By Alexander Gammerman, Zhiyuan Luo, Jesús Vega, Vladimir Vovk
This ebook constitutes the refereed complaints 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 subject matters on conception of conformal prediction; purposes of conformal prediction; and desktop learning.
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Am. Stat. Assoc. 102, 359–378 (2007) 5. : Evolved decision trees as conformal predictors. G. ) Proceedings of the 2013 IEEE Conference on Evolutionary Computation, vol. 1, pp. 794–1801. Cancun, Mexico (2013) 6. : Handwritten digit recognition with a back-propagation network. S. ) Advances in Neural Information Processing Systems 2, pp. 396–404. Morgan Kaufmann, San Francisco, CA (1990) 7. : Testing Statistical Hypotheses, 2nd edn. Springer, New York (1986) 8. : Distribution free prediction sets.
The individual test examples, and so in this introductory section we only discuss the former. This section assumes that the reader knows the basic deﬁnitions of the theory of conformal prediction, but they will be given in Sect. 2, which can be consulted now. , , p. 96; introduced in ). This criterion does not depend on the choice of a signiﬁcance level . – Whether the prediction is a singleton (the ideal case), multiple (an ineﬃcient prediction), or empty (a supereﬃcient prediction) at a given signiﬁcance level .
1), (6) 44 V. Vovk and D. Pavlovic where a is a binary string (starting from 1) and the number of 1 s in the 1, . . , 1 is k − 1 ∈ N0 (this sentence is the deﬁnition of a = a(n) and k = k(n) in terms of n). If the binary representation of n does not contain any 0s, a and k are undeﬁned, and we set Un := ∅. Otherwise, set Un := LkA , where A ∈ N is the number whose binary representation is a. In other words, U consists of the components of Lk , k ∈ N; namely, Lk1 is placed in U as U3×2k−1 −1 and then Lk2 , Lk3 , .