Efficient learning of marginal distributions from noisy and noiseless observations. Model: Tree-structured Ising model.
Last revision: Dec 2019 (Matlab R2019b) Author: Konstantinos Nikolakakis
The purpose of this code is to support the (JMLR) paper: "Predictive Learning on Hidden Tree-Structured Ising Models" by Konstantinos E. Nikolakakis, Dionysios S. Kalogerias, Anand D. Sarwate.
Any part of this code used in your work should cite the above publication. This code is provided "as is" to support the ideals of reproducible research. Any issues with this code should be reported by email to k.nikolakakis@rutgers.edu.
The code is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License available at https://creativecommons.org/licenses/by-nc-sa/4.0/.
Description: Predictive_Learning.m generates a tree-structured Ising model (over p nodes) and samples based on that model. Structure estimation is performed on the original and noisy data of the underlying model. Noise is generated by a Binary symmetric channel. The goal is to accurately estimate the marginal distributions of the model. First, we compute the estimated distribution from noisy data, then the code estimates the average error of "small-set Total Variation" (accurace on the pairwise marginals) and the probability of the estimated distribution to exceed a predefined positive number γ>0 (for instance γ=0.03). Results: 3D plot of the "ssTV" see Average_ssTV.pdf, a 3D plot for the error probability in Error_probability.pdf. Finally, the heat map (Heat_map.pdf) shows that our theoretical bounds are consistent and tight (the red lines represents what our theory suggests for the sufficient number of samples).
Requires: UndirectedMaximumSpanningTree.m by Guangdi Li (2009). Maximum Weight Spanning tree (Undirected), MATLAB Central File Exchange. Revised by Konstantinos Nikolakakis (2019).