Skip to main content
    • Aa
    • Aa

Valid Generalisation from Approximate Interpolation

  • Martin Anthony (a1), Peter Bartlett (a2), Yuval Ishai (a3) and John Shawe-Taylor (a4)

Let and be sets of functions from domain X to ℝ. We say that validly generalises from approximate interpolation if and only if for each η > 0 and ∈, δ ∈ (0,1) there is m0(η, ∈, δ) such that for any function t and any probability distribution on X, if m > m0 then with m-probability at least 1 – δ, a sample X = (x1, X2,…,xm) ∈ Xm satisfies

We find conditions that are necessary and sufficient for to validly generalise from approximate interpolation, and we obtain bounds on the sample length m0{η,∈,δ) in terms of various parameters describing the expressive power of .

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] L. G. Valiant (1984) A theory of the learnable. Comm. ACM 27(11) 11341142.

[2] A. Blumer , A. Ehrenfeucht , D. Haussler and M. K. Warmuth (1989) Learnability and the Vapnik-Chervonenkis dimension. J. ACM 36(4) 929965.

[5] D. Haussler (1992) Decision theoretic generalizations of the PAC model for neural net and other learning applications Information and Computation 100 78150.

[7] P. L. Bartlett , P. M. Long and R. C. Williamson (1994) Fat-shattering and the learnability of real-valued functions. Proceedings 7th Annual ACM Conference on Computational Learning Theory. ACM Press. (J. Computer and System Sciences. To appear.)

[8] E. D. Sontag (1992) Feedforward nets for interpolation and classification. J. Computer and System Sciences 45 2048.

[12] V. N. Vapnik and A. Ya. Chervonenkis (1971) On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications 16(2) 264280.

[20] D. Angluin and L. Valiant (1979) Fast probabilistic algorithms for Hamiltonian circuits and matchings. J. Computer and System Sciences 18 155193.

[21] B. K. Natarajan (1989) On learning sets and functions. Machine Learning 4 6797.

[22] M. Anthony and J. Shawe-Taylor (1993) A result of Vapnik with applications. Discrete Appl. Math. 47 207217.

[23] S. Ben-David , N. Cesa-Bianchi , D. Haussler and P. Long (1992) Characterizations of learnability for classes of {0,...,n}-valued functions. J. Computer and System Sciences 50 7486.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 3 *
Loading metrics...

Abstract views

Total abstract views: 21 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 30th May 2017. This data will be updated every 24 hours.