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Nonparametric Estimation using Influence Functions

This is a Matlab Implementation of our Nonparametric Estimators using Influence Functions. For more details, read our paper on Arxiv: http://arxiv.org/abs/1411.4342

Functionals & Features

• Currently, our implementation covers the following functionals, Entropies: Shannon Entropy, Conditional Shannon Entropy Mutual Informations: Shannon MI, Conditional Shannon MI Divergences: Chi-squared, Hellinger, KL Divergence, Tsallis, Renyi, Conditional KL, Conditional Tsallis
• In addition to the estimators, we also produce asymptotic confidence intervals for the estimators.
• Since all estimators are nonparametric, they work well only in under 4-6 dimensions depending on the problem.

Installation and Getting Started

• Run ifSetup.m with the path to the installation as the argument. This adds all subdirectories to the matlab workspace and you are good to go.
• To get started, see the demos directory. demos.m illustrates a very simple use case.
• demo1.m ... demo4.m illustrate all functionals in different settings. We re
• See parseCommonParams for setting of hyperparameters. We recommend using the default settings unless you are very familiar with the paper.

Citation

If you use this library in your academic work please cite our paper: "Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations", Kirthevasan Kandasamy, Akshay Krishnamurthy, Barnabas Poczos, Larry Wasserman, James Robins.

License

This software is released under GNU GPL v3(>=) License. Please read LICENSE.txt for more information.

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

"Copyright 2015 Kirthevasan Kandasamy"

Acknowledgements

We thank Zoltán Szabó from UCL for pointing out some bugs in a previous version of this software.

• Some of the above estimators also appear in the ITE toolbox: https://bitbucket.org/szzoli/ite/
• For questions/ bug reports please email [email protected]