Journal of Data Science

In the last few decades, the size of spatial and spatio-temporal datasets in many research areas has rapidly increased with the development of data collection technologies. As a result, classical statistical methods in spatial statistics are facing computational challenges. For example, the kriging predictor in geostatistics becomes prohibitive on traditional hardware architectures for large datasets as it requires high computing power and memory footprint when dealing with large dense matrix operations. Over the years, various approximation methods have been proposed to address such computational issues, however, the community lacks a holistic process to assess their approximation efficiency. To provide a fair assessment, in 2021, we organized the first competition on spatial statistics for large datasets, generated by our ExaGeoStat software, and asked participants to report the results of estimation and prediction. Thanks to its widely acknowledged success and at the request of many participants, we organized the second competition in 2022 focusing on predictions for more complex spatial and spatio-temporal processes, including univariate nonstationary spatial processes, univariate stationary space-time processes, and bivariate stationary spatial processes. In this paper, we describe in detail the data generation procedure and make the valuable datasets publicly available for a wider adoption. Then, we review the submitted methods from fourteen teams worldwide, analyze the competition outcomes, and assess the performance of each team.

Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present nonstationary anisotropies. This paper proposes a generic approach to model Gaussian Random Fields (GRFs) on compact Riemannian manifolds that bridges the gap between existing works on nonstationary GRFs and random fields on manifolds. This approach can be applied to any smooth compact manifolds, and in particular to any compact surface. By defining a Riemannian metric that accounts for the preferential directions of correlation, our approach yields an interpretation of the nonstationary geometric anisotropies as resulting from local deformations of the domain. We provide scalable algorithms for the estimation of the parameters and for optimal prediction by kriging and simulation able to tackle very large grids. Stationary and nonstationary illustrations are provided.

We describe our implementation of the multivariate Matérn model for multivariate spatial datasets, using Vecchia’s approximation and a Fisher scoring optimization algorithm. We consider various pararameterizations for the multivariate Matérn that have been proposed in the literature for ensuring model validity, as well as an unconstrained model. A strength of our study is that the code is tested on many real-world multivariate spatial datasets. We use it to study the effect of ordering and conditioning in Vecchia’s approximation and the restrictions imposed by the various parameterizations. We also consider a model in which co-located nuggets are correlated across components and find that forcing this cross-component nugget correlation to be zero can have a serious impact on the other model parameters, so we suggest allowing cross-component correlation in co-located nugget terms.

This paper presents an empirical study of a recently compiled workforce analytics data-set modeling employment outcomes of Engineering students. The contributions reported in this paper won the data challenge of the ACM IKDD 2016 Conference on Data Science. Two problems are addressed - regression using heterogeneous information types and the extraction of insights/trends from data to make recommendations; these goals are supported by a range of visualizations. Whereas the data-set is specific to a nation, the underlying techniques and visualization methods are generally applicable. Gaussian processes are proposed to model and predict salary as a function of heterogeneous independent attributes. Key novelties the GP approach brings to the domain of understanding workforce analytics are (a) statistically sound notion of uncertainty of prediction that is data dependent, (b) automatic relevance determination of various independent attributes to the dependent variable (salary),(c) seamless incorporation of both numeric and string attributes within the same regression frame- work without dichotomization; specifically, string attributes include single-word or categorical (e.g. gender) or nominal attributes (e.g. college tier) or multi-word attributes (e.g. specialization) and (d) treatment of all data as being correlated towards making predictions. Insights from both predictive modeling approaches and data analysis were used to suggest factors, that if improved, might lead to better starting salaries for Engineering students. A range of visualization techniques were used to extract key employment patterns from the data.

Abstract: This paper evaluates the efficacy of a machine learning approach to data fusion using convolved multi-output Gaussian processes in the context of geological resource modeling. It empirically demonstrates that information integration across multiple information sources leads to superior estimates of all the quantities being modeled, compared to modeling them individually. Convolved multi-output Gaussian processes provide a powerful approach for simultaneous modeling of multiple quantities of interest while taking correlations between these quantities into consideration. Experiments are performed on large scale data taken from a mining context.