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Code for our paper:
"Adaptive Geo-Topological Independence Criterion"
by Baihan Lin (Columbia), Nikolaus Kriegeskorte (Columbia).
For the latest full paper: https://arxiv.org/abs/1810.02923
All the experimental results can be reproduced using the code in this repository. Feel free to contact me by doerlbh@gmail.com if you have any question about our work.
Abstract
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the variables, promising robust power across scenarios. Building on the distance correlation, we introduce a family of adaptive independence criteria based on nonlinear monotonic transformations of distances. We show that these criteria, like the distance correlation and RKHS-based criteria, provide dependence indicators. We propose a class of adaptive (multi-threshold) test statistics, which form the basis for permutation tests. These tests empirically outperform some of the established tests in average and worst-case statistical sensitivity across a range of univariate and multivariate relationships, offer useful insights to the data and may deserve further exploration.
Note: This repository contains early benchmarking codes that generated our empirical results. We are still cleaning up this repository for easy access and run instructions. Stay tuned.
Language: MATLAB
Platform: MacOS, Linux, Windows
by Baihan Lin, April 2018
If you find this work helpful, please try the models out and cite our works. Thanks!
@article{lin2018adaptive,
title={Adaptive Geo-Topological Independence Criterion},
author={Lin, Baihan and Kriegeskorte, Nikolaus},
journal={arXiv preprint arXiv:1810.02923},
year={2018}
}
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Permutation test for different multivariate association patterns
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Permutation test with varying sample sizes
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Permutation test with varying dimensions
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Permutation test with varying additive noises
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Permutation test with interfering relationships in different dimensions
- MATLAB
- This code repository borrows existing MATLAB functions and scripts from many helpful sources. We thank their contributions and don't own the copy right for those functions.
About
Code for our paper: "Adaptive Geo-Topological Independence Criterion".