The Experts below are selected from a list of 3012 Experts worldwide ranked by ideXlab platform
Sri A Ranga - One of the best experts on this subject based on the ideXlab platform.
-
rii type recurrence generalized eigenvalue problem and orthogonal polynomials on the unit circle
Linear Algebra and its Applications, 2019Co-Authors: Mourad E H Ismail, Sri A RangaAbstract:Abstract We consider a sequence of polynomials { P n } n ≥ 0 satisfying a special R I I type recurrence relation where the zeros of P n are simple and lie on the real line. It turns out that the polynomial P n , for any n ≥ 2 , is the characteristic polynomial of a simple n × n generalized eigenvalue problem. It is shown that with this R I I type recurrence relation one can always associate a positive measure on the unit circle. The Orthogonality Property satisfied by P n with respect to this measure is also obtained. Finally, examples are given to justify the results.
-
a class of orthogonal functions given by a three term recurrence formula
IEEE Communications Magazine, 2015Co-Authors: Cleonice F Bracciali, J H Mccabe, Teresa E Perez, Sri A RangaAbstract:The main goal in this manuscript is to present a class of functions satisfying a certain Orthogonality Property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to the class of symmetric orthogonal polynomials on $[-1,1]$, has a complete connection to the orthogonal polynomials on the unit circle. Quadrature rules and other properties based on the zeros of these functions are also considered.
Hongseok Namkoong - One of the best experts on this subject based on the ideXlab platform.
-
robust causal inference under covariate shift via worst case subpopulation treatment effects
arXiv: Machine Learning, 2020Co-Authors: Sookyo Jeong, Hongseok NamkoongAbstract:We propose the worst-case treatment effect (WTE) across all subpopulations of a given size, a conservative notion of topline treatment effect. Compared to the average treatment effect (ATE), whose validity relies on the covariate distribution of collected data, WTE is robust to unanticipated covariate shifts, and positive findings guarantee uniformly valid treatment effects over subpopulations. We develop a semiparametrically efficient estimator for the WTE, leveraging machine learning-based estimates of the heterogeneous treatment effect and propensity score. By virtue of satisfying a key (Neyman) Orthogonality Property, our estimator enjoys central limit behavior---oracle rates with true nuisance parameters---even when estimates of nuisance parameters converge at slower rates. For both randomized trials and observational studies, we establish a semiparametric efficiency bound, proving that our estimator achieves the optimal asymptotic variance. On real datasets where robustness to covariate shift is of core concern, we illustrate the non-robustness of ATE under even mild distributional shift, and demonstrate that the WTE guards against brittle findings that are invalidated by unanticipated covariate shifts.
-
robust causal inference under covariate shift via worst case subpopulation treatment effects
2020Co-Authors: Sookyo Jeong, Hongseok NamkoongAbstract:We propose the worst-case treatment effect (WTE) across all subpopulations of a given size, a conservative notion of topline treatment effect. Compared to the average treatment effect (ATE) that solely relies on the covariate distribution of collected data, WTE is robust to unanticipated covariate shifts, and ensures positive findings guarantee uniformly valid treatment effects over underrepresented minority groups. We develop a semiparametrically efficient estimator for the WTE, leveraging machine learning-based estimates of heterogenous treatment effects and propensity scores. By virtue of satisfying a key (Neyman) Orthogonality Property, our estimator enjoys central limit behavior---oracle rates with true nuisance parameters---even when estimates of nuisance parameters converge at slower rates. For both observational and randomized studies, we prove that our estimator achieves the optimal asymptotic variance, by establishing a semiparametric efficiency lower bound. On real datasets where robustness to covariate shift is of core concern, we illustrate the non-robustness of ATE under even mild distributional shift, and demonstrate that the WTE guards against brittle findings that are invalidated by unanticipated covariate shifts.
S. M. A. Salehin - One of the best experts on this subject based on the ideXlab platform.
-
J Sign Process Syst DOI 10.1007/s11265-009-0435-3 Localizing Lung Sounds: Eigen Basis Decomposition for Localizing Sources Within a Circular Array of Sensors
2014Co-Authors: S. M. A. SalehinAbstract:Abstract Lung disorders or injury can result in changes in the production of lung sounds both spectrally and regionally. Localizing these lung sounds can provide information to the extent and location of the disorder. Difference in arrival times at a set of sensors and triangulation were previously proposed for acoustic imaging of the chest. We propose two algorithms for acoustic imaging using a set of eigen basis functions of the Helmholtz wave equation. These algorithms remove the sensor location contribution from the multi sensor recordings using either an Orthogonality Property or a least squares based estimation after which a spatial minimum variance (MV) spectrum is applied to estimate the source locations. The use of these eigen basis functions allows possible extension to a lung sound model consisting of layered cylindrical media. Theoretical analysis of the relationship of resolution to frequency and noise power was derived and simulations verified the results obtained. Further, a Nyquist’s criteria for localizing sources within a circular array shows that the radius of region where sources can be localized is inversely proportional to the frequency of sound.The resolution analysis and modified Nyquist criteria can be used for determining the number of sensors required at a given noise level, for a required resolution, frequenc
-
Localizing Lung Sounds: Eigen Basis Decomposition for Localizing Sources Within a Circular Array of Sensors
Journal of Signal Processing Systems, 2011Co-Authors: S. M. A. Salehin, Thushara D. AbhayapalaAbstract:Lung disorders or injury can result in changes in the production of lung sounds both spectrally and regionally. Localizing these lung sounds can provide information to the extent and location of the disorder. Difference in arrival times at a set of sensors and triangulation were previously proposed for acoustic imaging of the chest. We propose two algorithms for acoustic imaging using a set of eigen basis functions of the Helmholtz wave equation. These algorithms remove the sensor location contribution from the multi sensor recordings using either an Orthogonality Property or a least squares based estimation after which a spatial minimum variance (MV) spectrum is applied to estimate the source locations. The use of these eigen basis functions allows possible extension to a lung sound model consisting of layered cylindrical media. Theoretical analysis of the relationship of resolution to frequency and noise power was derived and simulations verified the results obtained. Further, a Nyquist’s criteria for localizing sources within a circular array shows that the radius of region where sources can be localized is inversely proportional to the frequency of sound.The resolution analysis and modified Nyquist criteria can be used for determining the number of sensors required at a given noise level, for a required resolution, frequency range, and radius of region for which sources need to be localized.
Sookyo Jeong - One of the best experts on this subject based on the ideXlab platform.
-
robust causal inference under covariate shift via worst case subpopulation treatment effects
arXiv: Machine Learning, 2020Co-Authors: Sookyo Jeong, Hongseok NamkoongAbstract:We propose the worst-case treatment effect (WTE) across all subpopulations of a given size, a conservative notion of topline treatment effect. Compared to the average treatment effect (ATE), whose validity relies on the covariate distribution of collected data, WTE is robust to unanticipated covariate shifts, and positive findings guarantee uniformly valid treatment effects over subpopulations. We develop a semiparametrically efficient estimator for the WTE, leveraging machine learning-based estimates of the heterogeneous treatment effect and propensity score. By virtue of satisfying a key (Neyman) Orthogonality Property, our estimator enjoys central limit behavior---oracle rates with true nuisance parameters---even when estimates of nuisance parameters converge at slower rates. For both randomized trials and observational studies, we establish a semiparametric efficiency bound, proving that our estimator achieves the optimal asymptotic variance. On real datasets where robustness to covariate shift is of core concern, we illustrate the non-robustness of ATE under even mild distributional shift, and demonstrate that the WTE guards against brittle findings that are invalidated by unanticipated covariate shifts.
-
robust causal inference under covariate shift via worst case subpopulation treatment effects
2020Co-Authors: Sookyo Jeong, Hongseok NamkoongAbstract:We propose the worst-case treatment effect (WTE) across all subpopulations of a given size, a conservative notion of topline treatment effect. Compared to the average treatment effect (ATE) that solely relies on the covariate distribution of collected data, WTE is robust to unanticipated covariate shifts, and ensures positive findings guarantee uniformly valid treatment effects over underrepresented minority groups. We develop a semiparametrically efficient estimator for the WTE, leveraging machine learning-based estimates of heterogenous treatment effects and propensity scores. By virtue of satisfying a key (Neyman) Orthogonality Property, our estimator enjoys central limit behavior---oracle rates with true nuisance parameters---even when estimates of nuisance parameters converge at slower rates. For both observational and randomized studies, we prove that our estimator achieves the optimal asymptotic variance, by establishing a semiparametric efficiency lower bound. On real datasets where robustness to covariate shift is of core concern, we illustrate the non-robustness of ATE under even mild distributional shift, and demonstrate that the WTE guards against brittle findings that are invalidated by unanticipated covariate shifts.
Xiaodong Wang - One of the best experts on this subject based on the ideXlab platform.
-
iterative receivers for space time block coded ofdm systems in dispersive fading channels
IEEE Transactions on Wireless Communications, 2002Co-Authors: Xiaodong WangAbstract:We consider the design of iterative receivers for space-time block-coded orthogonal frequency-division multiplexing (STBC-OFDM) systems in unknown wireless dispersive fading channels, with or without outer channel coding. First, we propose a maximum-likelihood (ML) receiver for STBC-OFDM systems based on the expectation-maximization (EM) algorithm. By assuming that the fading processes remain constant over the duration of one STBC code word and by exploiting the Orthogonality Property of the STBC as well as the OFDM modulation, we show that the EM-based receiver has a very low computational complexity and that the initialization of the EM receiver is based on the linear minimum mean square error (MMSE) channel estimate for both the pilot and the data transmission. Since the actual fading processes may vary within one STBC code word, we also analyze the effect of a modeling mismatch on the receiver performance and show both analytically and through simulations that the performance degradation due to such a mismatch is negligible for practical Doppler frequencies. We further propose a turbo receiver based on the maximum a posteriori-EM algorithm for STBC-OFDM systems with outer channel coding. Compared with the previous noniterative receiver employing a decision-directed linear channel estimator, the iterative receivers proposed here significantly improve the receiver performance and can approach the ML performance in typical wireless channels with very fast fading, at a reasonable computational complexity well suited for real-time implementations.
