Bulk gene expression profiling, which aggregates pooled RNA across cells within a biological sample, remains important in the single-cell era because it is typically less noisy, more sensitive, and more cost-effective than single-cell assays. Accordingly, a growing body of computational methods seeks to recover causal relations among genes from bulk expression data. However, aggregation is a lossy, non-invertible coarsening of the underlying cellular system, and it remains unclear whether and under what conditions causal relations are recoverable from aggregated bulk gene expression data. To answer this, we formalize recoverability under aggregation through two notions of consistency: functional-form consistency and conditional-independence consistency. We then derive necessary and sufficient conditions for recoverability, showing that these properties are preserved only under linear aggregations (e.g., sum/mean) coupled with affine structural equations. To assess the practical plausibility of these conditions, analyses of four bulk and four single-cell gene expression datasets further reveal that the estimated pairwise regulatory functions among genes deviate from linearity in both data types, providing limited empirical support for the linearity assumptions required for recoverability. Together, these results caution against recovering causal relations from aggregated bulk expression data without strong additional assumptions.
Causal Discovery from Heteroscedastic Stochastic Dynamical Systems under Imperfect Physical Models
Department of Mechanical & Industrial Engineering（机械与工业工程系）；Northeastern University（东北大学）；Department of Industrial Engineering and Management Sciences（工业工程与管理科学系）；Department of Mechanical Engineering（机械工程系）；Northwestern University（西北大学）
Causal Learner: A Toolbox for Causal Structure and Markov Blanket Learning
School of Computer Science and Technology, Anhui University（安徽大学计算机科学与技术学院）；School of Computer and Information, Hefei University of Technology（合肥工业大学计算机与信息学院）；UniSA STEM, University of South Australia（南澳大学UniSA STEM）
$\texttt{causalAssembly}$: Generating Realistic Production Data for Benchmarking Causal Discovery
Technical University of Munich（慕尼黑工业大学）；Robert Bosch GmbH（罗伯特·博世有限公司）；University of Applied Sciences Kempten（肯普滕应用科学大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
