# Probing the Information Theoretical Roots of Spatial Dependence Measures

arXiv: https://arxiv.org/abs/2405.18459 · HTML: https://mlsanity.com/paper/2405.18459/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 8 of 8)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [GeoCLIP: Clip-Inspired Alignment between Locations and Images for Effective Worldwide Geo-localization](https://mlsanity.com/paper/2309.16020/) (2023)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks](https://mlsanity.com/paper/2310.06743/) (2023)
- [Spatial Implicit Neural Representations for Global-Scale Species Mapping](https://mlsanity.com/paper/2306.02564/) (2023)
- [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021)
- [Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions](https://mlsanity.com/paper/2306.17624/) (2023)

## Built on by (most cited first, 3 of 3)

- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [Whose Truth? Pluralistic Geo-Alignment for (Agentic) AI](https://mlsanity.com/paper/2508.05432/) (2025)
- [GeoBS: Information-Theoretic Quantification of Geographic Bias in AI Models](https://mlsanity.com/paper/2509.23482/) (2025)

## Abstract (arXiv)

Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data samples contain less than expected information. Similarly, spatial data, e.g., remotely sensed imagery, that is easy to compress is also likely to show significant spatial autocorrelation. Formulating our (highly specific) core concepts of spatial information theory in the widely used language of information theory opens new perspectives on their differences and similarities and also fosters cross-disciplinary collaboration, e.g., with the broader AI/ML communities. Interestingly, however, this intuitive relation is challenging to formalize and generalize, leading prior work to rely mostly on experimental results, e.g., for describing landscape patterns. In this work, we will explore the information theoretical roots of spatial autocorrelation, more specifically Moran's I, through the lens of self-information (also known as surprisal) and provide both formal proofs and experiments.