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Isao Yamada - One of the best experts on this subject based on the ideXlab platform.

  • hierarchical convex optimization by the hybrid Steepest Descent Method with proximal splitting operators enhancements of svm and lasso
    2019
    Co-Authors: Isao Yamada, Masao Yamagishi
    Abstract:

    The breakthrough ideas in the modern proximal splitting Methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In this paper, we present practical algorithmic strategies for the hierarchical convex optimization problems which require further strategic selection of a most desirable vector from the solution set of the standard convex optimization. The proposed algorithms are established by applying the hybrid Steepest Descent Method to special nonexpansive operators designed through the art of proximal splitting. We also present applications of the proposed strategies to certain unexplored hierarchical enhancements of the support vector machine and the Lasso estimator.

  • fejer monotone hybrid Steepest Descent Method for affinely constrained and composite convex minimization tasks
    Optimization, 2018
    Co-Authors: Konstantinos Slavakis, Isao Yamada
    Abstract:

    This paper introduces the Fejer-monotone hybrid Steepest Descent Method (FM-HSDM), a new member to the HSDM family of algorithms, for solving affinely constrained minimization tasks in real Hilbert...

  • poisson image restoration with likelihood constraint via hybrid Steepest Descent Method
    International Conference on Acoustics Speech and Signal Processing, 2013
    Co-Authors: Shunsuke Ono, Isao Yamada
    Abstract:

    This paper proposes a likelihood constrained optimization framework for Poisson image restoration. The likelihood constrained problem considered in this paper is the minimization of convex priors over the level set of the negative-log-likelihood function of the Poisson distribution. It has advantages in parameter selection compared with the minimization of the weighted sum of convex priors and the negative-log-likelihood function, which has been used in conventional Methods. The level set is characterized as the fixed point set of a certain quasi-nonexpansive operator, which enables us to apply the hybrid Steepest Descent Method to solve the constrained problem. The proposed framework not only can handle the level set of any convex function whose subgradient is available but also does not require any computationally-expensive procedure such as operator inversion and inner loop. Illustrative numerical examples are also presented.

  • efficient parallel computation of the stochastic mv pure estimator by the hybrid Steepest Descent Method
    International Conference on Artificial Intelligence and Soft Computing, 2012
    Co-Authors: Tomasz Piotrowski, Isao Yamada
    Abstract:

    In this paper we consider the problem of efficient computation of the stochastic MV-PURE estimator which is a reduced-rank estimator designed for robust linear estimation in ill-conditioned inverse problems. Our motivation for this result stems from the fact that the reduced-rank estimation by the stochastic MV-PURE estimator, while avoiding the problem of regularization parameter selection appearing in a common regularization technique used in inverse problems and machine learning, presents computational challenge due to nonconvexity induced by the rank constraint. To combat this problem, we propose a recursive scheme for computation of the general form of the stochastic MV-PURE estimator which does not require any matrix inversion and utilize the inherently parallel hybrid Steepest Descent Method. We verify efficiency of the proposed scheme in numerical simulations.

  • robust wideband beamforming by the hybrid Steepest Descent Method
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: Konstantinos Slavakis, Isao Yamada
    Abstract:

    This paper uses the hybrid Steepest Descent Method (HSDM) to design robust smart antennas. Several design criteria as well as robustness are mathematically described by a finite collection of closed convex sets in a real Euclidean space. Desirable beamformers are defined as points of the generalized convex feasible set which is well defined even in the case of inconsistent design criteria. A quadratic cost function is formed by the correlations of the incoming data, and the HSDM constructs a point sequence that (strongly) converges to the (unique) minimizer of the cost function over the generalized convex feasible set. Numerical examples validate the proposed design.

Konstantinos Slavakis - One of the best experts on this subject based on the ideXlab platform.

  • the stochastic fejer monotone hybrid Steepest Descent Method and the hierarchical rls
    IEEE Transactions on Signal Processing, 2019
    Co-Authors: Konstantinos Slavakis
    Abstract:

    This paper introduces the stochastic Fejer-monotone hybrid Steepest Descent Method (S-FM-HSDM) to solve affinely constrained and composite convex minimization tasks. The minimization task is not known exactly; noise contaminates the information about the composite loss function and the affine constraints. S-FM-HSDM generates sequences of random variables that, under certain conditions and with respect to a probability space, converge point-wise to solutions of the noiseless minimization task. S-FM-HSDM enjoys desirable attributes of optimization techniques such as splitting of variables and constant step size (learning rate). Furthermore, it provides a novel way of exploiting the information about the affine constraints via fixed-point sets of appropriate nonexpansive mappings. Among the offsprings of S-FM-HSDM, the hierarchical recursive least squares (HRLS) takes advantage of S-FM-HSDM's versatility toward affine constraints and offers a novel twist to LS by generating sequences of estimates that converge to solutions of a hierarchical optimization task: minimize a convex loss over the set of minimizers of the ensemble LS loss. Numerical tests on a sparsity-aware LS task show that HRLS compares favorably to several state-of-the-art convex, as well as non-convex, stochastic-approximation, and online-learning counterparts.

  • fejer monotone hybrid Steepest Descent Method for affinely constrained and composite convex minimization tasks
    Optimization, 2018
    Co-Authors: Konstantinos Slavakis, Isao Yamada
    Abstract:

    This paper introduces the Fejer-monotone hybrid Steepest Descent Method (FM-HSDM), a new member to the HSDM family of algorithms, for solving affinely constrained minimization tasks in real Hilbert...

  • robust wideband beamforming by the hybrid Steepest Descent Method
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: Konstantinos Slavakis, Isao Yamada
    Abstract:

    This paper uses the hybrid Steepest Descent Method (HSDM) to design robust smart antennas. Several design criteria as well as robustness are mathematically described by a finite collection of closed convex sets in a real Euclidean space. Desirable beamformers are defined as points of the generalized convex feasible set which is well defined even in the case of inconsistent design criteria. A quadratic cost function is formed by the correlations of the incoming data, and the HSDM constructs a point sequence that (strongly) converges to the (unique) minimizer of the cost function over the generalized convex feasible set. Numerical examples validate the proposed design.

  • Computation of symmetric positive definite Toeplitz matrices by the hybrid Steepest Descent Method
    Signal Processing, 2003
    Co-Authors: Konstantinos Slavakis, Isao Yamada, Kohichi Sakaniwa
    Abstract:

    This paper studies the problem of finding the nearest symmetric positive definite Toeplitz matrix to a given symmetric one. Additional design constraints, which are also formed as closed convex sets in the real Hilbert space of all symmetric matrices, are imposed on the desired matrix. An algorithmic solution to the problem given by the hybrid Steepest Descent Method is established also in the case of inconsistent design constraints.

  • spectrum estimation of real vector wide sense stationary processes by the hybrid Steepest Descent Method
    International Conference on Acoustics Speech and Signal Processing, 2002
    Co-Authors: Konstantinos Slavakis, Isao Yamada, Kohichi Sakaniwa
    Abstract:

    It is well-known that the unbiased estimate of the covariance matrix of a real vector wide sense stationary process is not necessarily positive semidefinite. By defining the real Hilbert space of all symmetric matrices, the conditions for a symmetric matrix to be positive definite, block Toeplitz, as well as to satisfy other design constraints, are formed as closed convex sets. This paper demonstrates that the problem of approximating the unbiased estimate of the covariance matrix of a real vector wide sense stationary process over the intersection of those closed convex sets in an optimal way can be resolved by the Hybrid Steepest Descent Method. An optimal solution is also provided even when inconsistent constraints are met, i.e., whenever the intersection of the closed convex sets is empty. The numerical results exhibit significant improvement of the proposed Method over the standard estimates of the covariance matrix.

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

G. C. Bento - One of the best experts on this subject based on the ideXlab platform.

Antoine Soubeyran - One of the best experts on this subject based on the ideXlab platform.