# Multivariate quantile regression via Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2609.23906 · HTML: https://mlsanity.com/paper/2609.23906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Gaussian Process Conditional Density Estimation](https://mlsanity.com/paper/1810.12750/) (2018)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [KASAM: Spline Additive Models for Function Approximation](https://mlsanity.com/paper/2205.06376/) (2022)
- [CatBoostLSS -- An extension of CatBoost to probabilistic forecasting](https://mlsanity.com/paper/2001.02121/) (2020)
- [Modelling non-linear control systems using the discrete Urysohn operator](https://mlsanity.com/paper/1802.01700/) (2018)
- [Composite Quantile Regression With XGBoost Using the Novel Arctan Pinball Loss](https://mlsanity.com/paper/2406.02293/) (2024)
- [Concurrent training methods for Kolmogorov-Arnold networks: Disjoint datasets and FPGA implementation](https://mlsanity.com/paper/2512.18921/) (2025)
- [Multivariate Uncertainty Quantification with Tomographic Quantile Forests](https://mlsanity.com/paper/2512.16383/) (2025)

## Abstract (arXiv)

This paper introduces a novel algorithm for predicting conditional joint distributions of vector-valued targets in stochastic systems whose randomness is intrinsic rather than arising from observation errors or additive noise. Multivariate quantile regression also involves modeling conditional joint distributions but represents a less challenging task. It predicts the probability that vector-valued targets fall within predefined regions, identifies regions corresponding to predefined probability levels, or performs both tasks simultaneously. The proposed identification technique employs ensembles of Kolmogorov-Arnold networks (KANs) as flexible function approximators. Although the suggested technique is not theoretically restricted to KANs, KANs are particularly well suited to the proposed construction and are therefore used throughout this study. In addition to the training procedure, this work introduces a new discrepancy measure for joint distributions and a goodness-of-fit (GoF) test based on it. This GoF test was initially developed to validate and calibrate the proposed identification technique and is used here in an ad hoc manner. Although the test could be tabulated for broader use, such a tabulation is not pursued in this work. The test is also applicable more generally.