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Spatial interaction and spatial autocorrelation are two different fields of geo-spatial analysis, revealing the internal relationship between the two fields will help to develop the theory and method of geographical analysis. This paper is…
Spatial data display correlation between observations collected at neighboring locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features and thereby…
We propose a novel estimation procedure for models with endogenous variables in the presence of spatial correlation based on Eigenvector Spatial Filtering. The procedure, called Moran's $I$ 2-Stage Lasso (Mi-2SL), uses a two-stage Lasso…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
Diagnostics such as Moran's index and approximate profile likelihood-based estimators (APLE) for Gaussian spatial autoregressive models are widely used in exploratory data analysis to assess the strength of spatial dependence. Yet, although…
This work proposes a method to evaluate synthetic tabular data generated to augment small sample datasets. While data augmentation techniques can increase sample counts for machine learning applications, traditional validation approaches…
As a rule statistical measures are often vulnerable to the presence of outliers and spatial correlation coefficients, critical in the assessment of spatial data, remain susceptible to this inherent flaw. In contexts where data originates…
Introducing training-time augmentations is a key technique to enhance generalization and prepare deep neural networks against test-time corruptions. Inspired by the success of generative diffusion models, we propose a novel approach of…
The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed…
In using data assimilation to import information from observations to estimate parameters and state variables of a model, one must assume a distribution for the noise in the measurements and in the model errors. Using the path integral…
Sampling-based motion planning is a well-established approach in autonomous driving, valued for its modularity and analytical tractability. In complex urban scenarios, however, uniform or heuristic sampling often produces many infeasible or…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
The measurement of Doppler velocity shifts in spectra is a ubiquitous theme in astronomy, usually handled by computing the cross-correlation of the signals, and finding the location of its maximum. This paper addresses the problem of the…
Localization is essential in ensemble-based data assimilation because finite ensembles produce noisy covariance estimates, causing spurious updates and excessive loss of ensemble variance. In subsurface applications, localization is usually…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…
To derive the auto-covariance function from a sampled and time-limited signal or the cross-covariance function from two such signals, the mean values must be estimated and removed from the signals. If no a priori information about the…
Low-cost air pollution sensors, offering hyper-local characterization of pollutant concentrations, are becoming increasingly prevalent in environmental and public health research. However, low-cost air pollution data can be noisy, biased by…
In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…
The idea of spatial crosscorrelation was conceived of long ago. However, unlike the related spatial autocorrelation, the theory and method of spatial crosscorrelation analysis have remained undeveloped. This paper presents a set of models…