  Distributed automatic speech recognition (ASR) requires to aggregate outputs
of distributed deep neural network (DNN)-based models. This work studies the
use of submodular functions to design a rank aggregation on score-based
permutations, which can be used for distributed ASR systems in both supervised
and unsupervised modes. Specifically, we compose an aggregation rank function
based on the Lovasz Bregman divergence for setting up linear structured convex
and nested structured concave functions. The algorithm is based on stochastic
gradient descent (SGD) and can obtain well-trained aggregation models. Our
experiments on the distributed ASR system show that the submodular rank
aggregation can obtain higher speech recognition accuracy than traditional
aggregation methods like Adaboost. Code is available
online~\footnote{https://github.com/uwjunqi/Subrank}.
