Related papers: Rethinking Inductive Bias in Geographically Neural…
Confronted with the spatial heterogeneity of real estate market, some traditional research utilized Geographically Weighted Regression (GWR) to estimate the house price. However, its kernel function is non-linear, elusive, and complex to…
Convolutional Neural Networks define an exceptionally powerful class of models, but are still limited by the lack of ability to be spatially invariant to the input data in a computationally and parameter efficient manner. In this work we…
Sheaf Neural Networks (SNNs) naturally extend Graph Neural Networks (GNNs) by endowing a cellular sheaf over the graph, equipping nodes and edges with vector spaces and defining linear mappings between them. While the attached geometric…
Artificial neural networks can acquire many aspects of human knowledge from data, making them promising as models of human learning. But what those networks can learn depends upon their inductive biases -- the factors other than the data…
Due to insufficient local area information, numerical weather prediction (NWP) may yield biases for specific areas. Previous studies correct biases mainly by employing handcrafted features or applying data-driven methods intuitively,…
Gravity inversion is the problem of estimating subsurface density distributions from observed gravitational field data. We consider the two-dimensional (2D) case, in which recovering density models from one-dimensional (1D) measurements…
The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…
Understanding the complex nature of spatial information is crucial for problem solving in social and environmental sciences. This study investigates how the underlying patterns of spatial data can significantly influence the outcomes of…
Learning models whose predictions are invariant under multiple environments is a promising approach for out-of-distribution generalization. Such models are trained to extract features $X_{\text{inv}}$ where the conditional distribution $Y…
Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as…
In this paper, we propose the $\textit{geometric invariance hypothesis (GIH)}$, which argues that the input space curvature of a neural network remains invariant under transformation in certain architecture-dependent directions during…
The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian…
Modeling spatial heterogeneity in the data generation process is essential for understanding and predicting geographical phenomena. Despite their prevalence in geospatial tasks, neural network models usually assume spatial stationarity,…
Geographically weighted regression (GWR) is a popular tool for modeling spatial heterogeneity in a regression model. However, the current weighting function used in GWR only considers the geographical distance, while the attribute…
A main purpose of spatial data analysis is to predict the objective variable for the unobserved locations. Although Geographically Weighted Regression (GWR) is often used for this purpose, estimation instability proves to be an issue. To…
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor…
Tackling pattern recognition problems in areas such as computer vision, bioinformatics, speech or text recognition is often done best by taking into account task-specific statistical relations between output variables. In structured…
The issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature. Multiple authors have offered perspectives and potential…
GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW)…
Just like weights, bias terms are the learnable parameters of many popular machine learning models, including neural networks. Biases are thought to enhance the representational power of neural networks, enabling them to solve a variety of…