Semi-parametric Network Structure Discovery Models

TL;DR

This paper introduces a semi-parametric network structure discovery model that combines Gaussian processes with sparsity and weights, enabling flexible, uncertainty-aware network inference from continuous data.

Contribution

It presents a novel model integrating Gaussian processes with network sparsity, along with an efficient inference algorithm and stability analysis, advancing network discovery methods.

Findings

Outperforms previous approaches on three applications

Provides uncertainty quantification in network structure discovery

Demonstrates stability and efficiency of the proposed method

Abstract

We propose a network structure discovery model for continuous observations that generalizes linear causal models by incorporating a Gaussian process (GP) prior on a network-independent component, and random sparsity and weight matrices as the network-dependent parameters. This approach provides flexible modeling of network-independent trends in the observations as well as uncertainty quantification around the discovered network structure. We establish a connection between our model and multi-task GPs and develop an efficient stochastic variational inference algorithm for it. Furthermore, we formally show that our approach is numerically stable and in fact numerically easy to carry out almost everywhere on the support of the random variables involved. Finally, we evaluate our model on three applications, showing that it outperforms previous approaches. We provide a qualitative and quantitative analysis of the structures discovered for domains such as the study of the full genome regulation of the yeast Saccharomyces cerevisiae.