The Experts below are selected from a list of 727566 Experts worldwide ranked by ideXlab platform

Kenneth A Bollen - One of the best experts on this subject based on the ideXlab platform.

  • Directlingam a Direct Method for learning a linear non gaussian structural equation model
    Journal of Machine Learning Research, 2011
    Co-Authors: Shohei Shimizu, Takanori Inazumi, Yasuhiro Sogawa, Aapo Hyvarinen, Yoshinobu Kawahara, Takashi Washio, Patrik O Hoyer, Kenneth A Bollen
    Abstract:

    Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, that is, a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional Methods. However, existing estimation Methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new Direct Method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous Methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, that is, if all the model assumptions are met and the sample size is infinite.

  • Directlingam a Direct Method for learning a linear non gaussian structural equation model
    arXiv: Machine Learning, 2011
    Co-Authors: Shohei Shimizu, Takanori Inazumi, Yasuhiro Sogawa, Aapo Hyvarinen, Yoshinobu Kawahara, Takashi Washio, Patrik O Hoyer, Kenneth A Bollen
    Abstract:

    Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, i.e., a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional Methods. However, existing estimation Methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new Direct Method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous Methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.

Y. A. Shamash - One of the best experts on this subject based on the ideXlab platform.

  • Direct Method of Constructing H _2-Suboptimal Controllers: Continuous-Time Systems
    Journal of Optimization Theory and Applications, 1998
    Co-Authors: A. Saberi, P. Sannuti, Y. A. Shamash
    Abstract:

    An H _2-suboptimal control problem is defined and analyzed. Then, an algorithm called H _2-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation Method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a Direct eigenvalue assignment Method to come up with a sequence of H _2-suboptimal state feedback gains. Also, although the sequence of H _2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H _2-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H _2-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The Direct Method of constructing H _2-suboptimal controllers developed here has a number of advantages over the perturbation Method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.

  • Direct Method of Constructing H _2-Suboptimal Controllers: Discrete-Time Systems
    Journal of Optimization Theory and Applications, 1998
    Co-Authors: A. Saberi, P. Sannuti, Y. A. Shamash
    Abstract:

    For discrete-time systems, an H _2-suboptimal control problem is defined and analyzed. Then, an algorithm called H _2-suboptimal state feedback gain sequence (Algorithm A1) is developed. Rather than utilizing a perturbation Method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a Direct eigenvalue assignment Method to come up with a sequence of H _2-suboptimal state feedback gains. Also, although the sequence of H _2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H _2-suboptimal estimator-based measurement feedback controllers. Three different estimator structures (prediction, current, and reduced-order estimators) are considered. For a given H _2-suboptimal state feedback gain, a sequence of estimator gains for any of the three estimators considered can be constructed by merely dualizing Algorithm A1. The Direct Method of constructing H _2-suboptimal controllers developed here has a number of advantages over the perturbation Method, e.g., it has the ability to design all three types of estimator-based controllers while still maintaining throughout the design the computational simplicity of it. This paper is the discrete-time version of Ref. 1. There are some conceptual similarities as well as fundamental differences between the H _2-suboptimal control problems for continuous-time and discrete-time systems. The fundamental differences arise mainly from the fact that, in contrast to continuous-time systems, for discrete-time systems the infimum of the H _2-norm over the class of strictly proper controllers is in general different from the infimum of the H _2-norm over the class of proper controllers.

Shohei Shimizu - One of the best experts on this subject based on the ideXlab platform.

  • Directlingam a Direct Method for learning a linear non gaussian structural equation model
    Journal of Machine Learning Research, 2011
    Co-Authors: Shohei Shimizu, Takanori Inazumi, Yasuhiro Sogawa, Aapo Hyvarinen, Yoshinobu Kawahara, Takashi Washio, Patrik O Hoyer, Kenneth A Bollen
    Abstract:

    Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, that is, a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional Methods. However, existing estimation Methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new Direct Method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous Methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, that is, if all the model assumptions are met and the sample size is infinite.

  • Directlingam a Direct Method for learning a linear non gaussian structural equation model
    arXiv: Machine Learning, 2011
    Co-Authors: Shohei Shimizu, Takanori Inazumi, Yasuhiro Sogawa, Aapo Hyvarinen, Yoshinobu Kawahara, Takashi Washio, Patrik O Hoyer, Kenneth A Bollen
    Abstract:

    Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, i.e., a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional Methods. However, existing estimation Methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new Direct Method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous Methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.

H Q He - One of the best experts on this subject based on the ideXlab platform.

  • a Direct Method to determine the parallel mean free path of solar energetic particles with adiabatic focusing
    The Astrophysical Journal, 2012
    Co-Authors: H Q He
    Abstract:

    The parallel mean free path of solar energetic particles (SEPs), which is determined by physical properties of SEPs as well as those of solar wind, is a very important parameter in space physics to study the transport of charged energetic particles in the heliosphere, especially for space weather forecasting. In space weather practice, it is necessary to find a quick approach to obtain the parallel mean free path of SEPs for a solar event. In addition, the adiabatic focusing effect caused by a spatially varying mean magnetic field in the solar system is important to the transport processes of SEPs. Recently, Shalchi presented an analytical description of the parallel diffusion coefficient with adiabatic focusing. Based on Shalchi's results, in this paper we provide a Direct analytical formula as a function of parameters concerning the physical properties of SEPs and solar wind to Directly and quickly determine the parallel mean free path of SEPs with adiabatic focusing. Since all of the quantities in the analytical formula can be Directly observed by spacecraft, this Direct Method would be a very useful tool in space weather research. As applications of the Direct Method, we investigate the inherent relations between the parallel mean free path and various parameters concerning physical properties of SEPs and solar wind. Comparisons of parallel mean free paths with and without adiabatic focusing are also presented.

A. Saberi - One of the best experts on this subject based on the ideXlab platform.

  • Direct Method of Constructing H _2-Suboptimal Controllers: Continuous-Time Systems
    Journal of Optimization Theory and Applications, 1998
    Co-Authors: A. Saberi, P. Sannuti, Y. A. Shamash
    Abstract:

    An H _2-suboptimal control problem is defined and analyzed. Then, an algorithm called H _2-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation Method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a Direct eigenvalue assignment Method to come up with a sequence of H _2-suboptimal state feedback gains. Also, although the sequence of H _2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H _2-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H _2-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The Direct Method of constructing H _2-suboptimal controllers developed here has a number of advantages over the perturbation Method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.

  • Direct Method of Constructing H _2-Suboptimal Controllers: Discrete-Time Systems
    Journal of Optimization Theory and Applications, 1998
    Co-Authors: A. Saberi, P. Sannuti, Y. A. Shamash
    Abstract:

    For discrete-time systems, an H _2-suboptimal control problem is defined and analyzed. Then, an algorithm called H _2-suboptimal state feedback gain sequence (Algorithm A1) is developed. Rather than utilizing a perturbation Method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a Direct eigenvalue assignment Method to come up with a sequence of H _2-suboptimal state feedback gains. Also, although the sequence of H _2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H _2-suboptimal estimator-based measurement feedback controllers. Three different estimator structures (prediction, current, and reduced-order estimators) are considered. For a given H _2-suboptimal state feedback gain, a sequence of estimator gains for any of the three estimators considered can be constructed by merely dualizing Algorithm A1. The Direct Method of constructing H _2-suboptimal controllers developed here has a number of advantages over the perturbation Method, e.g., it has the ability to design all three types of estimator-based controllers while still maintaining throughout the design the computational simplicity of it. This paper is the discrete-time version of Ref. 1. There are some conceptual similarities as well as fundamental differences between the H _2-suboptimal control problems for continuous-time and discrete-time systems. The fundamental differences arise mainly from the fact that, in contrast to continuous-time systems, for discrete-time systems the infimum of the H _2-norm over the class of strictly proper controllers is in general different from the infimum of the H _2-norm over the class of proper controllers.