Conformal function
A one-dimensional function that maps high-dimensional data to conformal scores. The pushforward distribution of this function determines the validity of the conformal test martingale and the size of its blind spots.
Timeline (last 90 days)
The conformal test martingale (CTM) is a special case of the e-process, in which a conformal function A maps each data point to a conformal score and computes a conformal p-value, which are then combined into an e-process for sequential testing.
Any distribution shift that keeps the pushforward distribution P∘A⁻¹ unchanged leaves the distribution of the conformal p-values unchanged, and is thus invisible to all CTMs based on the conformal function A.
This blind spot is not due to insufficient statistical power but is a fundamental limitation determined by the definition of the conformal function.
The paper formalizes the blind spot via the A-equivalence class [P]_A: all distributions that have the same pushforward distribution as P under A form an equivalence class.
When the conformal function A is the Neyman-Pearson likelihood ratio, the secret component vanishes, the A-equivalence class degenerates to a single point or an extremely restricted set, and the CTM's blind spot is minimized.
In practical applications, one should try to choose a conformal function that retains more discriminative information, or combine multiple conformal functions to build a composite test, in order to reduce the blind spot.
All Facts (6)
The conformal test martingale (CTM) is a special case of the e-process, in which a conformal function A maps each data point to a conformal score and computes a conformal p-value, which are then combined into an e-process for sequential testing.
50%UnverifiedAny distribution shift that keeps the pushforward distribution P∘A⁻¹ unchanged leaves the distribution of the conformal p-values unchanged, and is thus invisible to all CTMs based on the conformal function A.
50%UnverifiedThis blind spot is not due to insufficient statistical power but is a fundamental limitation determined by the definition of the conformal function.
50%UnverifiedThe paper formalizes the blind spot via the A-equivalence class [P]_A: all distributions that have the same pushforward distribution as P under A form an equivalence class.
50%UnverifiedWhen the conformal function A is the Neyman-Pearson likelihood ratio, the secret component vanishes, the A-equivalence class degenerates to a single point or an extremely restricted set, and the CTM's blind spot is minimized.
50%UnverifiedIn practical applications, one should try to choose a conformal function that retains more discriminative information, or combine multiple conformal functions to build a composite test, in order to reduce the blind spot.
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