<p>I think the proper reference is:</p>

<pre><code>@article{Dudley1967290,
    Author = {R.M Dudley},
    Doi = {http://dx.doi.org/10.1016/0022-1236(67)90017-1},
    Issn = {0022-1236},
    Journal = {Journal of Functional Analysis},
    Number = {3},
    Pages = {290 - 330},
    Title = {The sizes of compact subsets of Hilbert space and continuity of Gaussian processes},
    Url = {http://www.sciencedirect.com/science/article/pii/0022123667900171},
    Volume = {1},
    Year = {1967},
    Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0022123667900171},
    Bdsk-Url-2 = {http://dx.doi.org/10.1016/0022-1236(67)90017-1}}
</code></pre>

<p>See Theorem 3.1. for the relevant result, although stated in terms of continuity of Gaussian processes.</p>

CC BY-SA 3.0
2014-01-05T22:08:01.137Z
2014-01-05T22:08:01.137Z
Sasho Nikolov
<p>Dudley's chaining integral is commonly used to bound <a href="http://en.wikipedia.org/wiki/Rademacher_complexity" rel="nofollow">Rademacher complexities</a>. 
I recall seeing several papers give this as the reference</p>

<pre><code>@ARTICLE{MR512411,
  author = {Dudley, R. M.},
  title = {Central limit theorems for empirical measures},
  journal = {Ann. Probab.},
  year = {1978},
  volume = {6},
  pages = {899--929 (1979)},
  number = {6},
  coden = {APBYAE},
  fjournal = {The Annals of Probability},
  issn = {0091-1798},
  mrclass = {60F05 (28C20 60B10 60F17)},
  mrnumber = {MR512411 (81k:60029a)},
  mrreviewer = {P. R{\'e}v{\'e}sz}
}
</code></pre>

<p>but I don't think the result in question actually appears in that paper. 
Could anyone point me to the definitive reference?</p>

<reference-request><machine-learning><lg.learning>
Reference for Dudley's chaining integral
Aryeh
# Reference for Dudley's chaining integral

(Asked by: username_0 on 2014-01-05)

Dudley's chaining integral is commonly used to bound Rademacher complexities. 
I recall seeing several papers give this as the reference
@ARTICLE{MR512411,
  author = {Dudley, R. M.},
  title = {Central limit theorems for empirical measures},
  journal = {Ann. Probab.},
  year = {1978},
  volume = {6},
  pages = {899--929 (1979)},
  number = {6},
  coden = {APBYAE},
  fjournal = {The Annals of Probability},
  issn = {0091-1798},
  mrclass = {60F05 (28C20 60B10 60F17)},
  mrnumber = {MR512411 (81k:60029a)},
  mrreviewer = {P. R{\'e}v{\'e}sz}
}

but I don't think the result in question actually appears in that paper. 
Could anyone point me to the definitive reference?

**Tags:** reference-request, machine-learning, lg.learning


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## 1 answers

### Answer by username_1 on 2014-01-05. Score: 4 | Accepted answer

I think the proper reference is:
@article{Dudley1967290,
    Author = {R.M Dudley},
    Doi = {http://dx.doi.org/10.1016/0022-1236(67)90017-1},
    Issn = {0022-1236},
    Journal = {Journal of Functional Analysis},
    Number = {3},
    Pages = {290 - 330},
    Title = {The sizes of compact subsets of Hilbert space and continuity of Gaussian processes},
    Url = {http://www.sciencedirect.com/science/article/pii/0022123667900171},
    Volume = {1},
    Year = {1967},
    Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0022123667900171},
    Bdsk-Url-2 = {http://dx.doi.org/10.1016/0022-1236(67)90017-1}}

See Theorem 3.1. for the relevant result, although stated in terms of continuity of Gaussian processes.


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