![Logo](/decargroup/hessian_sum_mixtures/raw/main/figs/hessians.png)
A nonlinear least squares Hessian for Gaussian Mixture Factors. Our method explicitly uses the chain rule to take into account the LogSumExp nonlinearity proper to negative log-likelihoods of Gaussian Mixtures. A method to maintain compatibility with standard nonlinear least-squares solvers is provided. This repository contains the companion code and supplementary material for our submission to IEEE Robotics and Automation Letters titled "A Hessian for Gaussian Mixture Likelihoods in Nonlinear Least Squares".
Install general requirements using
pip install -r requirements.txt
Initialize navlie submodule using
git submodule update --init
Install the navlie submodule,
pip install -e ./navlie
Install the project library using
pip install -e ./mixtures
Run tests using
cd tests; pytest
This was developed in Python 3.10.1. A virtualenv is recommended.
Please run the corresponding bash script,
cd ./scripts/bash_scripts_paper_results
./run_all.sh
The key functionality of this project is in the gaussian_mixtures.py
file in the
mixtures
library. Errors corresponding to the components are provided to initialize
the Gaussian Mixture factors, which then mix the component errors and Jacobians to provide
the final mixture error and jacobian.
Supplementary material with jacobian derivations is provided in supplementary.pdf
.
If you find this code useful, please consider citing our arxiv submission,
@misc{korotkine2024hessian,
title={A Hessian for Gaussian Mixture Likelihoods in Nonlinear Least Squares},
author={Vassili Korotkine and Mitchell Cohen and James Richard Forbes},
year={2024},
eprint={2404.05452},
archivePrefix={arXiv},
primaryClass={cs.RO}
}
Distributed under the MIT License. See LICENSE.txt
for more information. -->
Vassili Korotkine - @decargroup - vassili.korotkine@mail.mcgill.ca
Project Link: https://github.com/decargroup/hessian_sum_mixtures
- The project is built on top of the navlie library for on-manifold state estimation.
- The project is funded via the Natural Sciences and Engineering Research Council of Canada (NSERC) Alliance Grant in collaboration with Denso Corporation.