The Experts below are selected from a list of 210156 Experts worldwide ranked by ideXlab platform

Hui Zou - One of the best experts on this subject based on the ideXlab platform.

  • strong oracle optimality of folded concave penalized estimation
    Annals of Statistics, 2014
    Co-Authors: Jianqing Fan, Lingzhou Xue, Hui Zou
    Abstract:

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local Linear Approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local Linear Approximation. In addition, once the oracle estimator is obtained, the local Linear Approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse Linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

  • strong oracle optimality of folded concave penalized estimation
    arXiv: Statistics Theory, 2012
    Co-Authors: Jianqing Fan, Lingzhou Xue, Hui Zou
    Abstract:

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local Linear Approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local Linear Approximation. In addition, once the oracle estimator is obtained, the local Linear Approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, that is, sparse Linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

Marco Storace - One of the best experts on this subject based on the ideXlab platform.

  • Piecewise-Linear Approximation of the Hindmarsh-Rose neuron model
    Journal of Physics: Conference Series, 2008
    Co-Authors: Daniele Linaro, Federico Bizzarri, Marco Storace
    Abstract:

    This paper is concerned with the Approximation of the Hindmarsh and Rose neuron model, which is able to reproduce the main neuronal behaviours, in view of its circuit implementation. The method is based on two main tools: a piecewise-Linear Approximation technique and bifurcation analysis. The piecewise-Linear Approximation of the Hindmarsh and Rose model is obtained by solving a mixed-integer optimization problem by a genetic algorithm. The result obtained exhibits a good degree of similarity to the original model, both from a qualitative and a quantitative standpoint.

  • pwl Approximation of the hindmarsh rose neuron model in view of its circuit implementation
    European Conference on Circuit Theory and Design, 2007
    Co-Authors: Federico Bizzarri, Daniele Linaro, Marco Storace
    Abstract:

    A two-dimensional piecewise-Linear Approximation of the Hindmarsh-Rose neuron model is obtained, in view of its circuit implementation. The obtained Approximation is checked by varying two bifurcation parameters. The brute-force two-dimensional bifurcation diagram of the original model is compared with the one of the piecewise-Linear Approximation, showing that the Approximation is able to reproduce the main qualitative behaviours (quiescency, spiking, bursting, chaotic dynamics) of the original model.

  • piecewise Linear Approximation of nonLinear dynamical systems
    IEEE Transactions on Circuits and Systems I-regular Papers, 2004
    Co-Authors: Marco Storace, O De Feo
    Abstract:

    The piecewise-Linear (PWL) Approximation technique developed by Julia/spl acute/n et al. in the past few years is applied to find approximate models of dynamical systems dependent on given numbers of state variables and parameters. Referring to some significant examples, i.e., topological normal forms, it is shown that a PWL dynamical system approximating a given smooth system can preserve its main features. In particular, if the Approximation accuracy increases, the equivalence between approximating and approximated systems shifts from qualitative to quantitative. The validity of the proposed approach is eventually tested by use of a severe nonLinear example, i.e., the Rosenzweig-MacArthur system, which describes the population dynamics in a tritrophic food chain model.

Jianqing Fan - One of the best experts on this subject based on the ideXlab platform.

  • strong oracle optimality of folded concave penalized estimation
    Annals of Statistics, 2014
    Co-Authors: Jianqing Fan, Lingzhou Xue, Hui Zou
    Abstract:

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local Linear Approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local Linear Approximation. In addition, once the oracle estimator is obtained, the local Linear Approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse Linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

  • strong oracle optimality of folded concave penalized estimation
    arXiv: Statistics Theory, 2012
    Co-Authors: Jianqing Fan, Lingzhou Xue, Hui Zou
    Abstract:

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local Linear Approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local Linear Approximation. In addition, once the oracle estimator is obtained, the local Linear Approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, that is, sparse Linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

Lingzhou Xue - One of the best experts on this subject based on the ideXlab platform.

  • strong oracle optimality of folded concave penalized estimation
    Annals of Statistics, 2014
    Co-Authors: Jianqing Fan, Lingzhou Xue, Hui Zou
    Abstract:

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local Linear Approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local Linear Approximation. In addition, once the oracle estimator is obtained, the local Linear Approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse Linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

  • strong oracle optimality of folded concave penalized estimation
    arXiv: Statistics Theory, 2012
    Co-Authors: Jianqing Fan, Lingzhou Xue, Hui Zou
    Abstract:

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local Linear Approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local Linear Approximation. In addition, once the oracle estimator is obtained, the local Linear Approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, that is, sparse Linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

Marcio Giacomoni - One of the best experts on this subject based on the ideXlab platform.

  • a new derivative free Linear Approximation for solving the network water flow problem with convergence guarantees
    arXiv: Optimization and Control, 2020
    Co-Authors: Shen Wang, Lina Sela, Ahmad F Taha, Marcio Giacomoni, Nikolaos Gatsis
    Abstract:

    Addressing challenges in urban water infrastructure systems including aging infrastructure, supply uncertainty, extreme events, and security threats, depend highly on water distribution networks modeling emphasizing the importance of realistic assumptions, modeling complexities, and scalable solutions. In this study, we propose a derivative-free, Linear Approximation for solving the network water flow problem (WFP). The proposed approach takes advantage of the special form of the nonLinear head loss equations and, after the transformation of variables and constraints, the WFP reduces to a Linear optimization problem that can be efficiently solved by modern Linear solvers. Ultimately, the proposed approach amounts to solving a series of Linear optimization problems. We demonstrate the proposed approach through several case studies and show that the approach can model arbitrary network topologies and various types of valves and pumps, thus providing modeling flexibility. Under mild conditions, we show that the proposed Linear Approximation converges. We provide sensitivity analysis and discuss in detail the current limitations of our approach and suggest solutions to overcome these. All the codes, tested networks, and results are freely available on Github for research reproducibility.

  • state estimation in water distribution networks through a new successive Linear Approximation
    Conference on Decision and Control, 2019
    Co-Authors: Shen Wang, Lina Sela, Ahmad F Taha, Nikolaos Gatsis, Marcio Giacomoni
    Abstract:

    State estimation (SE) of water distribution networks (WDNs) is difficult to solve due to nonLinearity/nonconvexity of water flow models, uncertainties from parameters and demands, lack of redundancy of measurements, and inaccurate flow and pressure measurements. This paper proposes a new, scalable successive Linear Approximation to solve the SE problem in WDNs. The approach amounts to solving either a sequence of Linear or quadratic programs—depending on the operators’ objectives. The proposed successive Linear Approximation offers a seamless way of dealing with valve/pump model nonconvexities, is different than a first order Taylor series Linearization, and can be incorporated into with robust uncertainty modeling. Two simple test-cases are adopted to illustrate the effectiveness of proposed approach using head measurements at select nodes.

  • state estimation in water distribution networks through a new successive Linear Approximation
    arxiv:eess.SY, 2019
    Co-Authors: Shen Wang, Lina Sela, Ahmad F Taha, Nikolaos Gatsis, Marcio Giacomoni
    Abstract:

    State estimation (SE) of water distribution networks (WDNs) is difficult to solve due to nonLinearity/nonconvexity of water flow models, uncertainties from parameters and demands, lack of redundancy of measurements, and inaccurate flow and pressure measurements. This paper proposes a new, scalable successive Linear Approximation to solve the SE problem in WDNs. The approach amounts to solving either a sequence of Linear or quadratic programs---depending on the operators' objectives. The proposed successive Linear Approximation offers a seamless way of dealing with valve/pump model nonconvexities, is different than a first order Taylor series Linearization, and can incorporate with robust uncertainty modeling. Two simple testcases are adopted to illustrate the effectiveness of proposed approach using head measurements at select nodes.