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Sparsity-aware estimation of nonlinear Volterra kernels

Sparsity-aware estimation of nonlinear Volterra kernels,10.1109/CAMSAP.2009.5413323,Vassilis Kekatos,Daniele Angelosante,Georgios B. Giannakis

Sparsity-aware estimation of nonlinear Volterra kernels   (Citations: 3)
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The Volterra series expansion has well-documented merits for modeling smooth nonlinear systems. Given that nature itself is parsimonious and models with minimal degrees of freedom are attractive from a system identification viewpoint, estimating sparse Volterra models is of paramount importance. Based on input-output data, existing estimators of Volterra kernels are sparsity agnostic because they rely on standard (possibly recursive) least-squares approaches. Instead, the present contribution develops batch and recursive algorithms for estimating sparse Volterra kernels using the least-absolute shrinkage and selection operator (Lasso) along with its recent weighted and online variants. Analysis and simulations demonstrate that weighted (recursive) Lasso has the potential to obviate the ¿curse of dimensionality,¿ especially in the under-determined case where input-output data are less than the number of unknowns dictated by the order of the expansion and the memory of the kernels.
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    • ...Part of the results of this work was presented at CAMSAP, Aruba, Dutch Antilles, December 2009 [15]...
    • ...Sparse Volterra channel estimators are proposed in [15] and [17]...
    • ...2 After our conference precursor [15], we became aware of a recent result in [18], which relates to Lemma 3. The differences are: i) only the th-order term in expansion (33) is considered in [18]; and ii) inputs adhere to the binary { 1} alphabet in [18], as opposed to the ternary one in Lemma 3. Fig. 1. MSE of (a) batch and (b) adaptive Volterra estimators...

    Vassilis Kekatoset al. Sparse Volterra and Polynomial Regression Models: Recoverability and E...

    • ...Future research will focus on linear interdependencies with memory as well as non-linear interdependencies using sparse Volterra models along the lines of [8]...

    Daniele Angelosanteet al. Sparse graphical modeling of piecewise-stationary time series

    • ...Confined to the area of system identification, [4] exploits the sparsity of the Volterra series of a nonlinear system, and applies the least absolute shrinkage and selection operator (LASSO) for nonlinear system identification...

    Wei Shiet al. Sparsity-enhanced linear time-invariant MIMO system identification

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