherent uncertainty and…
Automated sentiment classification (SC) on short text fragments has received increasing attention in recent years. Performing SC on unseen domains with few or no labeled samples can significantly affect the classification performance due to…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
The direct simulation Monte Carlo (DSMC) method is a widely used stochastic particle approach to solving the Boltzmann equation. However, its computational cost remains a major drawback, which can be attributed to statistical errors when…
Interest in equilibrium-based sampling methods has grown with recent advances in computational hardware and Markov state modeling (MSM) methods, yet outstanding questions remain that hinder widespread adoption. Namely, how do sampling…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…
Semi-Supervised Learning (SSL) has become a preferred paradigm in many deep learning tasks, which reduces the need for human labor. Previous studies primarily focus on effectively utilising the labelled and unlabeled data to improve…
Limited transferability hinders the performance of deep learning models when applied to new application scenarios. Recently, unsupervised domain adaptation (UDA) has achieved significant progress in addressing this issue via learning…
This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…