# Geographic ratemaking with spatial embeddings

arXiv: https://arxiv.org/abs/2104.12852 · HTML: https://mlsanity.com/paper/2104.12852/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 74 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Advances in Pre-Training Distributed Word Representations](https://mlsanity.com/paper/1712.09405/) (2017)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [Urban2Vec: Incorporating Street View Imagery and POIs for Multi-Modal Urban Neighborhood Embedding](https://mlsanity.com/paper/2001.11101/) (2020)
- [Embedding Geographic Locations for Modelling the Natural Environment using Flickr Tags and Structured Data](https://mlsanity.com/paper/1810.12091/) (2018)

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

- [A Fair Pricing Model via Adversarial Learning](https://mlsanity.com/paper/2202.12008/) (2022)
- [A multi-view contrastive learning framework for spatial embeddings in risk modelling](https://mlsanity.com/paper/2511.17954/) (2025)
- [Revealing Geography-Driven Signals in Zone-Level Claim Frequency Models: An Empirical Study using Environmental and Visual Predictors](https://mlsanity.com/paper/2604.21893/) (2026)

## Abstract (arXiv)

Spatial data is a rich source of information for actuarial applications: knowledge of a risk's location could improve an insurance company's ratemaking, reserving or risk management processes. Insurance companies with high exposures in a territory typically have a competitive advantage since they may use historical losses in a region to model spatial risk non-parametrically. Relying on geographic losses is problematic for areas where past loss data is unavailable. This paper presents a method based on data (instead of smoothing historical insurance claim losses) to construct a geographic ratemaking model. In particular, we construct spatial features within a complex representation model, then use the features as inputs to a simpler predictive model (like a generalized linear model). Our approach generates predictions with smaller bias and smaller variance than other spatial interpolation models such as bivariate splines in most situations. This method also enables us to generate rates in territories with no historical experience.