Related papers: Spatial Process Approximations: Assessing Their Ne…
Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…
The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…
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…
One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial…
Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role it also forms an integral part of estimation of functionals such as the…
Planning safe paths is a major building block in robot autonomy. It has been an active field of research for several decades, with a plethora of planning methods. Planners can be generally categorised as either trajectory optimisers or…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…
Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
Machine learning (ML) models, such as SVM, for tasks like classification and clustering of sequences, require a definition of distance/similarity between pairs of sequences. Several methods have been proposed to compute the similarity…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Optimal allocation of scarce resources is a common problem for decision makers faced with choosing a limited number of locations for intervention. Spatiotemporal prediction models could make such decisions data-driven. A recent performance…
In health-pollution cohort studies, accurate predictions of pollutant concentrations at new locations are needed, since the locations of fixed monitoring sites and study participants are often spatially misaligned. For multi-pollution data,…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…