Related papers: Deep Compositional Spatial Models
Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…
We introduce an integrodifferential extension of the edge-enhancing anisotropic diffusion model for image denoising. By accumulating weighted structural information on multiple scales, our model is the first to create anisotropy through…
The nonlinear matter power spectrum in cosmology describes how matter density fluctuations vary with scale in the universe, providing critical insights into large-scale structure formation. The matter power spectrum includes both smooth…
Spatial nonstationarity, the location variance of features' statistical distributions, is ubiquitous in many natural settings. For example, in geological reservoirs rock matrix porosity varies vertically due to geomechanical compaction…
Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
Motivated by a large ground-level ozone dataset, we propose a new computationally efficient additive approximate Gaussian process. The proposed method incorporates a computational-complexity-reduction method and a separable covariance…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…
The current availability of soil moisture data over large areas comes from satellite remote sensing technologies (i.e., radar-based systems), but these data have coarse resolution and often exhibit large spatial information gaps. Where data…
Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent…
We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
Deep implicit functions (DIFs), as a kind of 3D shape representation, are becoming more and more popular in the 3D vision community due to their compactness and strong representation power. However, unlike polygon mesh-based templates, it…
Spatial coherence plays an important role in several real-world applications ranging from imaging to communication. As a result, its accurate characterization and measurement are extremely crucial for its optimal application. However,…
We introduce a novel class of non-stationary covariance functions for random fields on linear networks that allows both the variance and the correlation range of the random field to vary spatially. The proposed covariance functions are…
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…