DAG trend filtering for genomic denoising via higher-order Bayesian networks and DAG shrinkage processes.

Graph-based denoising is a critical preprocessing step for analyzing noisy data, particularly in genomic applications where gene regulatory networks exhibit inherent directional dependencies. This paper introduces a directed acyclic graph trend filtering (GTF) framework that leverages novel higher-order Bayesian networks and graphical shrinkage processes to enhance local adaptivity in signal smoothing along the directed edges of a graph. Unlike traditional GTF, which is based on undirected graphs, the proposed method explicitly respects the directional structure of graphs, improving interpretability and accuracy in capturing dependencies. We employ a Hamiltonian Monte Carlo algorithm for efficient posterior inference. Through simulations and genomic applications, the proposed method outperforms a state-of-the-art GTF algorithm in terms of mean squared error reduction and signal-to-noise ratio improvement, demonstrating its utility in recovering true signals while accounting for meaningful structural information.