Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed proportionate recursive least squares (PRLS) algorithm for sparse system identification, we propose to introduce the proportionate updating (PU) mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC (CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination of two PRMCC filters. For PRMCC, its stability condition and mean-square performance were analyzed. Based on the analysis, optimal parameter selection in nonstationary environments was obtained. Performance study of CPRMCC was also provided and showed that the CPRMCC performs at least as well as the better component PRMCC filter in steady state. Numerical simulations of sparse system identification corroborate the advantage of proposed algorithms as well as the validity of theoretical analysis

Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it also helps alleviate the effects of stochastic gradient noise and measurement noise through a continuous learning process. We analyze the mean-square-error performance of the algorithm in some detail, including its transient and steady-state behavior. We also apply the diffusion algorithm to two problems: distributed estimation with sparse parameters and distributed localization. Compared to well-studied incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are robust to node and link failure. Diffusion methods also endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving such dynamic cost functions with moving targets are common in the context of biological networks.Comment: 34 pages, 6 figures, to appear in IEEE Transactions on Signal Processing, 201

Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The combination weights that are used by the nodes to fuse information from their neighbors play a critical role in influencing the adaptation and tracking abilities of the network. This paper first investigates the mean-square performance of general adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges, quantization errors, and model non-stationarities. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution in a distinct way, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weights. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory.Comment: 36 pages, 7 figures, to appear in IEEE Transactions on Signal Processing, June 201