The Experts below are selected from a list of 170772 Experts worldwide ranked by ideXlab platform
Tengyuan Liang - One of the best experts on this subject based on the ideXlab platform.
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statistical inference for the population landscape via moment adjusted stochastic gradients
2019Co-Authors: Tengyuan LiangAbstract:Modern statistical inference tasks often require iterative optimization methods to compute the Solution. Convergence analysis from an optimization viewpoint informs us only how well the Solution is approximated numerically but overlooks the sampling nature of the data. In contrast, recognizing the randomness in the data, statisticians are keen to provide uncertainty quantification, or confidence, for the Solution obtained by using iterative optimization methods. The paper makes progress along this direction by introducing moment‐adjusted stochastic gradient descent: a new stochastic optimization method for statistical inference. We establish non‐asymptotic theory that characterizes the statistical distribution for certain iterative methods with optimization guarantees. On the statistical front, the theory allows for model misspecification, with very mild conditions on the data. For optimization, the theory is flexible for both convex and non‐convex cases. Remarkably, the moment adjusting idea motivated from ‘error standardization’ in statistics achieves a similar effect to acceleration in first‐order optimization methods that are used to fit generalized linear models. We also demonstrate this acceleration effect in the non‐convex setting through numerical experiments.
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statistical inference for the population landscape via moment adjusted stochastic gradients
2017Co-Authors: Tengyuan LiangAbstract:Modern statistical inference tasks often require iterative optimization methods to approximate the Solution. Convergence analysis from optimization only tells us how well we are approximating the Solution deterministically, but overlooks the sampling nature of the data. However, due to the randomness in the data, statisticians are keen to provide uncertainty quantification, or confidence, for the answer obtained after certain steps of optimization. Therefore, it is important yet challenging to understand the sampling distribution of the iterative optimization methods. This paper makes some progress along this direction by introducing a new stochastic optimization method for statistical inference, the moment adjusted stochastic gradient descent. We establish non-asymptotic theory that characterizes the statistical distribution of the iterative methods, with good optimization guarantee. On the statistical front, the theory allows for model misspecification, with very mild conditions on the data. For optimization, the theory is flexible for both the convex and non-convex cases. Remarkably, the moment adjusting idea motivated from "error standardization" in statistics achieves similar effect as Nesterov's acceleration in optimization, for certain convex problems as in fitting generalized linear models. We also demonstrate this acceleration effect in the non-convex setting through experiments.
K Sarabandi - One of the best experts on this subject based on the ideXlab platform.
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simulation of near ground long distance radiowave propagation over terrain using nystrom method with phase extraction technique and fmm acceleration
2009Co-Authors: Dahan Liao, K SarabandiAbstract:A 2D surface integral equation-based NystrOumlm solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described. As forward scattering is the dominant mechanism for the near-ground wave propagation scenario, the associated rapidly-varying phase components of the integral equation kernel and Solution unknowns are deduced and isolated in advance and subsequently built into the solver. It is shown that by applying this method, when combining with an adaptive surface segmentation routine, as few as one to two average unknowns per wavelength is adequate in obtaining accurate Solutions. This significantly reduces the memory storage and computational expense for the simulation of long-distance propagation effects. The efficiency of this method is further improved by incorporating it into the framework of the fast multipole scheme. The full details of the algorithm are discussed, along with performance comparisons of the new solver to a regular NystrOumlm solver for terrain surfaces in terms of Solution Convergence.
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simulation of near ground long distance radiowave propagation over terrain using nystrom method with phase extraction technique and fmm acceleration
2008Co-Authors: Dahan Liao, K SarabandiAbstract:Propagation of radiowaves over complex irregular terrain profiles at near-grazing angles is studied using an efficient numerical solver. In supporting signal coverage prediction for such specialized systems in which the transmitter and receiver are in extreme proximity to the ground, available studies have been limited to the dependence upon site-specific, empirical-based models. The usefulness of these models is restricted as they cannot be applied to general radio configurations and propagation environments. Propagation over irregular terrain surfaces remains to be a challenging open problem demanding ongoing analysis; the unique properties of near-earth propagation such as surface wave propagation, non-plane wave propagation, and higher order reflection and diffraction phenomena pose additional constraints that often beset the validity of classical analytical ray tracing and physical optics techniques and their heuristic extensions. As such, when improved Solution accuracy is required, full-wave simulation routines, despite their computational inefficiency, are employed to assess near-earth propagation parameters. A new 2D surface integral equation-based Nystrom solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described. As forward scattering is the dominant mechanism at the near-ground region, the associated rapidly-varying phase components of the integral equation kernel and Solution unknowns are deduced and isolated in advance and subsequently built into the solver. It is shown that by applying this method, as few as one to two average unknowns per wavelength is adequate in obtaining accurate Solutions. This significantly reduces the memory storage and computational expense for the simulation of long-distance propagation effects. The efficiency of this method is further improved by incorporating it into the framework of the fast multipole method (FMM). The full details of the algorithm are discussed; Solution Convergence comparisons with the regular Nystrom solver for terrain surfaces are also presented.
J Peraire - One of the best experts on this subject based on the ideXlab platform.
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unstructured grid finite element methods for fluid mechanics
1998Co-Authors: K Morgan, J PeraireAbstract:The development of unstructured grid-based, finite-element methods for the simulation of fluid flows is reviewed. The review concentrates on Solution techniques for the compressible Euler and Navier-Stokes equations, employing methods which are based upon a Galerkin discretization in space together with an appropriate finite-difference representation in time. It is assumed that unstructured assemblies of triangles are used to achieve the spatial discretization in two dimensions, with unstructured assemblies of tetrahedra employed in the three-dimensional case. Adaptive grid procedures are discussed and methods for accelerating the iterative Solution Convergence are considered. The areas of incompressible flow modelling and optimization are also included.
Dahan Liao - One of the best experts on this subject based on the ideXlab platform.
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simulation of near ground long distance radiowave propagation over terrain using nystrom method with phase extraction technique and fmm acceleration
2009Co-Authors: Dahan Liao, K SarabandiAbstract:A 2D surface integral equation-based NystrOumlm solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described. As forward scattering is the dominant mechanism for the near-ground wave propagation scenario, the associated rapidly-varying phase components of the integral equation kernel and Solution unknowns are deduced and isolated in advance and subsequently built into the solver. It is shown that by applying this method, when combining with an adaptive surface segmentation routine, as few as one to two average unknowns per wavelength is adequate in obtaining accurate Solutions. This significantly reduces the memory storage and computational expense for the simulation of long-distance propagation effects. The efficiency of this method is further improved by incorporating it into the framework of the fast multipole scheme. The full details of the algorithm are discussed, along with performance comparisons of the new solver to a regular NystrOumlm solver for terrain surfaces in terms of Solution Convergence.
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simulation of near ground long distance radiowave propagation over terrain using nystrom method with phase extraction technique and fmm acceleration
2008Co-Authors: Dahan Liao, K SarabandiAbstract:Propagation of radiowaves over complex irregular terrain profiles at near-grazing angles is studied using an efficient numerical solver. In supporting signal coverage prediction for such specialized systems in which the transmitter and receiver are in extreme proximity to the ground, available studies have been limited to the dependence upon site-specific, empirical-based models. The usefulness of these models is restricted as they cannot be applied to general radio configurations and propagation environments. Propagation over irregular terrain surfaces remains to be a challenging open problem demanding ongoing analysis; the unique properties of near-earth propagation such as surface wave propagation, non-plane wave propagation, and higher order reflection and diffraction phenomena pose additional constraints that often beset the validity of classical analytical ray tracing and physical optics techniques and their heuristic extensions. As such, when improved Solution accuracy is required, full-wave simulation routines, despite their computational inefficiency, are employed to assess near-earth propagation parameters. A new 2D surface integral equation-based Nystrom solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described. As forward scattering is the dominant mechanism at the near-ground region, the associated rapidly-varying phase components of the integral equation kernel and Solution unknowns are deduced and isolated in advance and subsequently built into the solver. It is shown that by applying this method, as few as one to two average unknowns per wavelength is adequate in obtaining accurate Solutions. This significantly reduces the memory storage and computational expense for the simulation of long-distance propagation effects. The efficiency of this method is further improved by incorporating it into the framework of the fast multipole method (FMM). The full details of the algorithm are discussed; Solution Convergence comparisons with the regular Nystrom solver for terrain surfaces are also presented.
K Morgan - One of the best experts on this subject based on the ideXlab platform.
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unstructured grid finite element methods for fluid mechanics
1998Co-Authors: K Morgan, J PeraireAbstract:The development of unstructured grid-based, finite-element methods for the simulation of fluid flows is reviewed. The review concentrates on Solution techniques for the compressible Euler and Navier-Stokes equations, employing methods which are based upon a Galerkin discretization in space together with an appropriate finite-difference representation in time. It is assumed that unstructured assemblies of triangles are used to achieve the spatial discretization in two dimensions, with unstructured assemblies of tetrahedra employed in the three-dimensional case. Adaptive grid procedures are discussed and methods for accelerating the iterative Solution Convergence are considered. The areas of incompressible flow modelling and optimization are also included.