# Decentralized Learning of Tree-Structured Gaussian Graphical Models from Noisy Data

arXiv: https://arxiv.org/abs/2109.10642 · HTML: https://mlsanity.com/paper/2109.10642/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 15 of 15)

- [Speeding Up Distributed Machine Learning Using Codes](https://mlsanity.com/paper/1512.02673/) (2015)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Robust Graph Learning from Noisy Data](https://mlsanity.com/paper/1812.06673/) (2018)
- [Learning a Tree-Structured Ising Model in Order to Make Predictions](https://mlsanity.com/paper/1604.06749/) (2016)
- [Distributed Learning over Unreliable Networks](https://mlsanity.com/paper/1810.07766/) (2018)
- [Predictive Learning on Hidden Tree-Structured Ising Models](https://mlsanity.com/paper/1812.04700/) (2018)
- [Robust estimation of tree structured Gaussian Graphical Model](https://mlsanity.com/paper/1901.08770/) (2019)
- [Robust Estimation of Tree Structured Ising Models](https://mlsanity.com/paper/2006.05601/) (2020)
- [Timely Distributed Computation with Stragglers](https://mlsanity.com/paper/1910.03564/) (2019)
- [SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples](https://mlsanity.com/paper/2101.08917/) (2021)
- [Learning of Tree-Structured Gaussian Graphical Models on Distributed Data under Communication Constraints](https://mlsanity.com/paper/1809.08067/) (2018)
- [Exact Asymptotics for Learning Tree-Structured Graphical Models with Side Information: Noiseless and Noisy Samples](https://mlsanity.com/paper/2005.04354/) (2020)
- [Marginal Likelihoods for Distributed Parameter Estimation of Gaussian Graphical Models](https://mlsanity.com/paper/1303.4756/) (2013)
- [Structure Learning of Sparse GGMs over Multiple Access Networks](https://mlsanity.com/paper/1812.10437/) (2018)
- [Learning Data Dependency with Communication Cost](https://mlsanity.com/paper/1804.10942/) (2018)

## Abstract (arXiv)

This paper studies the decentralized learning of tree-structured Gaussian graphical models (GGMs) from noisy data. In decentralized learning, data set is distributed across different machines (sensors), and GGMs are widely used to model complex networks such as gene regulatory networks and social networks. The proposed decentralized learning uses the Chow-Liu algorithm for estimating the tree-structured GGM. In previous works, upper bounds on the probability of incorrect tree structure recovery were given mostly without any practical noise for simplification. While this paper investigates the effects of three common types of noisy channels: Gaussian, Erasure, and binary symmetric channel. For Gaussian channel case, to satisfy the failure probability upper bound δ > 0 in recovering a d-node tree structure, our proposed theorem requires only O(log(fracdδ)) samples for the smallest sample size (n) comparing to the previous literature citeNikolakakis with O(log4(fracdδ)) samples by using the positive correlation coefficient assumption that is used in some important works in the literature. Moreover, the approximately bounded Gaussian random variable assumption does not appear in citeNikolakakis. Given some knowledge about the tree structure, the proposed Algorithmic Bound will achieve obviously better performance with small sample size (e.g., < 2000) comparing with formulaic bounds. Finally, we validate our theoretical results by performing simulations on synthetic data sets.