  This paper proposes a distributed version of Determinant Point Processing
(DPP) inference to enhance multi-source data diversification under limited
communication bandwidth. DPP is a popular probabilistic approach that improves
data diversity by enforcing the repulsion of elements in the selected subsets.
The well-studied Maximum A Posteriori (MAP) inference in DPP aims to identify
the subset with the highest diversity quantified by DPP. However, this approach
is limited by the presumption that all data samples are available at one point,
which hinders its applicability to real-world applications such as traffic
datasets where data samples are distributed across sources and communication
between them is band-limited.
  Inspired by the techniques used in Multiple-Input Multiple-Output (MIMO)
communication systems, we propose a strategy for performing MAP inference among
distributed sources. Specifically, we show that a lower bound of the
diversity-maximized distributed sample selection problem can be treated as a
power allocation problem in MIMO systems. A determinant-preserved sparse
representation of selected samples is used to perform sample precoding in local
sources to be processed by DPP. Our method does not require raw data exchange
among sources, but rather a band-limited feedback channel to send lightweight
diversity measures, analogous to the CSI message in MIMO systems, from the
center to data sources. The experiments show that our scalable approach can
outperform baseline methods, including random selection, uninformed individual
DPP with no feedback, and DPP with SVD-based feedback, in both i.i.d and
non-i.i.d setups. Specifically, it achieves 1 to 6 log-difference diversity
gain in the latent representation of CIFAR-10, CIFAR-100, StanfordCars, and
GTSRB datasets.
