Summary and Contributions: Discrete Determinantal Point Processes (DPPs) are probability distributions over subsets of a finite set of (feature) vectors where the probability of each subset is proportional to the volume of the parallelogram that they span. Since these distributions capture the negative correlations between items, they have been extensively employed in subset selection tasks where diversity is preferred. MAP estimation for DPPs is a well-studied problem which formally given a set of vectors and an integer k asks a for a subset of k items with (approximately) highest volume (probability); this objective functions can be translated as the most diverse subset of size k . The problem is shown to be hard. In particular, there is an exponential O(1) k lower bound on the approximation factor in the offline setting. This work studies the MAP estimation for DPPs in a specific streaming setting as follows: Vectors arrive in a stream and upon arrival of any vectors, the algorithm has to decide either store it (permanently) in the memory or erase it.