The Experts below are selected from a list of 94674 Experts worldwide ranked by ideXlab platform
Hamid Jafarkhani - One of the best experts on this subject based on the ideXlab platform.
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multi user analog beamforming in millimeter wave mimo systems based on path angle information
IEEE Transactions on Wireless Communications, 2019Co-Authors: Lisi Jiang, Hamid JafarkhaniAbstract:We aim to design an analog-only beamforming scheme for downlink multi-user mm-wave systems to optimize the beamforming gain and the inter-user interference at the same time. Traditional analog beamforming schemes, such as the beam selection method, use the array Response Vector corresponding to the strongest path of the channel to generate a beam pointing to the user. In multi-user systems, such schemes will lead to large inter-user interference, especially when the users are closely located. In this paper, we formulate a multi-objective problem to strike a balance between the beamforming gain and the inter-user interference. To solve the problem, we first use the weighted-sum method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the analog beamforming with constant-magnitude constraints tractable. Furthermore, to alleviate the effects of the channel estimation and feedback quantization errors, we design a robust beamforming scheme to provide robustness against imperfect channel information. We first develop a channel error model for the scattering clustered channel model, which can serve as a general channel error model for the mm-wave channels. Then, we formulate a multi-objective problem using the stochastic approach to suppress the interference and enhance the beamforming gain at the same time. The simulation results show that our proposed non-robust multi-user analog beamformer outperforms the traditional analog beamforming method when the SNR is high and our proposed robust beamformer can provide up to 109% improvement in the sum-rate compared with the beam selection method.
Michael I Jordan - One of the best experts on this subject based on the ideXlab platform.
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Support union recovery in high-dimensional multivariate regression
2011Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In multivariate regression, a K-dimensional Response Vector is regressed upon a common set of p covariates, with a matrix B ∗ ∈ R p×K of regression coefficients. We study the behavior of the multivariate group Lasso,inwhich block regularization based on the ℓ1/ℓ2 norm is used for support union recovery, or recovery of the set of s rows for which B ∗ is nonzero. Under highdimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter θ(n,p,s): = n/[2ψ(B ∗ ) log(p − s)]. Heren is the sample size, and ψ(B ∗ ) is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the K-regression coefficient Vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences (n,p,s)such that θ(n,p,s) exceeds a critical level θu, and fails for sequences such that θ(n,p,s) lies below a critical level θℓ. For the special case of the standard Gaussian ensemble, we show that θℓ = θu so that the characterization is sharp. The sparsity-overlap function ψ(B ∗ ) reveals that, if the design is uncorrelated on the active rows, ℓ1/ℓ2 regularization for multivariate regression never harms performance relative to an ordinary Lasso approach and can yield substantial improvements in sample complexity (up to a factor of K) when the coefficient Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems. 1. Introduction. Th
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union support recovery in high dimensional multivariate regression
2008Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In multivariate regression, a $K$-dimensional Response Vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\in\mathbb{R}^{p\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the $\ell_1/\ell_2$ norm is used for support union recovery, or recovery of the set of $s$ rows for which $B^*$ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter $\theta(n,p,s):=n/[2\psi(B^*)\log(p-s)]$. Here $n$ is the sample size, and $\psi(B^*)$ is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the $K$-regression coefficient Vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences $(n,p,s)$ such that $\theta(n,p,s)$ exceeds a critical level $\theta_u$, and fails for sequences such that $\theta(n,p,s)$ lies below a critical level $\theta_{\ell}$. For the special case of the standard Gaussian ensemble, we show that $\theta_{\ell}=\theta_u$ so that the characterization is sharp. The sparsity-overlap function $\psi(B^*)$ reveals that, if the design is uncorrelated on the active rows, $\ell_1/\ell_2$ regularization for multivariate regression never harms performance relative to an ordinary Lasso approach and can yield substantial improvements in sample complexity (up to a factor of $K$) when the coefficient Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems.
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support union recovery in high dimensional multivariate regression
arXiv: Machine Learning, 2008Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In multivariate regression, a $K$-dimensional Response Vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\in\mathbb{R}^{p\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the $\ell_1/\ell_2$ norm is used for support union recovery, or recovery of the set of $s$ rows for which $B^*$ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter $\theta(n,p,s):=n/[2\psi(B^*)\log(p-s)]$. Here $n$ is the sample size, and $\psi(B^*)$ is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the $K$-regression coefficient Vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences $(n,p,s)$ such that $\theta(n,p,s)$ exceeds a critical level $\theta_u$, and fails for sequences such that $\theta(n,p,s)$ lies below a critical level $\theta_{\ell}$. For the special case of the standard Gaussian ensemble, we show that $\theta_{\ell}=\theta_u$ so that the characterization is sharp. The sparsity-overlap function $\psi(B^*)$ reveals that, if the design is uncorrelated on the active rows, $\ell_1/\ell_2$ regularization for multivariate regression never harms performance relative to an ordinary Lasso approach and can yield substantial improvements in sample complexity (up to a factor of $K$) when the coefficient Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems.
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union support recovery in high dimensional multivariate regression
Allerton Conference on Communication Control and Computing, 2008Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In the problem of multivariate regression, a K-dimensional Response Vector is regressed upon a common set of p covariates, with a matrix B* isin RopfptimesK of regression coefficients. We study the behavior of the group Lasso using lscr1/lscr2 regularization for the union support problem, meaning that the set of s rows for which B* is non-zero is recovered exactly. Studying this problem under high-dimensional scaling, we show that group Lasso recovers the exact row pattern with high probability over the random design and noise for scalings of (n, p, s) such that the sample complexity parameter given by thetas(n, p, s) := n/[2psi(B*) log(p - s)] exceeds a critical threshold. Here n is the sample size, p is the ambient dimension of the regression model, s is the number of non-zero rows, and psi(B*) is a sparsity-overlap function that measures a combination of the sparsities and overlaps of the K-regression coefficient Vectors that constitute the model. This sparsity-overlap function reveals that, if the design is uncorrelated on the active rows, block lscr1/lscr2 regularization for multivariate regression never harms performance relative to an ordinary Lasso approach, and can yield substantial improvements in sample complexity (up to a factor of K) when the regression Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the group Lasso.
Lisi Jiang - One of the best experts on this subject based on the ideXlab platform.
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multi user analog beamforming in millimeter wave mimo systems based on path angle information
IEEE Transactions on Wireless Communications, 2019Co-Authors: Lisi Jiang, Hamid JafarkhaniAbstract:We aim to design an analog-only beamforming scheme for downlink multi-user mm-wave systems to optimize the beamforming gain and the inter-user interference at the same time. Traditional analog beamforming schemes, such as the beam selection method, use the array Response Vector corresponding to the strongest path of the channel to generate a beam pointing to the user. In multi-user systems, such schemes will lead to large inter-user interference, especially when the users are closely located. In this paper, we formulate a multi-objective problem to strike a balance between the beamforming gain and the inter-user interference. To solve the problem, we first use the weighted-sum method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the analog beamforming with constant-magnitude constraints tractable. Furthermore, to alleviate the effects of the channel estimation and feedback quantization errors, we design a robust beamforming scheme to provide robustness against imperfect channel information. We first develop a channel error model for the scattering clustered channel model, which can serve as a general channel error model for the mm-wave channels. Then, we formulate a multi-objective problem using the stochastic approach to suppress the interference and enhance the beamforming gain at the same time. The simulation results show that our proposed non-robust multi-user analog beamformer outperforms the traditional analog beamforming method when the SNR is high and our proposed robust beamformer can provide up to 109% improvement in the sum-rate compared with the beam selection method.
Guillaume Obozinski - One of the best experts on this subject based on the ideXlab platform.
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Support union recovery in high-dimensional multivariate regression
2011Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In multivariate regression, a K-dimensional Response Vector is regressed upon a common set of p covariates, with a matrix B ∗ ∈ R p×K of regression coefficients. We study the behavior of the multivariate group Lasso,inwhich block regularization based on the ℓ1/ℓ2 norm is used for support union recovery, or recovery of the set of s rows for which B ∗ is nonzero. Under highdimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter θ(n,p,s): = n/[2ψ(B ∗ ) log(p − s)]. Heren is the sample size, and ψ(B ∗ ) is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the K-regression coefficient Vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences (n,p,s)such that θ(n,p,s) exceeds a critical level θu, and fails for sequences such that θ(n,p,s) lies below a critical level θℓ. For the special case of the standard Gaussian ensemble, we show that θℓ = θu so that the characterization is sharp. The sparsity-overlap function ψ(B ∗ ) reveals that, if the design is uncorrelated on the active rows, ℓ1/ℓ2 regularization for multivariate regression never harms performance relative to an ordinary Lasso approach and can yield substantial improvements in sample complexity (up to a factor of K) when the coefficient Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems. 1. Introduction. Th
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union support recovery in high dimensional multivariate regression
2008Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In multivariate regression, a $K$-dimensional Response Vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\in\mathbb{R}^{p\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the $\ell_1/\ell_2$ norm is used for support union recovery, or recovery of the set of $s$ rows for which $B^*$ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter $\theta(n,p,s):=n/[2\psi(B^*)\log(p-s)]$. Here $n$ is the sample size, and $\psi(B^*)$ is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the $K$-regression coefficient Vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences $(n,p,s)$ such that $\theta(n,p,s)$ exceeds a critical level $\theta_u$, and fails for sequences such that $\theta(n,p,s)$ lies below a critical level $\theta_{\ell}$. For the special case of the standard Gaussian ensemble, we show that $\theta_{\ell}=\theta_u$ so that the characterization is sharp. The sparsity-overlap function $\psi(B^*)$ reveals that, if the design is uncorrelated on the active rows, $\ell_1/\ell_2$ regularization for multivariate regression never harms performance relative to an ordinary Lasso approach and can yield substantial improvements in sample complexity (up to a factor of $K$) when the coefficient Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems.
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support union recovery in high dimensional multivariate regression
arXiv: Machine Learning, 2008Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In multivariate regression, a $K$-dimensional Response Vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\in\mathbb{R}^{p\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the $\ell_1/\ell_2$ norm is used for support union recovery, or recovery of the set of $s$ rows for which $B^*$ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter $\theta(n,p,s):=n/[2\psi(B^*)\log(p-s)]$. Here $n$ is the sample size, and $\psi(B^*)$ is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the $K$-regression coefficient Vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences $(n,p,s)$ such that $\theta(n,p,s)$ exceeds a critical level $\theta_u$, and fails for sequences such that $\theta(n,p,s)$ lies below a critical level $\theta_{\ell}$. For the special case of the standard Gaussian ensemble, we show that $\theta_{\ell}=\theta_u$ so that the characterization is sharp. The sparsity-overlap function $\psi(B^*)$ reveals that, if the design is uncorrelated on the active rows, $\ell_1/\ell_2$ regularization for multivariate regression never harms performance relative to an ordinary Lasso approach and can yield substantial improvements in sample complexity (up to a factor of $K$) when the coefficient Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems.
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union support recovery in high dimensional multivariate regression
Allerton Conference on Communication Control and Computing, 2008Co-Authors: Guillaume Obozinski, Martin J Wainwright, Michael I JordanAbstract:In the problem of multivariate regression, a K-dimensional Response Vector is regressed upon a common set of p covariates, with a matrix B* isin RopfptimesK of regression coefficients. We study the behavior of the group Lasso using lscr1/lscr2 regularization for the union support problem, meaning that the set of s rows for which B* is non-zero is recovered exactly. Studying this problem under high-dimensional scaling, we show that group Lasso recovers the exact row pattern with high probability over the random design and noise for scalings of (n, p, s) such that the sample complexity parameter given by thetas(n, p, s) := n/[2psi(B*) log(p - s)] exceeds a critical threshold. Here n is the sample size, p is the ambient dimension of the regression model, s is the number of non-zero rows, and psi(B*) is a sparsity-overlap function that measures a combination of the sparsities and overlaps of the K-regression coefficient Vectors that constitute the model. This sparsity-overlap function reveals that, if the design is uncorrelated on the active rows, block lscr1/lscr2 regularization for multivariate regression never harms performance relative to an ordinary Lasso approach, and can yield substantial improvements in sample complexity (up to a factor of K) when the regression Vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the group Lasso.
Aad Van Der Vaart - One of the best experts on this subject based on the ideXlab platform.
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bayesian linear regression with sparse priors
Annals of Statistics, 2015Co-Authors: Ismael Castillo, Johannes Schmidthieber, Aad Van Der VaartAbstract:We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse Vector, and to give optimal prediction of the Response Vector. It is also shown to select the correct sparse model, or at least the coefficients that are significantly different from zero. The asymptotic shape of the posterior distribution is characterized and employed to the construction and study of credible sets for uncertainty quantification.