Related papers: Uniform Error Bounds for Gaussian Process Regressi…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

One of the key benefits of model predictive control is the capability of controlling a system proactively in the sense of taking the future system evolution into account. However, often external disturbances or references are not a priori…

An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…

Generalization error bounds are essential for comprehending how well machine learning models work. In this work, we suggest a novel method, i.e., the Auxiliary Distribution Method, that leads to new upper bounds on expected generalization…

Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…

In this paper, a simple heuristic is proposed for the design of uncertainty aware predictive controllers for nonlinear models involving uncertain parameters. The method relies on Machine Learning-based approximation of ideal deterministic…

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

Expensive ultrasonic anemometers are usually required to measure wind speed accurately. The aim of this work is to overcome the loss of accuracy of a low cost hot-wire anemometer caused by the changes of air temperature, by means of a…

When first principle models cannot be derived due to the complexity of the real system, data-driven methods allow us to build models from system observations. As these models are employed in learning-based control, the quality of the data…

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…

The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often…

Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…

This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…

This paper proposes a hybrid Gaussian process (GP) approach to robust economic model predictive control under unknown future disturbances in order to reduce the conservatism of the controller. The proposed hybrid GP is a combination of two…