Corrected score methods for estimating Bayesian networks with error‐prone nodes

Abstract

Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error‐prone data. Two methods for inferring causal relationships between nodes in a network are proposed based on penalized estimation methods that account for measurement error and encourage sparsity. We discuss consistency of the proposed network estimators and develop an approach for selecting the tuning parameter in the penalized estimation methods. Empirical studies are carried out to compare the proposed methods with a naive method that ignores measurement error. Finally, we apply these methods to infer signaling networks using single cell flow cytometry data.

Detecting responsible nodes in differential Bayesian networks

“…In Step 1, we apply the frequentist node‐wise parent selection method proposed in our earlier work 17 to estimate a coefficients matrix that satisfies the acyclic constraint while encouraging sparsity. We then mismatch data with (estimated) graph structures when estimating causal effects again in Step 2 to obtain $$$ {\hat{\mathbf{B}}}^{(1)}\left({\hat{G}}_2\right) $$$ and $$$ {\hat{\mathbf{B}}}^{(2)}\left({\hat{G}}_1\right) $$$, which can (and usually do) differ from the coefficients matrix estimates in Step 1, that is, $$$ {\hat{\mathbf{B}}}^{(1)}\left({\hat{G}}_1\right) $$$ and $$$ {\hat{\mathbf{B}}}^{(2)}\left({\hat{G}}_2\right) $$$.…”

“…Step 1, we apply the frequentist node-wise parent selection method proposed in our earlier work 17 to estimate a coefficients matrix that satisfies the acyclic constraint while encouraging sparsity. We then mismatch data with (estimated) graph structures when estimating causal effects again in Step…”