Information-Geometric Blind Spots of Conformal Test Martingales
Conformal test martingales (CTMs) are e-processes for sequentially testing exchangeability via p-values produced by a conformity function $A$. However, any distribution shift that preserves the push-forward $P\circ A^{-1}$ leaves the p-value distribution invariant, rendering it invisible to every CTM based on $A$. We formalise this blind spot through the \emph{$A$-equivalence class} $[P]_A$ and show that, for any target distribution $T$, there is a unique closest element $Q^\ast\in[P]_A$ in KL divergence---the \emph{$A$-cryptic I-projection}---with explicit density $q^\ast(z) = t(z)\,p_S(A(z))/t_S(A(z))$ and a Pythagorean decomposition into detectable and cryptic components. When $A$ is t...
| Authors | Johan Hallberg Szabadváry |
|---|---|
| Primary category | stat.ML |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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