Related papers: Simultaneous Confidence Bands for Functional Data …
While the ground state of magnetic materials is in general well described on the basis of spin density functional theory (SDFT), the theoretical description of finite-temperature and non-equilibrium properties require an extension beyond…
Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can…
Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…
We produce a series of Central Limit Theorems (CLTs) associated to compact metric measure spaces $(K,d,\eta)$, with $\eta$ a reasonable probability measure. For the first CLT, we can ignore $\eta$ by isometrically embedding $K$ into…
Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused…
While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not…
Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for…
Modeling the relationship between vehicle speed and density on the road is a fundamental problem in traffic flow theory. Recent research found that using the least-squares (LS) method to calibrate single-regime speed-density models is…
Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints,…
The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson--Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Two methods of…
Semantic-aware 3D scene reconstruction is essential for autonomous robots to perform complex interactions. Semantic SLAM, an online approach, integrates pose tracking, geometric reconstruction, and semantic mapping into a unified framework,…
The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…
This paper presents a systematic method for synthesizing a Control Barrier Function (CBF) that encodes predictive information into a CBF. Unlike other methods, the synthesized CBF can account for changes and time-variations in the…
Multi-task regression attempts to exploit the task similarity in order to achieve knowledge transfer across related tasks for performance improvement. The application of Gaussian process (GP) in this scenario yields the non-parametric yet…
Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…
Spectroscopic redshift surveys offer great prospects for constraining the dark sector in cosmology. Future surveys will however be both deep and wide and will thus require an analysis in 3-dimensional spherical geometry. We review and…