Conformal and Probabilistic Prediction with Applications: by Alexander Gammerman, Zhiyuan Luo, Jesús Vega, Vladimir Vovk

By Alexander Gammerman, Zhiyuan Luo, Jesús Vega, Vladimir Vovk

This publication constitutes the refereed court cases of the fifth foreign Symposium on Conformal and Probabilistic Prediction with purposes, COPA 2016, held in Madrid, Spain, in April 2016.

The 14 revised complete papers awarded including 1 invited paper have been conscientiously reviewed and chosen from 23 submissions and canopy themes on thought of conformal prediction; purposes of conformal prediction; and computing device learning.

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8) Proof. Follow the proof of Lemma 1 replacing the “code” (0, 1, . . , 1) for Lk in (6) by any prefix-free description of Lk (with its bits written in the reverse order). Then the modification Lk≤N ⊆ U≤2k +1 −1+2k (N −1) of (7) with k := K(Lk ) implies that (8) holds for some universal prediction system, which, when combined with the statement of Lemma 1, implies that (8) holds for our chosen universal prediction system U. This is a corollary for laws of nature: Corollary 1. There is a constant C such that, for any law of nature L, the universal prediction system U satisfies L ⊆ U≤C2K(L) .

In the rest of this paper we will omit “weak” in “weak prediction system”. The most basic way of using a prediction system L for making a prediction in situation s = (σ, x) is as follows. Decide on the maximum number N of errors you are willing to make. Ignore all Ln apart from L1 , . . , LN in L, so that the prediction set in situation s is / Ln } . ΠLN (s) := {y ∈ 2 | ∀n ∈ {1, . . , N } : (s, y) ∈ Notice that this way we are guaranteed to make at most N mistakes: making a mistake eliminates at least one law in the list {L1 , .

Conformal Prediction for Reliable Machine Learning: Theory, Adaptations, and Applications, Chap. 1, pp. 3–19. uk/ Abstract. The paper presents an application of Conformal Predictors to a chemoinformatics problem of identifying activities of chemical compounds. The paper addresses some specific challenges of this domain: a large number of compounds (training examples), high-dimensionality of feature space, sparseness and a strong class imbalance. A variant of conformal predictors called Inductive Mondrian Conformal Predictor is applied to deal with these challenges.

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