Active Learning for Undirected Graphical Model Selection
This addresses the challenge of efficiently estimating statistical relationships in graphical models for data analysis, representing an incremental improvement over passive methods.
The paper tackles the problem of graphical model selection by proposing an active learning algorithm that adapts measurements based on prior information, proving it requires fewer measurements than passive methods under certain conditions, with numerical results validating these benefits.
This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all the measurements to have been collected before processing begins. We propose an active learning algorithm that uses junction tree representations to adapt future measurements based on the information gathered from prior measurements. We prove that, under certain conditions, our active learning algorithm requires fewer scalar measurements than any passive algorithm to reliably estimate a graph. A range of numerical results validate our theory and demonstrates the benefits of active learning.