Determining the Number of Non-Spurious Arcs in a Learned DAG Model: Investigation of a Bayesian and a Frequentist Approach

TL;DR

This paper compares Bayesian and frequentist methods for estimating the number of true, non-spurious arcs in learned graphical models, with applications to biological data like HIV vaccine design.

Contribution

It introduces both Bayesian and frequentist approaches to quantify non-spurious arcs in learned DAGs, including a novel FDR-based method and empirical validation.

Findings

Both methods accurately estimate true arcs on synthetic data.

The frequentist approach may outperform Bayesian in less representative models.

Application to HIV data demonstrates practical utility.

Abstract

In many application domains, such as computational biology, the goal of graphical model structure learning is to uncover discrete relationships between entities. For example, in our problem of interest concerning HIV vaccine design, we want to infer which HIV peptides interact with which immune system molecules (HLA molecules). For problems of this nature, we are interested in determining the number of nonspurious arcs in a learned graphical model. We describe both a Bayesian and frequentist approach to this problem. In the Bayesian approach, we use the posterior distribution over model structures to compute the expected number of true arcs in a learned model. In the frequentist approach, we develop a method based on the concept of the False Discovery Rate. On synthetic data sets generated from models similar to the ones learned, we find that both the Bayesian and frequentist approaches yield accurate estimates of the number of non-spurious arcs. In addition, we speculate that the frequentist approach, which is non-parametric, may outperform the parametric Bayesian approach in situations where the models learned are less representative of the data. Finally, we apply the frequentist approach to our problem of HIV vaccine design.