19,240 research outputs found
Compressive Diffusion Strategies Over Distributed Networks for Reduced Communication Load
We study the compressive diffusion strategies over distributed networks based
on the diffusion implementation and adaptive extraction of the information from
the compressed diffusion data. We demonstrate that one can achieve a comparable
performance with the full information exchange configurations, even if the
diffused information is compressed into a scalar or a single bit. To this end,
we provide a complete performance analysis for the compressive diffusion
strategies. We analyze the transient, steady-state and tracking performance of
the configurations in which the diffused data is compressed into a scalar or a
single-bit. We propose a new adaptive combination method improving the
convergence performance of the compressive diffusion strategies further. In the
new method, we introduce one more freedom-of-dimension in the combination
matrix and adapt it by using the conventional mixture approach in order to
enhance the convergence performance for any possible combination rule used for
the full diffusion configuration. We demonstrate that our theoretical analysis
closely follow the ensemble averaged results in our simulations. We provide
numerical examples showing the improved convergence performance with the new
adaptive combination method.Comment: Submitted to IEEE Transactions on Signal Processin
Single Bit and Reduced Dimension Diffusion Strategies Over Distributed Networks
We introduce novel diffusion based adaptive estimation strategies for
distributed networks that have significantly less communication load and
achieve comparable performance to the full information exchange configurations.
After local estimates of the desired data is produced in each node, a single
bit of information (or a reduced dimensional data vector) is generated using
certain random projections of the local estimates. This newly generated data is
diffused and then used in neighboring nodes to recover the original full
information. We provide the complete state-space description and the mean
stability analysis of our algorithms.Comment: Submitted to the IEEE Signal Processing Letter
A Multitask Diffusion Strategy with Optimized Inter-Cluster Cooperation
We consider a multitask estimation problem where nodes in a network are
divided into several connected clusters, with each cluster performing a
least-mean-squares estimation of a different random parameter vector. Inspired
by the adapt-then-combine diffusion strategy, we propose a multitask diffusion
strategy whose mean stability can be ensured whenever individual nodes are
stable in the mean, regardless of the inter-cluster cooperation weights. In
addition, the proposed strategy is able to achieve an asymptotically unbiased
estimation, when the parameters have same mean. We also develop an
inter-cluster cooperation weights selection scheme that allows each node in the
network to locally optimize its inter-cluster cooperation weights. Numerical
results demonstrate that our approach leads to a lower average steady-state
network mean-square deviation, compared with using weights selected by various
other commonly adopted methods in the literature.Comment: 30 pages, 8 figures, submitted to IEEE Journal of Selected Topics in
Signal Processin
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
Performance Limits of Stochastic Sub-Gradient Learning, Part II: Multi-Agent Case
The analysis in Part I revealed interesting properties for subgradient
learning algorithms in the context of stochastic optimization when gradient
noise is present. These algorithms are used when the risk functions are
non-smooth and involve non-differentiable components. They have been long
recognized as being slow converging methods. However, it was revealed in Part I
that the rate of convergence becomes linear for stochastic optimization
problems, with the error iterate converging at an exponential rate
to within an neighborhood of the optimizer, for some and small step-size . The conclusion was established under weaker
assumptions than the prior literature and, moreover, several important problems
(such as LASSO, SVM, and Total Variation) were shown to satisfy these weaker
assumptions automatically (but not the previously used conditions from the
literature). These results revealed that sub-gradient learning methods have
more favorable behavior than originally thought when used to enable continuous
adaptation and learning. The results of Part I were exclusive to single-agent
adaptation. The purpose of the current Part II is to examine the implications
of these discoveries when a collection of networked agents employs subgradient
learning as their cooperative mechanism. The analysis will show that, despite
the coupled dynamics that arises in a networked scenario, the agents are still
able to attain linear convergence in the stochastic case; they are also able to
reach agreement within of the optimizer
Performance Limits of Stochastic Sub-Gradient Learning, Part II: Multi-Agent Case
The analysis in Part I revealed interesting properties for subgradient
learning algorithms in the context of stochastic optimization when gradient
noise is present. These algorithms are used when the risk functions are
non-smooth and involve non-differentiable components. They have been long
recognized as being slow converging methods. However, it was revealed in Part I
that the rate of convergence becomes linear for stochastic optimization
problems, with the error iterate converging at an exponential rate
to within an neighborhood of the optimizer, for some and small step-size . The conclusion was established under weaker
assumptions than the prior literature and, moreover, several important problems
(such as LASSO, SVM, and Total Variation) were shown to satisfy these weaker
assumptions automatically (but not the previously used conditions from the
literature). These results revealed that sub-gradient learning methods have
more favorable behavior than originally thought when used to enable continuous
adaptation and learning. The results of Part I were exclusive to single-agent
adaptation. The purpose of the current Part II is to examine the implications
of these discoveries when a collection of networked agents employs subgradient
learning as their cooperative mechanism. The analysis will show that, despite
the coupled dynamics that arises in a networked scenario, the agents are still
able to attain linear convergence in the stochastic case; they are also able to
reach agreement within of the optimizer
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