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2009

Empirical Bernstein Bounds and Sample Variance Penalization

Maurer, Andreas, Pontil, Massimiliano

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We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size n.

The bounds lead us to consider sample variance penalization, a novel learning method which takes into account the empirical variance of the loss function.
We give conditions under which sample variance penalization is effective.
In particular, we present a bound on the excess risk incurred by the method.

Empirical Bernstein Bounds and Sample Variance Penalization · Around

Built on

Probability inequalities for sums of bounded random variables
W. Hoeffding · 1963
Earlier work this paper cites.
Relating data compression and learnability
N. Littlestone and M. K. Warmuth · 1986
Earlier work this paper cites.
The Nature of Statistical Learning Theory
V. Vapnik · 1995
Earlier work this paper cites.

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