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We consider decision making in a Markovian setup where the reward parameters are not known in advance. Our performance criterion is the gap between the performance of the best strategy that is chosen after the true parameter realization is revealed and the performance of the strategy that is chosen before the parameter realization is revealed. We call this gap the parametric regret. We consider two...
We consider the dimensionality-reduction problem for a contaminated data set in a very high dimensional space, i.e., the problem of finding a subspace approximation of observed data, where the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some outlying observations. We propose a High-dimension Robust Principal Component Analysis...
We consider two widely used notions in machine learning, namely: sparsity and algorithmic stability. Both notions are deemed desirable in designing algorithms, and are believed to lead to good generalization ability. In this paper, we show that these two notions contradict each other. That is, a sparse algorithm can not be stable and vice versa. Thus, one has to tradeoff sparsity and stability in...
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