Related papers: Reduced-space Gaussian Process Regression for Data…

Mapping near-field pollutant concentration is essential to track accidental toxic plume dispersion in urban areas. By solving a large part of the turbulence spectrum, large-eddy simulations (LES) have the potential to accurately represent…

We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential…

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…

Acquiring a substantial number of data points for training accurate machine learning (ML) models is a big challenge in scientific fields where data collection is resource-intensive. Here, we propose a novel approach for constructing a…

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…

We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at…

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…

We introduce a novel Gibbs Markov random field for spatial data on Cartesian grids based on the modified planar rotator (MPR) model of statistical physics. The MPR captures spatial correlations using nearest-neighbor interactions of…

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…

In Gaussian Process (GP) dynamical model learning for robot control, particularly for systems constrained by computational resources like small quadrotors equipped with low-end processors, analyzing stability and designing a stable…

Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…

Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic…