A result of Vapnik with applications: Discrete applied mathematics 47 (1993) 207–217
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ELSEVIER DISCRETE APPLIED Discrete Applied Mathematics 52 (1994) 211 MATHEMATICS Erratum A result of Vapnik with applications Discrete Applied Mathematics 47 (1993) 207-217 Martin Anthony”,“, John Shawe-Taylorb “Department of Mathematics, London School of Economics, Houghton Street, London WCZA ZAE, UK bDepartment of Computer Science, Royal Holloway, University of London, Egham, Surrey TWZOX OEX, UK The proof offered of Theorem 2.1 of [2] is incorrect. The correct proof should follow that given in [l], as follows. With the notation as in [2], one first observes that @(z) v2”(R) < max __ rs.sm InI ’ where O(z) = I{z~/i: TZER}~. Fix ZESTY, and let Ai, Rt for 1 < i < t be as in [2]. Noting that SZE R if and only if rz E R’ for some i between 1 and t, one has O(z) < xi= 1 O’(z). The result follows on bounding O’(z) as in [2]. References Cl] M. Anthony, Uniform convergence and learnability, Ph.D. Thesis, University of London (1991). [2] M. Anthony and J. Shawe-Taylor, A result of Vapnik with applications, Discrete Appl. Math. 47 (1993) 207-217. *Corresponding author. 0166-218X/94/$07.00 0 1994-Elsevier Science B.V. All rights reserved SSDI 0166-218X(94)00025-9
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Transcript of A result of Vapnik with applications: Discrete applied mathematics 47 (1993) 207–217
ELSEVIER
DISCRETE APPLIED
Discrete Applied Mathematics 52 (1994) 211
MATHEMATICS
Erratum
A result of Vapnik with applications
Discrete Applied Mathematics 47 (1993) 207-217
Martin Anthony”,“, John Shawe-Taylorb
“Department of Mathematics, London School of Economics, Houghton Street, London WCZA ZAE, UK
bDepartment of Computer Science, Royal Holloway, University of London, Egham, Surrey TWZOX OEX, UK
The proof offered of Theorem 2.1 of [2] is incorrect. The correct proof should follow
that given in [l], as follows. With the notation as in [2], one first observes that
@(z) v2”(R) < max __ rs.sm InI ’
where O(z) = I{z~/i: TZER}~. Fix ZESTY, and let Ai, Rt for 1 < i < t be as in [2].
Noting that SZE R if and only if rz E R’ for some i between 1 and t, one has
O(z) < xi= 1 O’(z). The result follows on bounding O’(z) as in [2].
References
Cl] M. Anthony, Uniform convergence and learnability, Ph.D. Thesis, University of London (1991).
[2] M. Anthony and J. Shawe-Taylor, A result of Vapnik with applications, Discrete Appl. Math. 47 (1993) 207-217.
*Corresponding author.
0166-218X/94/$07.00 0 1994-Elsevier Science B.V. All rights reserved SSDI 0166-218X(94)00025-9
