  We envision AI marketplaces to be platforms where consumers, with very less
data for a target task, can obtain a relevant model by accessing many private
data sources with vast number of data samples. One of the key challenges is to
construct a training dataset that matches a target task without compromising on
privacy of the data sources. To this end, we consider the following distributed
data summarizataion problem. Given K private source datasets denoted by
$[D_i]_{i\in [K]}$ and a small target validation set $D_v$, which may involve a
considerable covariate shift with respect to the sources, compute a summary
dataset $D_s\subseteq \bigcup_{i\in [K]} D_i$ such that its statistical
distance from the validation dataset $D_v$ is minimized. We use the popular
Maximum Mean Discrepancy as the measure of statistical distance. The
non-private problem has received considerable attention in prior art, for
example in prototype selection (Kim et al., NIPS 2016). Our work is the first
to obtain strong differential privacy guarantees while ensuring the quality
guarantees of the non-private version. We study this problem in a Parsimonious
Curator Privacy Model, where a trusted curator coordinates the summarization
process while minimizing the amount of private information accessed. Our
central result is a novel protocol that (a) ensures the curator accesses at
most $O(K^{\frac{1}{3}}|D_s| + |D_v|)$ points (b) has formal privacy guarantees
on the leakage of information between the data owners and (c) closely matches
the best known non-private greedy algorithm. Our protocol uses two hash
functions, one inspired by the Rahimi-Recht random features method and the
second leverages state of the art differential privacy mechanisms. We introduce
a novel "noiseless" differentially private auctioning protocol for winner
notification and demonstrate the efficacy of our protocol using real-world
datasets.
