# Reducing the dimensionality and granularity in hierarchical categorical variables

arXiv: https://arxiv.org/abs/2403.03613 · HTML: https://mlsanity.com/paper/2403.03613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Integrating Random Effects in Deep Neural Networks](https://mlsanity.com/paper/2206.03314/) (2022)
- [Machine Learning with High-Cardinality Categorical Features in Actuarial Applications](https://mlsanity.com/paper/2301.12710/) (2023)
- [On clustering levels of a hierarchical categorical risk factor](https://mlsanity.com/paper/2304.09046/) (2023)

## Built on by (most cited first, 1 of 1)

- [A multi-view contrastive learning framework for spatial embeddings in risk modelling](https://mlsanity.com/paper/2511.17954/) (2025)

## Abstract (arXiv)

Hierarchical categorical variables often exhibit many levels (high granularity) and many classes within each level (high dimensionality). This may cause overfitting and estimation issues when including such covariates in a predictive model. In current literature, a hierarchical covariate is often incorporated via nested random effects. However, this does not facilitate the assumption of classes having the same effect on the response variable. In this paper, we propose a methodology to obtain a reduced representation of a hierarchical categorical variable. We show how entity embedding can be applied in a hierarchical setting. Subsequently, we propose a top-down clustering algorithm which leverages the information encoded in the embeddings to reduce both the within-level dimensionality as well as the overall granularity of the hierarchical categorical variable. In simulation experiments, we show that our methodology can effectively approximate the true underlying structure of a hierarchical covariate in terms of the effect on a response variable, and find that incorporating the reduced hierarchy improves the balance between model fit and complexity. We apply our methodology on a real dataset and find that the reduced hierarchy is an improvement over the original hierarchical structure and reduced structures proposed in the literature.