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Robust Unsupervised Learning via L-statistic Minimization
Andreas Maurer · Daniela Angela Parletta · Andrea Paudice · Massimiliano Pontil

Wed Jul 21 05:40 PM -- 05:45 PM (PDT) @
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised learning. The key assumption is that the perturbing distribution is characterized by larger losses relative to a given class of admissible models. This is exploited by a general descent algorithm which minimizes an $L$-statistic criterion over the model class, weighting small losses more. Our analysis characterizes the robustness of the method in terms of bounds on the reconstruction error relative to the underlying unperturbed distribution. As a byproduct, we prove uniform convergence bounds with respect to the proposed criterion for several popular models in unsupervised learning, a result which may be of independent interest. Numerical experiments with \textsc{kmeans} clustering and principal subspace analysis demonstrate the effectiveness of our approach.

Author Information

Andreas Maurer
Daniela Angela Parletta (University of Genoa & Istituto Italiano di Tecnologia)
Andrea Paudice (University of Milan & Istituto Italiano di Tecnologia)
Massimiliano Pontil ( Istituto Italiano di Tecnologia & University College London)

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