**Competing with wild prediction rules.** / Vovk, Vladimir.

Research output: Working paper

Published

**Competing with wild prediction rules.** / Vovk, Vladimir.

Research output: Working paper

Vovk V. Competing with wild prediction rules. 2005 Dec 14.

@techreport{16a4760e03e349828605c3b55c496361,

title = "Competing with wild prediction rules",

abstract = "We consider the problem of on-line prediction competitive with a benchmarkclass of continuous but highly irregular prediction rules. It is known that if the benchmark class is a reproducing kernel Hilbert space, there exists a prediction algorithm whose average loss over the first N examples does not exceed the average loss of any prediction rule in the class plus a {"}regret term{"} of O(N^(-1/2)). The elements of some natural benchmark classes, however, are so irregular that these classes are not Hilbert spaces. In this paper we develop Banach-space methods to construct a prediction algorithm with a regret term of O(N^(-1/p)), where p is in [2,infty) and p-2 reflects the degree to which the benchmark class fails to be a Hilbert space.",

keywords = "cs.LG, I.2.6",

author = "Vladimir Vovk",

note = "28 pages, 3 figures",

year = "2005",

month = dec,

day = "14",

language = "English",

type = "WorkingPaper",

}

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T1 - Competing with wild prediction rules

AU - Vovk, Vladimir

N1 - 28 pages, 3 figures

PY - 2005/12/14

Y1 - 2005/12/14

N2 - We consider the problem of on-line prediction competitive with a benchmarkclass of continuous but highly irregular prediction rules. It is known that if the benchmark class is a reproducing kernel Hilbert space, there exists a prediction algorithm whose average loss over the first N examples does not exceed the average loss of any prediction rule in the class plus a "regret term" of O(N^(-1/2)). The elements of some natural benchmark classes, however, are so irregular that these classes are not Hilbert spaces. In this paper we develop Banach-space methods to construct a prediction algorithm with a regret term of O(N^(-1/p)), where p is in [2,infty) and p-2 reflects the degree to which the benchmark class fails to be a Hilbert space.

AB - We consider the problem of on-line prediction competitive with a benchmarkclass of continuous but highly irregular prediction rules. It is known that if the benchmark class is a reproducing kernel Hilbert space, there exists a prediction algorithm whose average loss over the first N examples does not exceed the average loss of any prediction rule in the class plus a "regret term" of O(N^(-1/2)). The elements of some natural benchmark classes, however, are so irregular that these classes are not Hilbert spaces. In this paper we develop Banach-space methods to construct a prediction algorithm with a regret term of O(N^(-1/p)), where p is in [2,infty) and p-2 reflects the degree to which the benchmark class fails to be a Hilbert space.

KW - cs.LG

KW - I.2.6

M3 - Working paper

BT - Competing with wild prediction rules

ER -