turns out to be possible to construct this separation oracle without knowing the quantity itself. This particular technique has not been as widely employed as the filtering algorithm, but is… Click to show full abstract
turns out to be possible to construct this separation oracle without knowing the quantity itself. This particular technique has not been as widely employed as the filtering algorithm, but is spiritually related to later ideas such as the non-convex analysis of Zhu et al. Since these early papers, researchers have explored a number of algorithmic questions including robust classification and regression, robustness in list-decoding models, sum-of-squares proofs for robustness, and non-convex optimization for robust recovery. The recent work has also moved beyond algorithmic questions to unearth new statistical insights, such as new estimators that work under fairly weak statistical assumptions, connections to minimum distance functionals introduced by Donoho and Liu, and robustness to new forms of corruptions defined by transportation metrics. For those interested in learning more, there are now several tutorials, expositions, and courses on these topics, including the thesis of one of the authors, a related course at University of Washington, and my own lecture notes.
               
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