Related papers: Scaling Up Bayesian Uncertainty Quantification for…

Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in…

Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values…

Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

EEG decoding systems based on deep neural networks have been widely used in decision making of brain computer interfaces (BCI). Their predictions, however, can be unreliable given the significant variance and noise in EEG signals. Previous…

Traditional neural networks provide deterministic predictions without inherent uncertainty estimates. While Bayesian Neural Networks (BNNs) offer a principled approach to uncertainty quantification, their computational complexity limits…

Recent advances in deep learning have shown that uncertainty estimation is becoming increasingly important in applications such as medical imaging, natural language processing, and autonomous systems. However, accurately quantifying…

Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…

We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression and neural operator learning (DeepONet). Specifically, we…

In the era of Big Data, scalable and accurate clustering algorithms for high-dimensional data are essential. We present new Bayesian Distance Clustering (BDC) models and inference algorithms with improved scalability while maintaining the…

We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the…

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

Even though Bayesian neural networks offer a promising framework for modeling uncertainty, active learning and incorporating prior physical knowledge, few applications of them can be found in the context of interatomic force modeling. One…

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…

Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…