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We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are in terms of excess losses, the differences between the instantaneous losses suffered by the algorithm and the ones of a given expert. We then demonstrate the interest of these bounds in the context of experts that report their confidences as a number in the interval [0,1] using a generic reduction to the standard setting. We conclude by two other applications in the standard setting, which improve the known bounds in case of small excess losses and show a bounded regret against i.i.d. sequences of losses.
We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on supervised learn
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerat
Establishing a theoretical analysis that explains why deep learning can outperform shallow learning such as kernel methods is one of the biggest issues in the deep learning literature. Towards answering this question, we evaluate excess risk of a dee
We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected based on
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers