  The deluge of networked data motivates the development of algorithms for
computation- and communication-efficient information processing. In this
context, three data-adaptive censoring strategies are introduced to
considerably reduce the computation and communication overhead of decentralized
recursive least-squares (D-RLS) solvers. The first relies on alternating
minimization and the stochastic Newton iteration to minimize a network-wide
cost, which discards observations with small innovations. In the resultant
algorithm, each node performs local data-adaptive censoring to reduce
computations, while exchanging its local estimate with neighbors so as to
consent on a network-wide solution. The communication cost is further reduced
by the second strategy, which prevents a node from transmitting its local
estimate to neighbors when the innovation it induces to incoming data is
minimal. In the third strategy, not only transmitting, but also receiving
estimates from neighbors is prohibited when data-adaptive censoring is in
effect. For all strategies, a simple criterion is provided for selecting the
threshold of innovation to reach a prescribed average data reduction. The novel
censoring-based (C)D-RLS algorithms are proved convergent to the optimal
argument in the mean-square deviation sense. Numerical experiments validate the
effectiveness of the proposed algorithms in reducing computation and
communication overhead.
