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Analysis of incremental augmented affine projection algorithm for distributed estimation of complex-valued signals
This paper considers the problem of distributed estimation in an incremental network when the measurements taken by the node follow a widely linear model. The proposed algorithm which we refer to it as incremental augmented affine projection algorithm (incAAPA) utilizes the full second order statistical information in the complex domain. Moreover, it exploits spatio-temporal diversity to improve the estimation performance. We derive steady-state performance metric of the incAAPA in terms of the mean-square deviation (MSD). We further derive sufficient conditions to ensure mean-square convergence. Our analysis illustrate that the proposed algorithm is able to process both second order circular (proper) and noncircular (improper) signals. The validity of the theoretical results and the good performance of the proposed algorithm are demonstrated by several computer simulations
Distributed Recursive Least-Squares: Stability and Performance Analysis
The recursive least-squares (RLS) algorithm has well-documented merits for
reducing complexity and storage requirements, when it comes to online
estimation of stationary signals as well as for tracking slowly-varying
nonstationary processes. In this paper, a distributed recursive least-squares
(D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless
sensor networks. Distributed iterations are obtained by minimizing a separable
reformulation of the exponentially-weighted least-squares cost, using the
alternating-minimization algorithm. Sensors carry out reduced-complexity tasks
locally, and exchange messages with one-hop neighbors to consent on the
network-wide estimates adaptively. A steady-state mean-square error (MSE)
performance analysis of D-RLS is conducted, by studying a stochastically-driven
`averaged' system that approximates the D-RLS dynamics asymptotically in time.
For sensor observations that are linearly related to the time-invariant
parameter vector sought, the simplifying independence setting assumptions
facilitate deriving accurate closed-form expressions for the MSE steady-state
values. The problems of mean- and MSE-sense stability of D-RLS are also
investigated, and easily-checkable sufficient conditions are derived under
which a steady-state is attained. Without resorting to diminishing step-sizes
which compromise the tracking ability of D-RLS, stability ensures that per
sensor estimates hover inside a ball of finite radius centered at the true
parameter vector, with high-probability, even when inter-sensor communication
links are noisy. Interestingly, computer simulations demonstrate that the
theoretical findings are accurate also in the pragmatic settings whereby
sensors acquire temporally-correlated data.Comment: 30 pages, 4 figures, submitted to IEEE Transactions on Signal
Processin
A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation
Stochastic approximation techniques play an important role in solving many
problems encountered in machine learning or adaptive signal processing. In
these contexts, the statistics of the data are often unknown a priori or their
direct computation is too intensive, and they have thus to be estimated online
from the observed signals. For batch optimization of an objective function
being the sum of a data fidelity term and a penalization (e.g. a sparsity
promoting function), Majorize-Minimize (MM) methods have recently attracted
much interest since they are fast, highly flexible, and effective in ensuring
convergence. The goal of this paper is to show how these methods can be
successfully extended to the case when the data fidelity term corresponds to a
least squares criterion and the cost function is replaced by a sequence of
stochastic approximations of it. In this context, we propose an online version
of an MM subspace algorithm and we study its convergence by using suitable
probabilistic tools. Simulation results illustrate the good practical
performance of the proposed algorithm associated with a memory gradient
subspace, when applied to both non-adaptive and adaptive filter identification
problems
Distributed Diffusion-Based LMS for Node-Specific Adaptive Parameter Estimation
A distributed adaptive algorithm is proposed to solve a node-specific
parameter estimation problem where nodes are interested in estimating
parameters of local interest, parameters of common interest to a subset of
nodes and parameters of global interest to the whole network. To address the
different node-specific parameter estimation problems, this novel algorithm
relies on a diffusion-based implementation of different Least Mean Squares
(LMS) algorithms, each associated with the estimation of a specific set of
local, common or global parameters. Coupled with the estimation of the
different sets of parameters, the implementation of each LMS algorithm is only
undertaken by the nodes of the network interested in a specific set of local,
common or global parameters. The study of convergence in the mean sense reveals
that the proposed algorithm is asymptotically unbiased. Moreover, a
spatial-temporal energy conservation relation is provided to evaluate the
steady-state performance at each node in the mean-square sense. Finally, the
theoretical results and the effectiveness of the proposed technique are
validated through computer simulations in the context of cooperative spectrum
sensing in Cognitive Radio networks.Comment: 13 pages, 6 figure
Mixed Regression via Approximate Message Passing
We study the problem of regression in a generalized linear model (GLM) with
multiple signals and latent variables. This model, which we call a matrix GLM,
covers many widely studied problems in statistical learning, including mixed
linear regression, max-affine regression, and mixture-of-experts. In mixed
linear regression, each observation comes from one of signal vectors
(regressors), but we do not know which one; in max-affine regression, each
observation comes from the maximum of affine functions, each defined via a
different signal vector. The goal in all these problems is to estimate the
signals, and possibly some of the latent variables, from the observations. We
propose a novel approximate message passing (AMP) algorithm for estimation in a
matrix GLM and rigorously characterize its performance in the high-dimensional
limit. This characterization is in terms of a state evolution recursion, which
allows us to precisely compute performance measures such as the asymptotic
mean-squared error. The state evolution characterization can be used to tailor
the AMP algorithm to take advantage of any structural information known about
the signals. Using state evolution, we derive an optimal choice of AMP
`denoising' functions that minimizes the estimation error in each iteration.
The theoretical results are validated by numerical simulations for mixed
linear regression, max-affine regression, and mixture-of-experts. For
max-affine regression, we propose an algorithm that combines AMP with
expectation-maximization to estimate intercepts of the model along with the
signals. The numerical results show that AMP significantly outperforms other
estimators for mixed linear regression and max-affine regression in most
parameter regimes.Comment: 44 pages. A shorter version of this paper will appear in the
proceedings of AISTATS 202
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