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We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…
Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Gaussian random fields with Mat\'ern covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Mat\'ern fields formulated as solutions to a…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Spatial regression models have a variety of applications in several fields ranging from economics to public health. Typically, it is of interest to select important exogenous predictors of the spatially autocorrelated response variable. In…
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…
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…
Machine learning and geostatistics are two fundamentally different frameworks for predicting and spatially mapping soil properties. Geostatistics leverages the spatial structure of soil properties, while machine learning captures the…
Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can…
We consider the problem of predicting values of a random process or field satisfying a linear model $y(x)=\theta^\top f(x) + \varepsilon(x)$, where errors $\varepsilon(x)$ are correlated. This is a common problem in kriging, where the case…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well. Existing prediction methods usually have…
Deep Learning has recently emerged as a perfect prognosis downscaling technique to compute high-resolution fields from large-scale coarse atmospheric data. Despite their promising results to reproduce the observed local variability, they…
In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible…
We study the spatio-temporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatio-temporal prediction is extensively studied in Machine Learning literature due to its critical real-life applications such…