Estimating conditional mutual information for discrete-continuous mixtures using multi-dimensional adaptive histograms

12Citations
Citations of this article
11Readers
Mendeley users who have this article in their library.

Abstract

Estimating conditional mutual information (CMI) is an essential yet challenging step in many machine learning and data mining tasks. Estimating CMI from data that contains both discrete and continuous variables, or even discrete-continuous mixture variables, is a particularly hard problem. In this paper, we show that CMI for such mixture variables, defined based on the Radon-Nikodym derivate, can be written as a sum of entropies, just like CMI for purely discrete or continuous data. Further, we show that CMI can be consistently estimated for discrete-continuous mixture variables by learning an adaptive histogram model. In practice, we estimate such a model by iteratively discretizing the continuous data points in the mixture variables. To evaluate the performance of our estimator, we benchmark it against state-of-the-art CMI estimators as well as evaluate it in a causal discovery setting.

Cite

CITATION STYLE

APA

Marx, A., Yang, L., & van Leeuwen, M. (2021). Estimating conditional mutual information for discrete-continuous mixtures using multi-dimensional adaptive histograms. In SIAM International Conference on Data Mining, SDM 2021 (pp. 387–395). Siam Society. https://doi.org/10.1137/1.9781611976700.44

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free