Learning Sparse Graphs for Prediction and Filtering of Multivariate Data Processes

TL;DR

This paper introduces a novel, tuning-free method for learning sparse, potentially directed graphs to improve multivariate data prediction and filtering, demonstrating significant performance gains on real-world datasets.

Contribution

The method is computationally efficient, does not require cross-validation, and can handle directed graphs and varying noise levels, advancing graph learning techniques.

Findings

Significant prediction performance improvements on real datasets

Efficient recursive graph learning without parameter tuning

Ability to learn directed and sparse graphs with noise variability

Abstract

We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the graph structure is learned recursively without the need for cross-validation or parameter tuning by building upon a hyperparameter-free framework. Our approach does not require the graph to be undirected and also accommodates varying noise levels across different nodes.Experiments using real-world datasets show that the proposed method offers significant performance gains in prediction, in comparison with the graphs frequently associated with these datasets.