Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a different node, and a limited number of gradient oracle calls is allowed at each node. In this framework, we introduce a convex optimization algorithm based on the stochastic gradient descent (SGD) updates. Particularly, we use a carefully designed time-dependent weighted averaging of the SGD iterates, which yields a convergence rate of $O\left(\frac{N\sqrt{N}}{T}\right)$ after $T$ gradient updates for each node on a network of $N$ nodes. We then show that after $T$ gradient oracle calls, the average SGD iterate achieves a mean square deviation (MSD) of $O\left(\frac{\sqrt{N}}{T}\right)$. This rate of convergence is optimal as it matches the performance lower bound up to constant terms. Similar to the SGD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SGD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets and widely studied network topologies

Efficient fetal-maternal ECG signal separation from two channel maternal abdominal ECG via diffusion-based channel selection

There is a need for affordable, widely deployable maternal-fetal ECG monitors to improve maternal and fetal health during pregnancy and delivery. Based on the diffusion-based channel selection, here we present the mathematical formalism and clinical validation of an algorithm capable of accurate separation of maternal and fetal ECG from a two channel signal acquired over maternal abdomen

Distributed Clustering and Learning Over Networks

Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this work, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and mis-detection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.Comment: 47 pages, 6 figure