Related papers: Spatial best linear unbiased prediction: A computa…
High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty…
We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to…
Multilevel estimators aim at reducing the variance of Monte Carlo statistical estimators, by combining samples generated with simulators of different costs and accuracies. In particular, the recent work of Schaden and Ullmann (2020) on the…
Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
This paper describes an implementation of the L-BFGS method designed to deal with two adversarial situations. The first occurs in distributed computing environments where some of the computational nodes devoted to the evaluation of the…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…
In this paper, we propose a framework for fast trajectory planning for unmanned aerial vehicles (UAVs). Our framework is reformulated from an existing bilevel optimization, in which the lower-level problem solves for the optimal trajectory…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
Neglecting complex aerodynamic effects hinders high-speed yet high-precision multirotor autonomy. In this paper, we present a computationally efficient learning-based model predictive controller that simultaneously optimizes a trajectory…
Reliable quantification of uncertainty in Mobile Laser Scanning (MLS) point clouds is essential for ensuring the accuracy and credibility of downstream applications such as 3D mapping, modeling, and change analysis. Traditional backward…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
The introduction of unexpected system disturbances and new system dynamics does not allow guaranteed continuous system stability. In this research we present a novel approach for detecting early failure indicators of non-linear highly…
With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…