Distributed Splitting-Over-Features Sparse Bayesian Learning with Alternating Direction Method of Multipliers

Abstract

In processing spatially distributed data, multi-agent robotic platforms equipped with sensors and computing capabilities are gaining interest for applications in inhospitable environments. In this work an algorithm for a distributed realization of sparse bayesian learning (SBL) is discussed for learning a static spatial process with the splitting-over-features approach over a network of interconnected agents. The observed process is modeled as a superposition of weighted kernel functions, or features as we call it, centered at the agent's measurement locations. SBL is then used to determine which feature is relevant for representing the spatial process. Using upper bounding convex functions, the SBL parameter estimation is formulated as 1-norm constrained optimization, which is solved distributively using alternating direction method of multipliers (ADMM) and averaged consensus. The performance of the method is demonstrated by processing real magnetic field data collected in a laboratory.

Consensus Based Distributed Sparse Bayesian Learning by Fast Marginal Likelihood Maximization

“…Consequently, the algorithm converges fast while having a fixed communication load on the network. As we will show, using simulations and real data studies, the proposed algorithm performs on par with the centralized versions in terms of normalized mean squared error (NMSE) and parameter sparsity, and outperforms the distributed SBL variant proposed in [18] for homogeneous learning.…”

“…[17], where a distributed estimate is calculated by loopy belief propagation. In [18] another version of a decentralized SBL method is presented, where an ARD version of SBL is implemented. Its key feature is guaranteed convergence.…”

“…The current paper proposes a modification of the algorithm in [18], which instead uses an incremental optimization of the SBL objective function. In essence, we propose a distributed version of the FMLM algorithm [15], [20] for SBL.…”

“…To the best of our knowledge, this is the first distributed implementation of FMLM. In contrast to [18], the proposed method does not require ADMM and is thus free of additional parameters regulating the convergence. Moreover, a network consensus is required only once, before the local computations commence.…”

Advances in Distributed Graph Filtering

“…Besides leading to a simple least squares problem, the design of the CEV FIR filter can also be computed distributively. Given that each node knows the desired filter response and the graph shift operator (i.e., the network structure), it can be shown that by reordering the columns of Ψ and the entries of θ the framework of splitting-over-features [37] can be employed for a decentralized estimation of θ.…”