Predicting joint outcomes with multivariate quantile regression networks
Multivariate quantile regression via Kolmogorov-Arnold Networks
Machine Learning
Summary
Predicting the probability of where several related outcomes might happen together is challenging, especially when randomness is part of how the system works rather than measurement flaws. This paper presents a new way to model such joint outcomes using special neural networks called Kolmogorov-Arnold networks (KANs). These networks help predict regions where outcomes fall with certain probabilities, improving understanding of complex randomness. The authors also introduce a new way to check how well their predictions match real data.
What this means in practice
- •For financial risk managers: Estimate the likelihood of multiple financial risk factors occurring simultaneously for better portfolio risk assessment.
- •For environmental modelers: Predict joint probabilities of climate variables to assess combined environmental risks like temperature and precipitation extremes.
Authors
Andrew Polar, Michael Poluektov
Abstract
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.