Probabilistic edge inference of gene networks with markov random field-based bayesian learning

Abstract

Current algorithms for gene regulatory network construction based on Gaussian graphical models focuses on the deterministic decision of whether an edge exists. Both the probabilistic inference of edge existence and the relative strength of edges are often overlooked, either because the computational algorithms cannot account for this uncertainty or because it is not straightforward in implementation. In this study, we combine the Bayesian Markov random field and the conditional autoregressive (CAR) model to tackle simultaneously these two tasks. The uncertainty of edge existence and the relative strength of edges can be measured and quantified based on a Bayesian model such as the CAR model and the spike-and-slab lasso prior. In addition, the strength of the edges can be utilized to prioritize the importance of the edges in a network graph. Simulations and a glioblastoma cancer study were carried out to assess the proposed model’s performance and to compare it with existing methods when a binary decision is of interest. The proposed approach shows stable performance and may provide novel structures with biological insights.

A Bayesian approach to differential edges with probabilistic interactions: applications in association and classification

“…The first one is related to the sample size , where can be taken as the integer closest to the ratio of the sample size to the number of nodes The same choice has been considered in Fan and Lv (2008) and Hung et al (2016) in ultrahigh dimensional variable selection problems. The second strategy relates to the sparsity of a single network, which usually ranges between 5% and 10% based on estimates with networks in public databases ( Leclerc 2008 , Huang et al 2022 ). Therefore, it is reasonable to assume the sparsity of D-Net is not larger than these values.…”

“…The hyperparameters in the spike-and-slab prior distributions are set as (spike) and (slab), respectively, to reflect the vague information about . The choice of these parameter values has little effect in the probabilistic inference, as demonstrated in Huang et al (2022) . The prior probability of the existence of a differential edge is set at 0.7 because it has passed the screening procedure.…”

“…Motivated by the application of leveraging quadratic discriminant analysis (QDA) in gene–gene interaction ( Xia et al 2015 ), here we translate the task of identifying the D-Net into the task of detecting interactions in a logistic regression model and consider the Bayesian logistic regression algorithm to conduct the probabilistic inference. The proposed Bayesian approach contains the Spike-and-Slab Lasso prior ( Ročková and George 2018 ) as the prior distribution of the interaction coefficient parameters, if they pass an a priori screening procedure based on sample correlation coefficients ( Huang 2022 , Huang et al 2022 ), and the resulting posterior probabilities are used to infer the candidate set of edges. To the best of our knowledge, the proposed PRobabilistic Interaction for Differential Edge (PRIDE) is the first study that provides probabilistic inference of differential edges.…”