New method estimates spatial weights matrix for lattice data, improving prediction accuracy.
problem Estimating spatial dependence structure for regular lattice data.
method Adaptive lasso with cross-sectional resampling to estimate sparse spatial weights matrix.
result Improves prediction accuracy of nitrogen dioxide concentrations.
Spatial Adapter adds structured spatial representation to frozen predictors.
problem Efficiently adding spatial structure to pre-trained models.
method Structured spatial decomposition and closed-form covariance for residual fields.
result Adapter improves spatial prediction and uncertainty quantification.
A new framework enhances IDW models for complex industrial datasets.
problem Low performance of IDW models in complex industrial datasets.
method Deep reinforcement learning network to enhance IDW models and learn hyperparameters.
result The proposed framework achieves differential spatial prediction and is more accurate than current IDW models.
Scalable method for regionalizing and extracting temporal patterns from time series data.
problem Static spatial snapshots and ad hoc regularization limit effective spatial analysis and resource management.
method Minimum description length principle for fully nonparametric spatial partitioning and time series archetypes.
result Accurately recovers planted regional structure and drivers in synthetic and empirical data.
Spatially-aware metrics improve uncertainty evaluation in segmentation.
problem Uncertainty evaluation metrics treat voxels independently, ignoring spatial context.
method Proposed three spatially aware metrics incorporating structural and boundary information.
result Improved alignment with clinically important factors and better discrimination between uncertainty patterns.
Agents can learn spatial structure from raw sensorimotor experience.
problem Understanding spatial knowledge and its emergence in autonomous agents.
method A simple sensorimotor predictive scheme applied to various agents and exploration types.
result Agents can capture spatial topology and metric regularity without prior knowledge or supervision.
MSFA clusters high-dimensional spatial data using spline-based covariance structures.
problem Clustering high-dimensional spatial data with flexible covariance structures.
method Mixture of spatial factor analyzers with spline-based covariance and matrix variate factor analyzers for dimensionality reduction.
result Proposed models accurately infer and differentiate distinct spatial patterns in tensor-variate data.
Flexible XVAE model for efficient spatial extremes simulation.
problem Complex tail dependence structures in spatial extremes processes.
method Variational autoencoder (XVAE) for modeling flexible and non-stationary dependence.
result XVAE provides fast inference and outperforms traditional models in high dimensions.
SpaceGAN enhances geospatial data using deep learning.
problem Challenges in modeling geospatial data with deep learning.
method SpaceGAN, a generative model that learns spatial structures through conditioning on neighbours.
result SpaceGAN produces synthetic samples faithful to real spatial patterns, improving data augmentation and model generalization.
Hybrid model integrates GATv2 and geostatistics for better spatial prediction and uncertainty.
problem Accurate spatial prediction and uncertainty quantification in epidemiology and risk analysis.
method Integrates Graph Attention Network (GATv2) with model-based geostatistics (MBG) to capture relational and spatial dependencies.
result Hybrid model improves predictive accuracy and uncertainty quantification compared to standalone models.
Study reveals how dengue spread patterns vary across different years in Recife, Brazil.
problem Understanding spatial organization of dengue transmission in urban areas.
method Spatial analysis of dengue cases using topological data analysis and Vietoris-Rips filtrations.
result Critical percolation thresholds define distinct geometric regimes of dengue spread.
Agents learn spatial structure without supervision.
problem Understanding spatial knowledge in autonomous agents.
method Sensorimotor predictive scheme applied to various agents and exploration types.
result Agents can learn egocentric spatial structure without supervision.
Spatial Deconfounder tackles interference and confounding in spatial data.
problem Interference and unmeasured spatial factors confound causal inference in spatial domains.
method Two-stage method using CVAE with spatial prior to reconstruct confounder, then estimate causal effects.
result Nonparametric identification of direct and spillover effects under weak assumptions.
New algorithm clusters hyperspectral images at multiple scales.
problem Clustering hyperspectral images at various scales.
method M-SRDL algorithm using spectral-spatial diffusion distances.
result More accurate clustering labels achieved with spatial regularization.
Spatial graph representation improves GNN performance.
problem GNNs struggle with distinguishing similar local structures in different graph locations.
method Proposes a spatial graph representation method to distinguish local structures and simplify graph downsampling.
result Proposed graph pooling method achieves competitive results.
iREPA shows spatial structure, not global semantic, drives generation performance in REPA.
problem Understanding what aspect of the target representation matters for generation.
method Empirical analysis of 27 vision encoders, two modifications to REPA.
result Spatial structure, not global semantic, drives generation performance.
A new model predicts financial volatility across firms using spatial correlations.
problem Predicting financial volatility across firms in a network.
method Heterogeneous spatiotemporal GARCH model with local likelihood estimation.
result The model captures spatial spillovers and contagion effects in financial networks.
GCNs model complex spatial patterns of POI check-ins.
problem Capturing complex spatial patterns in irregular data.
method Graph Convolutional Neural Networks (GCNs) for semi-supervised prediction.
result Demonstrates feasibility of GCNs for complex geographic data.
New method reduces spatial graphs while preserving their topological features.
problem Finding a smaller spatial graph with the same structure.
method Topological spatial graph coarsening approach based on triangle-aware graph filtration.
result Significant reduction in graph size while preserving topological information.
New method calculates bridge indices of spatial graphs using diagram colorings and Wirtinger number.
problem Calculating bridge indices for spatial graphs efficiently.
method Extending Wirtinger number to spatial graphs, implementing Python algorithm, combining algebraic structures and clasping techniques.
result Exact bridge indices for almost unknotted graphs of large bridge index.
Develops BASGCN for graph classification with improved feature learning.
problem Graph classification with information loss and imprecise representation.
method Transforms graphs into grid structures and defines a new spatial graph convolution operation.
result Reduces information loss and improves feature representation compared to existing models.
Proposes SGCN for spatially structured data.
problem Lack of node neighbor ordering in GCNs.
method Uses spatial features to learn from graphs with spatial positions.
result Empirically outperforms state-of-the-art methods.
A framework converts spatial data into embeddings for insurance risk modelling.
problem Improving underwriting precision and risk management in insurance with spatial data.
method Multi-view contrastive learning framework for generating spatial embeddings.
result Spatial embeddings consistently improve predictive accuracy across various models.
Physics-informed methods infer spatial dynamics from static snapshots, but limits exist.
problem Inferring spatial dynamics from static molecular patterns.
method Combining flexible representations with mechanistic constraints, analyzing structural identifiability, and adapting physics-informed schemes.
result Static spatial patterns can identify spatially varying dynamics, but limits exist due to modeling choices.
Dynamic models learn from sparse, interacting sub-systems.
problem Learning robust models for systems with local views and spatial locations.
method Abstracting the system as a collection of sparsely interacting sub-systems, each with a learned topology informed by spatial structure.
result Models are more robust to the number of available views and generalize better to novel tasks.
Spatial understanding is a fundamental problem with wide-reaching real-world applications. The representation of spatial knowledge is often modeled with spatial templates, i.e., regions of acceptability of two objects under an explicit spatial relationship (e.g., "on", "below", etc.). In contrast with prior work that r…
The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors, which can be interpreted as multiple feature maps of size 1x1. Such representations…
Agent Based Modeling (ABM) has become a widespread approach to model complex interactions. In this chapter after briefly summarizing some features of ABM the different approaches in modeling spatial interactions are discussed. It is stressed that agents can interact either indirectly through a shared environment and/or…
Paper proposes efficient multivariate spatial Fay-Herriot models using variational autoencoders.
problem Estimating population characteristics in small areas with limited data.
method Integrates multivariate spatial Fay-Herriot model with variational autoencoders to leverage spatial structure efficiently.
result Significant computational efficiency improvements for high-dimensional datasets.
Forecaster uses graph Transformers to forecast spatial and time-dependent data.
problem Complex spatial and temporal dependencies in data.
method Graph Transformer architecture with sparsification for spatial and temporal dependencies.
result Forecaster significantly outperforms state-of-the-art baselines in taxi demand forecasting.
Method reduces complexity of spatial interaction networks.
problem Complex spatial interaction networks.
method Empirical Bayes approach with tree partitioning and generalized double Pareto prior.
result Compact vectorial representations and interpretable visualizations.
EFDM models spatial point processes with variable cardinality using existence variables.
problem Challenges in extending diffusion models to variable-cardinality spatial point processes.
method Existence-field diffusion model (EFDM) that jointly models spatial locations and cardinality without discrete transitions.
result EFDM achieves improved modeling capability on datasets with varying cardinality.
Deep models predict spatial phenomena with better accuracy.
problem Nonstationary and anisotropic spatial data modeling.
method Deep compositional spatial models using deep learning and approximate Bayesian inference.
result Deep compositional models provide better predictions and uncertainty quantification.
Graph WaveNet models spatial-temporal graphs by learning hidden dependencies and long sequences.
problem Capturing hidden spatial dependencies and long-range temporal sequences in graphs.
method Graph WaveNet integrates adaptive dependency matrix learning and stacked dilated 1D convolution.
result Graph WaveNet outperforms existing methods on public traffic network datasets.
We introduce \textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for Y-oriented trivalent spatial graphs and handlebody-links. As part of this definition, we identify generating sets of Y-oriented Reid…
In this paper we show that space of spatial polygons in semi riemann space gives a Kahler manifold. We describe the tangent space and almost complex structure which has many computational advantages.
Spatial orderness metric improves CNN performance for non-spatial data.
problem Improving CNN performance for data lacking spatial order.
method Proposed spatial orderness metric to quantify spatial ordering.
result Adding convolutional layers is counterproductive for non-spatial data.
STG2Seq predicts multi-step passenger demand with graph and hierarchical structure.
problem Predicting passenger demand over multiple time horizons is challenging due to nonlinear and dynamic spatial-temporal dependencies.
method Proposes a graph-based model with a hierarchical graph convolutional structure to capture spatial and temporal correlations.
result Consistently outperforms baseline and state-of-the-art models on real-world datasets.
DCK improves air quality index prediction with probabilistic spatial models.
problem Non-Gaussian, complex spatial structure of air quality index.
method Deep classifier kriging (DCK) for non-Gaussian, nonlinear spatial prediction.
result DCK outperforms conventional methods in predictive accuracy and uncertainty quantification.
Novel SCUSUM detects weak spatial signals more efficiently.
problem Detecting weak clustered signals in spatial data.
method Spatial CUSUM (SCUSUM) using CUSUM procedure and false discovery rate control.
result SCUSUM achieves high classification accuracy for weak spatial signals.
Improved graph-based connectivity estimation using heat modelling.
problem Lack of explicit model-based, dynamic, multivariate, and directed connectivity estimation methods.
method Noise-driven heat modelling on graphs with relaxed assumptions and regularisation.
result Demonstrated ability to capture meaningful spatial structure across real-world datasets.
Gradient boosting for spatial regression models improves prediction accuracy.
problem Spatial data with autoregressive disturbances.
method Model-based gradient boosting algorithm for spatial regression models.
result Improves prediction accuracy on out-of-sample spatial data.
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these dependencies through a structured latent dynamical component, while a decoder predicts t…
This study proposes a graph partitioning method to improve spatial prediction models.
problem Improving interpretability of spatial prediction models in industries.
method Graph partitioning problem to minimize within-segment variances, formulated as mixed-integer quadratic programming.
result Approximation scheme efficiently identifies spatial segments, improving computational efficiency.
New modularity function improves clustering of spatially embedded networks.
problem Improving clustering in spatially embedded networks for unsupervised learning.
method Developed a new modularity function and compared its performance with existing methods.
result Our modularity function outperforms existing methods in partitioning 2D and 3D granular assemblies.
DeepKriging uses DNNs to predict spatial data with improved accuracy and scalability.
problem Predicting spatial processes with non-linear and non-Gaussian data.
method Adds an embedding layer of spatial coordinates with basis functions to DNNs.
result DeepKriging provides non-linear predictions with smaller approximation errors and is scalable for large datasets.
Language models trained on chess board states outperform those on moves, even with causal masking.
problem Applying causal masking to spatial data for training unimodal language models.
method Trained bidirectional and causal self-attention models on both spatial (board-based) and sequential (move-based) chess data.
result Models trained on spatial board states achieve stronger playing strength than those trained on sequential data, even with causal masking.
To better understand the spatial structure of large panels of economic and financial time series and provide a guideline for constructing semiparametric models, this paper first considers estimating a large spatial covariance matrix of the generalized m-dependent and β-mixing time series (with J variables and T…