A multi-view contrastive learning framework for spatial embeddings in risk modelling

Paper: arXiv 2511.17954

Authors: Freek Holvoet, Christopher Blier-Wong, Katrien Antonio

Abstract

Incorporating spatial information, particularly those influenced by climate, weather, and demographic factors, is crucial for improving underwriting precision and enhancing risk management in insurance. However, spatial data are often unstructured, high-dimensional, and difficult to integrate into predictive models. Embedding methods are needed to convert spatial data into meaningful representations for modelling tasks. We propose a novel multi-view contrastive learning framework for generating spatial embeddings that combine information from multiple spatial data sources. To train the model, we construct a spatial dataset that merges satellite imagery and OpenStreetMap features across Europe. The framework aligns these spatial views with coordinate-based encodings, producing low-dimensional embeddings that capture both spatial structure and contextual similarity. Once trained, the model generates embeddings directly from latitude-longitude pairs, enabling any dataset with coordinates to be enriched with meaningful spatial features without requiring access to the original spatial inputs. In a case study on French real estate prices, we compare models trained on raw coordinates against those using our spatial embeddings as inputs. The embeddings consistently improve predictive accuracy across generalised linear, additive, and boosting models, while providing interpretable spatial effects and demonstrating transferability to unseen regions.

Complexity vs Empirical Score

• Math Complexity: 6.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative multi-view contrastive learning framework to construct fine-grained regional spatial embeddings from multimodal data (satellite and OpenStreetMap features). It features solid mathematical foundations using spherical harmonics and demonstrates rigorous empirical validation across multiple machine learning models in a real estate pricing case study.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Improve risk modelling via low-dimensional<br>multi-view spatial embeddings"] --> B["Data Collection:<br>Satellite Imagery, OpenStreetMap,<br>& Coordinates (Europe)"]
    B --> C["Multi-View Contrastive Learning:<br>Align spatial views with<br>coordinate-based encodings"]
    C --> D["Embedding Generator:<br>Produce spatial embeddings directly<br>from Lat-Long pairs"]
    D --> E["Evaluation Case Study:<br>French Real Estate Price Prediction<br>(GLM, GAM, XGBoost)"]
    E --> F["Outcomes:<br>Improved accuracy, enhanced interpretability,<br>& high transferability to unseen regions"]

Cited References (163)

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8. Collective reserving using individual claims data (2022)

1 of 163 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.