  Maximizing a monotone submodular function is a fundamental task in machine
learning. In this paper, we study the deletion robust version of the problem
under the classic matroids constraint. Here the goal is to extract a small size
summary of the dataset that contains a high value independent set even after an
adversary deleted some elements. We present constant-factor approximation
algorithms, whose space complexity depends on the rank $k$ of the matroid and
the number $d$ of deleted elements. In the centralized setting we present a
$(3.582+O(\varepsilon))$-approximation algorithm with summary size $O(k +
\frac{d \log k}{\varepsilon^2})$. In the streaming setting we provide a
$(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory
$O(k + \frac{d \log k}{\varepsilon^2})$. We complement our theoretical results
with an in-depth experimental analysis showing the effectiveness of our
algorithms on real-world datasets.
