AGTIC

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.

Info

Language: MATLAB

Platform: MacOS, Linux, Windows

by Baihan Lin, April 2018

Citation

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}
}

Tasks

• Permutation test for different multivariate association patterns

• Permutation test with varying sample sizes

• Permutation test with varying dimensions

• Permutation test with varying additive noises

• Permutation test with interfering relationships in different dimensions

Requirements

• MATLAB

Acknowledgement

• 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.