Related papers: Gaussian Processes with Input Location Error and A…
Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and…
Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
In this paper, we investigate the following question: Can we obtain adversarially-trained models without training on adversarial examples? Our intuition is that training a model with inherent stochasticity, i.e., optimizing the parameters…
Recently, generalizable human Gaussian splatting from sparse-view inputs has been actively studied for the photorealistic human rendering. Most existing methods rely on explicit geometric constraints or predefined structural representations…
We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…
This paper proposes a predictive rate-selection framework based on Gaussian process (GP)-based radio map construction that is robust to location uncertainty. Radio maps are a promising tool for improving communication efficiency in 6G…
Active learning methods for emulating complex computer models that rely on stationary Gaussian processes tend to produce design points that uniformly fill the entire experimental region, which can be wasteful for functions which vary only…
We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…
We study a discrete-in-time data-assimilation algorithm based on nudging through a time-delayed feedback control in which the observational measurements have been contaminated by a Gaussian noise process. In the context of the…
In independent component analysis it is assumed that the observed random variables are linear combinations of latent, mutually independent random variables called the independent components. Our model further assumes that only the…
In this paper, we consider the problems of state estimation and false data injection detection in smart grid when the measurements are corrupted by colored Gaussian noise. By modeling the noise with the autoregressive process, we estimate…
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…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
We consider performing simulation experiments in the presence of covariates. Here, covariates refer to some input information other than system designs to the simulation model that can also affect the system performance. To make decisions,…