Research map / Probabilistic and scientific modeling / Causal discovery
On the Recoverability of Causal Relations from Bulk Gene Expression Data
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Formalizes when causal relations among genes remain recoverable from aggregated bulk expression, proving functional-form and conditional-independence consistency hold only under linear aggregation with affine structural equations, and finds pairwise gene functions are largely nonlinear in bulk and single-cell data.
Problem
Whether causal relations among genes inferred from aggregated bulk gene expression (sum/mean over cells) remain consistent with the underlying cell-level causal structure, and under what conditions this recoverability holds.
Approach
Defines functional-form and conditional-independence consistency under aggregation, proves necessary and sufficient conditions showing that only linear aggregation with affine structural equations (ANM/PNL) and linear Gaussian-type fork structures preserve them, and tests pairwise linearity empirically with GAM edf and affine-deviation scores.
Key results
- Synthetic experiments: precision of ANM recovery drops from 1.000 (raw) to 0.830 (agg) under linear mean aggregation with linear causal relations, and to 0.613 under median aggregation.
- Under nonlinear causal mechanisms with linear mean aggregation, ANM precision falls to 0.450 after aggregation.
- Real bulk and single-cell analyses find most gene pairs have low inverse-edf and affine-deviation linearity scores, indicating weak pairwise linearity.
Surprising findings
- Single-cell data show even less apparent linearity than bulk data, contrary to the expectation that bulk aggregation would smooth nonlinearity.
Limitations
- Does not provide a practical algorithm for recovering causal relations from bulk data; additional information is needed.
- Theoretical results cover only linear aggregation; conditions for nonlinear aggregation remain unclear.
- Empirical linearity diagnostics are indirect proxies and do not establish recoverability directly since ground-truth networks are unknown.
Experimental setup
Datasets: GSE39582 GSE20142 GSE57945 GSE245006 Adamson Norman Srivatsan Tian
Benchmarks: GSE39582 GSE20142 GSE57945 GSE245006 Adamson Norman Srivatsan Tian
Metrics: precision inverse edf affine-deviation score
Builds on: additive noise model post-nonlinear model PC algorithm DESeq2 Gemma
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