In many scientific and industrial applications, we are given a handful of instances (a 'small ensemble') of a spatially distributed quantity (a 'field') but would like to acquire many more. For example, a large ensemble of global temperature sensitivity fields from a climate model can help farmers, insurers, and governments plan appropriately. When acquiring more data is prohibitively expensive -- as is the case with climate models -- statistical emulation offers an efficient alternative for simulating synthetic yet realistic fields. However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity.

Spatial clustering is a crucial field, finding universal use across criminology, pathology, and urban planning. However, most spatial clustering algorithms cannot pull information from nearby nodes and suffer performance drops when dealing with higher dimensionality and large datasets, making them suboptimal for large-scale and high-dimensional clustering. Due to modern data growing in size and dimension, clustering algorithms become weaker when addressing multifaceted issues. To improve upon this, we develop ConstellationNet, a convolution neural network(CNN)-graph neural network(GNN) framework that leverages the embedding power of a CNN, the neighbor aggregation of a GNN, and a neural network's ability to deal with batched data to improve spatial clustering and classification with graph augmented predictions. ConstellationNet achieves state-of-the-art performance on both supervised classification and unsupervised clustering across several datasets, outperforming state-of-the-art classification and clustering while reducing model size and training time by up to tenfold and improving baselines by 10 times. Because of its fast training and powerful nature, ConstellationNet holds promise in fields like epidemiology and medical imaging, able to quickly train on new data to develop robust responses.

This research presents an Encoded Spatial Multi-Tier Federated Learning approach for a comprehensive evaluation of aggregated models for geospatial data. In the client tier, encoding spatial information is introduced to better predict the target outcome. The research aims to assess the performance of these models across diverse datasets and spatial attributes, highlighting variations in predictive accuracy. Using evaluation metrics such as accuracy, our research reveals insights into the complexities of spatial granularity and the challenges of capturing underlying patterns in the data. We extended the scope of federated learning (FL) by having multi-tier along with the functionality of encoding spatial attributes. Our N-tier FL approach used encoded spatial data to aggregate in different tiers. We obtained multiple models that predicted the different granularities of spatial data. Our findings underscore the need for further research to improve predictive accuracy and model generalization, with potential avenues including incorporating additional features, refining model architectures, and exploring alternative modeling approaches. Our experiments have several tiers representing different levels of spatial aspects. We obtained accuracy of 75.62% and 89.52% for the global model without having to train the model using the data constituted with the designated tier. The research also highlights the importance of the proposed approach in real-time applications.

Causal reasoning is often challenging with spatial data, particularly when handling high-dimensional inputs. To address this, we propose a neural network (NN) based framework integrated with an approximate Gaussian process to manage spatial interference and unobserved confounding. Additionally, we adopt a generalized propensity-score-based approach to address partially observed outcomes when estimating causal effects with continuous treatments. We evaluate our framework using synthetic, semi-synthetic, and real-world data inferred from satellite imagery. Our results demonstrate that NN-based models significantly outperform linear spatial regression models in estimating causal effects. Furthermore, in real-world case studies, NN-based models offer more reasonable predictions of causal effects, facilitating decision-making in relevant applications.

Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on assumptions such as normality, which often break down in large-scale, diverse datasets, leading to unreliable prediction intervals. While machine learning methods have emerged as powerful alternatives, they primarily focus on point predictions and provide limited mechanisms for uncertainty quantification. Conformal prediction, a distribution-free framework, offers valid prediction intervals without relying on parametric assumptions. However, existing conformal prediction methods are either not tailored for spatial settings, or existing ones for spatial data have relied on rather restrictive i.i.d. assumptions. In this paper, we propose Localized Spatial Conformal Prediction (LSCP), a conformal prediction method designed specifically for spatial data. LSCP leverages localized quantile regression to construct prediction intervals. Instead of i.i.d. assumptions, our theoretical analysis builds on weaker conditions of stationarity and spatial mixing, which is natural for spatial data, providing finite-sample bounds on the conditional coverage gap and establishing asymptotic guarantees for conditional coverage. We present experiments on both synthetic and real-world datasets to demonstrate that LSCP achieves accurate coverage with significantly tighter and more consistent prediction intervals across the spatial domain compared to existing methods.

In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. To address the limitations of the Gaussian models, a variety of skewed models has been proposed, of which the popularity has grown rapidly. These skewed models introduce parameters that govern skewness and tail weight. Among various proposals in the literature, unified skewed distributions, such as the Unified Skew-Normal (SUN), have received considerable attention. In this work, we revisit a more concise and intepretable re-parameterization of the SUN distribution and apply the distribution to random fields by constructing a generalized unified skew-normal (GSUN) spatial process. We demonstrate that the GSUN is a valid spatial process by showing its vanishing correlation in large distances and provide the corresponding spatial interpolation method. In addition, we develop an inference mechanism for the GSUN process using the concept of neural Bayes estimators with deep graphical attention networks (GATs) and encoder transformer. We show the superiority of our proposed estimator over the conventional CNN-based architectures regarding stability and accuracy by means of a simulation study and application to Pb-contaminated soil data. Furthermore, we show that the GSUN process is different from the conventional Gaussian processes and Tukey g-and-h processes, through the probability integral transform (PIT).

The Spatial Knowledge Graphs (SKG) are experiencing growing adoption as a means to model real-world entities, proving especially invaluable in domains like crisis management and urban planning. Considering that RDF specifications offer limited support for effectively managing spatial information, it's common practice to include text-based serializations of geometrical features, such as polygons and lines, as string literals in knowledge graphs. Consequently, Spatial Knowledge Graphs (SKGs) often rely on geo-enabled RDF Stores capable of parsing, interpreting, and indexing such serializations. In this paper, we leverage grid cells as the foundational element of SKGs and demonstrate how efficiently the spatial characteristics of real-world entities and their attributes can be encoded within knowledge graphs. Furthermore, we introduce a novel methodology for representing street networks in knowledge graphs, diverging from the conventional practice of individually capturing each street segment. Instead, our approach is based on tessellating the street network using grid cells and creating a simplified representation that could be utilized for various routing and navigation tasks, solely relying on RDF specifications.

Research status and development trends; on this basis, this report proposes three major challenges faced by large spatial data intelligent models today. This report focuses on the current research status of spatial data intelligent large-scale models and sorts out the research progress in four major thematic areas of spatial data intelligent large-scale models: cities, air and space remote sensing, geography, and transportation. This report systematically introduces the key technologies, characteristics and advantages, research status, future development and other core information of spatial data intelligent large models, involving spatiotemporal big data platforms, distributed computing, 3D virtual reality, space The basic performance of large models such as analysis and visualization, as well as the complex spatial comprehensive performance of large models such as geospatial intelligent computing, deep learning, high-performance processing of big data, geographical knowledge graphs, and geographical intelligent multi-scenario simulation, analyze the application of the above key technologies in spatial data The location and role of smart large models.

Geospatial data plays a central role in modeling our world, for which OpenStreetMap (OSM) provides a rich source of such data. While often spatial data is represented in a tabular format, a graph based representation provides the possibility to interconnect entities which would have been separated in a tabular representation. We propose in our paper a framework which supports a planet scale transformation of OpenStreetMap data into a Spatial Temporal Knowledge Graph. In addition to OpenStreetMap data, we align the different OpenStreetMap geometries on individual h3 grid cells. We compare our constructed spatial knowledge graph to other spatial knowledge graphs and outline our contribution in this paper. As a basis for our computation, we use Apache Sedona as a computational framework for our Spatial Temporal Knowledge Graph construction

Recently, nonlinear ICA has surfaced as a popular alternative to the many heuristic models used in deep representation learning and disentanglement. An advantage of nonlinear ICA is that a sophisticated identifiability theory has been developed; in particular, it has been proven that the original components can be recovered under sufficiently strong latent dependencies. Despite this general theory, practical nonlinear ICA algorithms have so far been mainly limited to data with one-dimensional latent dependencies, especially time-series data. In this paper, we introduce a new nonlinear ICA framework that employs $t$-process (TP) latent components which apply naturally to data with higher-dimensional dependency structures, such as spatial and spatio-temporal data. In particular, we develop a new learning and inference algorithm that extends variational inference methods to handle the combination of a deep neural network mixing function with the TP prior, and employs the method of inducing points for computational efficacy. On the theoretical side, we show that such TP independent components are identifiable under very general conditions. Further, Gaussian Process (GP) nonlinear ICA is established as a limit of the TP Nonlinear ICA model, and we prove that the identifiability of the latent components at this GP limit is more restricted. Namely, those components are identifiable if and only if they have distinctly different covariance kernels. Our algorithm and identifiability theorems are explored on simulated spatial data and real world spatio-temporal data.