By Robert E. Schapire

ISBN-10: 0262017180

ISBN-13: 9780262017183

Boosting is an method of computer studying in accordance with the belief of constructing a hugely actual predictor through combining many susceptible and misguided "rules of thumb." A remarkably wealthy conception has advanced round boosting, with connections to a variety of subject matters, together with facts, online game thought, convex optimization, and knowledge geometry. Boosting algorithms have additionally loved sensible luck in such fields as biology, imaginative and prescient, and speech processing. At a variety of instances in its historical past, boosting has been perceived as mysterious, debatable, even paradoxical.This ebook, written through the inventors of the strategy, brings jointly, organizes, simplifies, and considerably extends 20 years of study on boosting, featuring either thought and functions in a fashion that's obtainable to readers from varied backgrounds whereas additionally delivering an authoritative reference for complicated researchers. With its introductory therapy of all fabric and its inclusion of workouts in each bankruptcy, the booklet is suitable for path use to boot. The e-book starts off with a normal creation to computing device studying algorithms and their research; then explores the center thought of boosting, in particular its skill to generalize; examines a number of the myriad different theoretical viewpoints that support to provide an explanation for and comprehend boosting; offers sensible extensions of boosting for extra complicated studying difficulties; and at last provides a few complicated theoretical themes. various functions and sensible illustrations are provided all through.

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**Extra info for Boosting: Foundations and Algorithms**

**Sample text**

Then with probability at least 1 − δ, the hypothesis h produced by this algorithm satisfies err(h) ≤ m m−κ err(h) + κ ln m + ln(1/δ) . tex” — 10/1/2012 — 17:41 — page 41 42 2 Foundations of Machine Learning err(h) ≤ κ ln m + ln(1/δ) . m−κ Thus, for such algorithms it is the size κ of the compression scheme that acts as a complexity term. 7 Discussion We have explored three general methods for analyzing learning algorithms. The techniques are closely related, differing primarily in the complexity measure employed.

19) for every h ∈ H that is consistent with S. This theorem gives high-probability bounds on the true error of all consistent hypotheses. 19) states that, with probability at least 1 − δ, err(h) ≤ ε for every h ∈ H that is consistent with S (for values of ε as given in the theorem). In other words, using slightly different phrasing, each bound says that with probability at least 1 − δ, for every h ∈ H, if h is consistent with S, then err(h) ≤ ε. Or, formalizing these results in more precise, mathematical terms, the bounds state that with probability at least 1 − δ, the random variable sup {err(h) | h ∈ H is consistent with S} is at most ε.

Most importantly, such a guarantee of good performance is dependent on the data actually being generated by two normal distributions. 3. There, because the two distributions are far from normal, the threshold between positives and negatives that is found by incorrectly assuming normality ends up being well away from optimal, regardless of how much training data is provided. 1), but we see in this example that an over-dependence on this assumption can yield poor performance. On the other hand, a discriminative approach to this problem in which the best threshold rule is selected based on its training error would be very likely to perform well, since the optimal classifier is a simple threshold here as well.

### Boosting: Foundations and Algorithms by Robert E. Schapire

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