Related papers: Semi-intrusive uncertainty propagation for multisc…

We consider a multiphysics system with multiple component models coupled together through network coupling interfaces, i.e., a handful of scalars. If each component model contains uncertainties represented by a set of parameters, a…

Deep architecture such as hierarchical semi-Markov models is an important class of models for nested sequential data. Current exact inference schemes either cost cubic time in sequence length, or exponential time in model depth. These costs…

Semi-supervised learning has made significant strides in the medical domain since it alleviates the heavy burden of collecting abundant pixel-wise annotated data for semantic segmentation tasks. Existing semi-supervised approaches enhance…

Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully…

Among Bayesian methods, Monte-Carlo dropout provides principled tools for evaluating the epistemic uncertainty of neural networks. Its popularity recently led to seminal works that proposed activating the dropout layers only during…

Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…

A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted…

Machine learning (ML) models are increasingly being used in metrology applications. However, for ML models to be credible in a metrology context they should be accompanied by principled uncertainty quantification. This paper addresses the…

Discrete diffusion models have become highly effective across various domains. However, real-world applications often require the generative process to adhere to certain constraints. To this end, we propose a Sequential Monte Carlo (SMC)…

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…

We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…

We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…

Multifidelity uncertainty propagation combines the efficiency of low-fidelity models with the accuracy of a high-fidelity model to construct statistical estimators of quantities of interest. It is well known that the effectiveness of such…

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

Reliable uncertainty estimation is crucial for machine learning models, especially in safety-critical domains. While exact Bayesian inference offers a principled approach, it is often computationally infeasible for deep neural networks.…

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…