# Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

arXiv: https://arxiv.org/abs/1905.06220 · HTML: https://mlsanity.com/paper/1905.06220/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 5 of 5)

- [Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons](https://mlsanity.com/paper/2107.02397/) (2021)
- [Sparse online variational Bayesian regression](https://mlsanity.com/paper/2102.12261/) (2021)
- [Learning non-stationary and discontinuous functions using clustering, classification and Gaussian process modelling](https://mlsanity.com/paper/2211.16909/) (2022)
- [A Novel Cluster Classify Regress Model Predictive Controller Formulation; CCR-MPC](https://mlsanity.com/paper/2101.07655/) (2021)
- [Reservoir History Matching of the Norne field with generative exotic priors and a coupled Mixture of Experts -- Physics Informed Neural Operator Forward Model](https://mlsanity.com/paper/2406.00889/) (2024)

## Abstract (arXiv)

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.