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The air quality inference problem aims to utilize historical data from a limited number of observation sites to infer the air quality index at an unknown location. Considering the sparsity of data due to the high maintenance cost of the…
The generation of random spatial data on a computer is an important tool for understanding the behavior of spatial processes. In this paper we describe how to generate realizations from the main types of spatial processes, including…
In advanced mission concepts with high levels of autonomy, spacecraft need to internally model the pose and shape of nearby orbiting objects. Recent works in neural scene representations show promising results for inferring generic…
Markov random field (MRF) learning is intractable, and its approximation algorithms are computationally expensive. We target a small subset of MRF that is used frequently in computer vision. We characterize this subset with three concepts:…
This study aims to improve the accuracy of weather predictions by discovering spatial correlations between Earth observations and atmospheric states. Existing numerical weather prediction (NWP) systems predict future atmospheric states at…
Modelling individual objects in a scene as Neural Radiance Fields (NeRFs) provides an alternative geometric scene representation that may benefit downstream robotics tasks such as scene understanding and object manipulation. However, we…
In this work, we propose a novel adaptive grid mapping approach, the Adaptive Patched Grid Map, which enables a situational aware grid based perception for autonomous vehicles. Its structure allows a flexible representation of the…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
Successfully predicting gentrification could have many social and commercial applications; however, real estate sales are difficult to predict because they belong to a chaotic system comprised of intrinsic and extrinsic characteristics,…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity…
Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities…
Computing marginal distributions of discrete or semidiscrete Markov random fields (MRFs) is a fundamental, generally intractable problem with a vast number of applications in virtually all fields of science. We present a new family of…
There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging…
Accurate signal localization is critical for Internet of Things applications, but precise propagation models are often unavailable due to uncontrollable factors. Simplified models such as planar and spherical wavefront approximations are…
This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…
The Mat\'ern covariance function is a popular choice for modeling dependence in spatial environmental data. Standard Mat\'ern covariance models are, however, often computationally infeasible for large data sets. In this work, recent results…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…