# A Generalized Unscented Transformation for Probability Distributions

arXiv: https://arxiv.org/abs/2104.01958 · HTML: https://mlsanity.com/paper/2104.01958/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2021.

## Built on by (most cited first, 4 of 4)

- [Stochastic Physics-Informed Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.01621/) (2021)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [FORESEE: Prediction with Expansion-Compression Unscented Transform for Online Policy Optimization](https://mlsanity.com/paper/2209.12644/) (2022)
- [Few-sample Variational Inference of Bayesian Neural Networks with Arbitrary Nonlinearities](https://mlsanity.com/paper/2405.02063/) (2024)

## Abstract (arXiv)

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19.