  Data summarization has become a valuable tool in understanding even terabytes
of data. Due to their compelling theoretical properties, submodular functions
have been in the focus of summarization algorithms. These algorithms offer
worst-case approximations guarantees to the expense of higher computation and
memory requirements. However, many practical applications do not fall under
this worst-case, but are usually much more well-behaved. In this paper, we
propose a new submodular function maximization algorithm called ThreeSieves,
which ignores the worst-case, but delivers a good solution in high probability.
It selects the most informative items from a data-stream on the fly and
maintains a provable performance on a fixed memory budget. In an extensive
evaluation, we compare our method against $6$ other methods on $8$ different
datasets with and without concept drift. We show that our algorithm outperforms
current state-of-the-art algorithms and, at the same time, uses fewer
resources. Last, we highlight a real-world use-case of our algorithm for data
summarization in gamma-ray astronomy. We make our code publicly available at
https://github.com/sbuschjaeger/SubmodularStreamingMaximization.
