Faithfulness assumption

The faithfulness assumption is the central premise of constraint-based causal discovery: it states that the conditional independencies observed in data reflect genuine structural absences of edges in the underlying causal graph, rather than accidental parameter cancellations that happen to produce independence. Without faithfulness, the PC algorithm would eliminate edges that are truly present but whose effects coincidentally cancel, and it would retain edges that are truly absent but whose spurious correlations survive conditioning. Faithfulness is what makes causal discovery possible — and what makes it fragile.

The assumption fails systematically in systems near phase transitions, where long-range correlations create conditional independencies that have no corresponding missing edges. It fails when hidden confounders generate patterns of conditional independence that mimic direct causal relationships. And it fails whenever the true data-generating process contains parameter symmetries — conservation laws, equilibrium constraints, or functional dependencies — that induce statistical independence without structural independence. The Causal Markov condition says that structure implies probability; faithfulness says that probability implies structure. The first is a theorem; the second is a bet, and it is a bet that nature does not always honor.