Conformal Prediction for Distribution-to-Distribution Regression

The paper introduces a new conformal prediction framework for Distribution-to-Distribution Regression, addressing limitations of naive Split Conformal Prediction which produces non-interpretable sets. By operating in an orthogonal basis space, the method yields interpretable prediction sets while maintaining coverage guarantees. An adaptive variant achieving asymptotic conditional coverage is also presented, with empirical validation on synthetic and real-world data.

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