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Traditional regression models assume stationary relationships between predictors and responses, failing to capture the spatial heterogeneity present in many environmental, epidemiological, and ecological processes. To address this…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
This study demonstrates how to use the "spmoran" package implementing scalable spatial regression models for Gaussian and non-Gaussian data. Implemented models include spatially varying coefficient models, models with group effects, spatial…
With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…
Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate…
Gradient boosted trees are competition-winning, general-purpose, non-parametric regressors, which exploit sequential model fitting and gradient descent to minimize a specific loss function. The most popular implementations are tailored to…
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
Spatio-temporal models are widely used in many research areas including ecology. The recent proliferation of the use of in-situ sensors in streams and rivers supports space-time water quality modelling and monitoring in near real-time. A…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…