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Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Fast scanning probe microscopy enabled via machine learning allows for a broad range of nanoscale, temporally resolved physics to be uncovered. However, such examples for functional imaging are few in number. Here, using piezoresponse force…
Advances in hyperspectral imaging modes including electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM) bring forth the challenges of exploratory and subsequently physics-based analysis of…
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…
We propose to recover spectral details from RGB images of known spectral quantization by modeling natural spectra under Gaussian Processes and combining them with the RGB images. Our technique exploits Process Kernels to model the relative…
Gaussian Process (GP) regression is a popular and sample-efficient approach for many engineering applications, where observations are expensive to acquire, and is also a central ingredient of Bayesian optimization (BO), a highly prevailing…
Observations of exoplanet atmospheres in high resolution have the potential to resolve individual planetary absorption lines, despite the issues associated with ground-based observations. The removal of contaminating stellar and telluric…
A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction data (scanning-3DXRD) is presented and evaluated. Given an apriori known anisotropic compliance,…
Many datasets are in the form of tables of binned data. Performing regression on these data usually involves either reading off bin heights, ignoring data from neighbouring bins or interpolating between bins thus over or underestimating the…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and…
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results…
In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…