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Entropic Outlier Sparsification (EOS) is proposed as a robust computationalstrategy for the detection of data anomalies in a broad class of learningmethods, including the unsupervised problems (like detection of non-Gaussianoutliers in mostly-Gaussian data) and in the supervised learning withmislabeled data. EOS dwells on the derived analytic closed-form solution of the(weighted) expected error minimization problem subject to the Shannon entropyregularization. In contrast to common regularization strategies requiringcomputational costs that scale polynomial with the data dimension, identifiedclosed-form solution is proven to impose additional iteration costs that dependlinearly on statistics size and are independent of data dimension. Obtainedanalytic results also explain why the mixtures of spherically-symmetricGaussians - used heuristically in many popular data analysis algorithms -represent an optimal choice for the non-parametric probability distributionswhen working with squared Euclidean distances, combining expected errorminimality, maximal entropy/unbiasedness, and a linear cost scaling. Theperformance of EOS is compared to a range of commonly-used tools on syntheticproblems and on partially-mislabeled supervised classification problems frombiomedicine.

Robust learning of data anomalies with analytically-solvable entropic outlier sparsification