Semi-parametric Network Structure Discovery Models
This work addresses network structure discovery for researchers in fields like genomics, but it appears incremental as it builds on existing linear causal and Gaussian process models.
The authors tackled the problem of discovering network structures from continuous observations by proposing a semi-parametric model that generalizes linear causal models with Gaussian process priors and random sparsity, enabling flexible trend modeling and uncertainty quantification. They demonstrated that their approach outperforms previous methods in applications like yeast genome regulation analysis, though no specific numerical improvements were provided.
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.