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Normalized Online Learning     Normalized  Online Learning       2013/6/17
We introduce online learning algorithms which are independent of feature scales, proving regret bounds dependent on the ratio of scales existent in the data rather than the absolute scale. This has se...
Let ${X_k, kgeqslant 1}$ be a stationary Gaussian sequence with partial maximum $M_n=max{X_{k},1leqslant kleqslant n}$ and sample mean $overline{X}_n=sum_{k=1}^{n}X_{k}/n$. Suppose that some of the ra...
We investigate the invariance principle for set-indexed partial sums of a stationary field (X ) d of martingale-di?erence or independent random variables kk-Z under standard normalization or self-norm...
Christian Houdre has kindly pointed us to a paper by A. Fuks, A. Joffe and J. Teugels, where their Theorem 5.3 is our Proposition 3 in the case 0
We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize...
We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize...
In a non-parametric framework, we establish some non-asymptotic bounds for self-normalized sums and quadratic forms in the multivariate case for symmetric and general random variables. This bounds are...
We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pe˜na. The keystone is the introduction of a new notion of random variable heav...

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