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5.9 From IC to discovery
Infinitesimal causality supplies a population-level geometric diagnostic. BRIDGE and SKFM, developed in Chapter 11, turn that diagnostic into an estimation and model-selection pipeline. The distinction is important:
Each arrow requires assumptions. Field estimation needs support and regularity. Projection needs stable rank. Interpreting a residual as evidence about latent structure needs a causal model class and an identifiability argument. Selecting a repair needs held-out improvement and uncertainty control.
An IC signal may influence causal structure only when the protocol semantics, visible span, rank and separation conditions, estimation error, and competing non-latent explanations are explicit. Otherwise the correct output is the geometric obstruction itself, accompanied by abstention from a stronger causal claim.
This disciplined boundary is what makes infinitesimal causality useful to LINCS. It gives a precise interaction obstruction while keeping diagnosis, causal interpretation, and repair admission as separate stages.
It also illustrates how the causal lesson enters mainstream learning. The intervention protocol makes the external domain actionable; the LINCS sketch makes the model, estimator, and discovery pipeline actionable. A trustworthy system must record which level was changed. Improving the learner’s structural model is not evidence that the corresponding domain intervention has been identified.