# Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction

arXiv: https://arxiv.org/abs/2309.00781 · HTML: https://mlsanity.com/paper/2309.00781/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Builds on (most cited first, 6 of 6)

- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [A Survey on Ensemble Learning under the Era of Deep Learning](https://mlsanity.com/paper/2101.08387/) (2021)
- [Distribution Preserving Multiple Hypotheses Prediction for Uncertainty Modeling](https://mlsanity.com/paper/2110.02858/) (2021)

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

- [Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity](https://mlsanity.com/paper/2509.02792/) (2025)

## Abstract (arXiv)

Multi-modal problems can be effectively addressed using multiple hypothesis frameworks, but integrating these frameworks into learning models poses significant challenges. This paper introduces a Structured Radial Basis Function Network (s-RBFN) as an ensemble of multiple hypothesis predictors for regression. During the training of the predictors, first the centroidal Voronoi tessellations are formed based on their losses and the true labels, representing geometrically the set of multiple hypotheses. Then, the trained predictors are used to compute a structured dataset with their predictions, including centers and scales for the basis functions. A radial basis function network, with each basis function focused on a particular hypothesis, is subsequently trained using this structured dataset for multiple hypotheses prediction. The s-RBFN is designed to train efficiently while controlling diversity in ensemble learning parametrically. The least-squares approach for training the structured ensemble model provides a closed-form solution for multiple hypotheses and structured predictions. During the formation of the structured dataset, a parameter is employed to avoid mode collapse by controlling tessellation shapes. This parameter provides a mechanism to balance diversity and generalization performance for the s-RBFN. The empirical validation on two multivariate prediction datasets-air quality and energy appliance predictions-demonstrates the superior generalization performance and computational efficiency of the structured ensemble model compared to other models and their single-hypothesis counterparts.