In classification, every confidence predictor that is valid under IID data can be transformed into a conformal predictor with an explicit, constant-free bound on the loss of efficiency.
Relations between randomness deficiencies
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abstract
The notion of random sequence was introduced by Martin-Loef in 1966. At the same time he defined the so-called randomness deficiency function that shows how close are random sequences to non-random (in some natural sense). Other deficiency functions can be obtained from the Levin-Schnorr theorem, that describes randomness in terms of Kolmogorov complexity. The difference between all of these deficiencies is bounded by a logarithmic term. In this paper we show that the difference between some deficiencies can be as large as possible.
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Randomness, exchangeability, and conformal prediction
In classification, every confidence predictor that is valid under IID data can be transformed into a conformal predictor with an explicit, constant-free bound on the loss of efficiency.