  In this paper, we introduce adversarially robust streaming algorithms for
central machine learning and algorithmic tasks, such as regression and
clustering, as well as their more general counterparts, subspace embedding,
low-rank approximation, and coreset construction. For regression and other
numerical linear algebra related tasks, we consider the row arrival streaming
model. Our results are based on a simple, but powerful, observation that many
importance sampling-based algorithms give rise to adversarial robustness which
is in contrast to sketching based algorithms, which are very prevalent in the
streaming literature but suffer from adversarial attacks. In addition, we show
that the well-known merge and reduce paradigm in streaming is adversarially
robust. Since the merge and reduce paradigm allows coreset constructions in the
streaming setting, we thus obtain robust algorithms for $k$-means, $k$-median,
$k$-center, Bregman clustering, projective clustering, principal component
analysis (PCA) and non-negative matrix factorization. To the best of our
knowledge, these are the first adversarially robust results for these problems
yet require no new algorithmic implementations. Finally, we empirically confirm
the robustness of our algorithms on various adversarial attacks and demonstrate
that by contrast, some common existing algorithms are not robust.
  (Abstract shortened to meet arXiv limits)
