Related papers: Reduced Basis Kriging for Big Spatial Fields
Exact Kriging and conditional simulation (CS) for uncertainty quantification are computationally infeasible for modern spatial analyses with large numbers of observations and dense prediction grids. We present a rapid approximation to the…
The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective…
Multi-robot flocking possesses extraordinary advantages over a single-robot system in diverse domains, but it is challenging to ensure safe and optimal performance in congested environments. Hence, this paper is focused on the investigation…
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.…
Super-resolving the coarse outputs of global climate simulations, termed downscaling, is crucial in making political and social decisions on systems requiring long-term climate change projections. Existing fast super-resolution techniques,…
We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent…
In this paper, we model the dependencies among the items that are recommended to a user in a collaborative-filtering problem via a Gaussian Markov Random Field (MRF). We build upon Besag's auto-normal parameterization and pseudo-likelihood,…
Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond…
The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear…
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…
Gaussian random field (GRF) models are widely used in spatial statistics to capture spatially correlated error. We investigate the results of replacing Gaussian processes with Laplace moving averages (LMAs) in spatial generalized linear…
In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…
This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…
Gaussian process fitting, or kriging, is often used to create a model from a set of data. Many available software packages do this, but we show that very different results can be obtained from different packages even when using the same…
We propose a method with better predictions at extreme values than the standard method of Kriging. We construct our predictor in two ways: by penalizing the mean squared error through conditional bias and by penalizing the conditional…
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…
Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…
Spatio-temporal kriging is an important problem in web and social applications, such as Web or Internet of Things, where things (e.g., sensors) connected into a web often come with spatial and temporal properties. It aims to infer knowledge…
Random projection (RP) is a powerful dimension reduction technique widely used in the analysis of high dimensional data. We demonstrate how this technique can be used to improve the computational efficiency of gravitational wave searches…
Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a…