Related papers: Linking Gaussian Process regression with data-driv…
Various frameworks have been proposed to predict mechanical system responses by combining data from different fidelities for design optimization and uncertainty quantification as reviewed by Fern\'andez-Godino et al. and Peherstorfer et…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling. This limitation motivates the development of…
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…
Spatially misaligned data can be fused by using a Bayesian melding model that assumes that underlying all observations there is a spatially continuous Gaussian random field process. This model can be used, for example, to predict air…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…
Many science and engineering problems rely on expensive computational simulations, where a multi-fidelity approach can accelerate the exploration of a parameter space. We study efficient allocation of a simulation budget using a Gaussian…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where datasets pertaining…
To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at…
To estimate accurately the parameters of a regression model, the sample size must be large enough relative to the number of possible predictors for the model. In practice, sufficient data is often lacking, which can lead to overfitting of…
How can we explain the influence of training data on black-box models? Influence functions (IFs) offer a post-hoc solution by utilizing gradients and Hessians. However, computing the Hessian for an entire dataset is resource-intensive,…
Computer simulations are indispensable for analyzing complex systems, yet high-fidelity models often incur prohibitive computational costs. Multi-fidelity frameworks address this challenge by combining inexpensive low-fidelity simulations…
We propose a new scalable multi-class Gaussian process classification approach building on a novel modified softmax likelihood function. The new likelihood has two benefits: it leads to well-calibrated uncertainty estimates and allows for…
Federated learning (FL) facilitates the secure utilization of decentralized images, advancing applications in medical image recognition and autonomous driving. However, conventional FL faces two critical challenges in real-world deployment:…
Relational databases are extensively utilized in a variety of modern information system applications, and they always carry valuable data patterns. There are a huge number of data mining or machine learning tasks conducted on relational…
Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations,…
Multi-fidelity Reinforcement Learning (RL) frameworks efficiently utilize computational resources by integrating analysis models of varying accuracy and costs. The prevailing methodologies, characterized by transfer learning, human-inspired…
Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…