# CEC-MMR: Cross-Entropy Clustering Approach to Multi-Modal Regression

arXiv: https://arxiv.org/abs/2504.07301 · HTML: https://mlsanity.com/paper/2504.07301/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 14 of 14)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [Flow-Grounded Spatial-Temporal Video Prediction from Still Images](https://mlsanity.com/paper/1807.09755/) (2018)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Trustworthy Multimodal Regression with Mixture of Normal-inverse Gamma Distributions](https://mlsanity.com/paper/2111.08456/) (2021)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Noise Regularization for Conditional Density Estimation](https://mlsanity.com/paper/1907.08982/) (2019)
- [Bayesian Prediction of Future Street Scenes using Synthetic Likelihoods](https://mlsanity.com/paper/1810.00746/) (2018)
- [The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variables](https://mlsanity.com/paper/1705.07111/) (2017)
- [An implicit function learning approach for parametric modal regression](https://mlsanity.com/paper/2002.06195/) (2020)
- [Active Function Cross-Entropy Clustering](https://mlsanity.com/paper/1502.01943/) (2015)
- [How do Mixture Density RNNs Predict the Future?](https://mlsanity.com/paper/1901.07859/) (2019)

## Abstract (arXiv)

In practical applications of regression analysis, it is not uncommon to encounter a multitude of values for each attribute. In such a situation, the univariate distribution, which is typically Gaussian, is suboptimal because the mean may be situated between modes, resulting in a predicted value that differs significantly from the actual data. Consequently, to address this issue, a mixture distribution with parameters learned by a neural network, known as a Mixture Density Network (MDN), is typically employed. However, this approach has an important inherent limitation, in that it is not feasible to ascertain the precise number of components with a reasonable degree of accuracy. In this paper, we introduce CEC-MMR, a novel approach based on Cross-Entropy Clustering (CEC), which allows for the automatic detection of the number of components in a regression problem. Furthermore, given an attribute and its value, our method is capable of uniquely identifying it with the underlying component. The experimental results demonstrate that CEC-MMR yields superior outcomes compared to classical MDNs.