4,481 research outputs found
Non-convex Global Minimization and False Discovery Rate Control for the TREX
The TREX is a recently introduced method for performing sparse
high-dimensional regression. Despite its statistical promise as an alternative
to the lasso, square-root lasso, and scaled lasso, the TREX is computationally
challenging in that it requires solving a non-convex optimization problem. This
paper shows a remarkable result: despite the non-convexity of the TREX problem,
there exists a polynomial-time algorithm that is guaranteed to find the global
minimum. This result adds the TREX to a very short list of non-convex
optimization problems that can be globally optimized (principal components
analysis being a famous example). After deriving and developing this new
approach, we demonstrate that (i) the ability of the preexisting TREX heuristic
to reach the global minimum is strongly dependent on the difficulty of the
underlying statistical problem, (ii) the new polynomial-time algorithm for TREX
permits a novel variable ranking and selection scheme, (iii) this scheme can be
incorporated into a rule that controls the false discovery rate (FDR) of
included features in the model. To achieve this last aim, we provide an
extension of the results of Barber & Candes (2015) to establish that the
knockoff filter framework can be applied to the TREX. This investigation thus
provides both a rare case study of a heuristic for non-convex optimization and
a novel way of exploiting non-convexity for statistical inference
Pattern Division Multiple Access with Large-scale Antenna Array
In this paper, pattern division multiple access with large-scale antenna
array (LSA-PDMA) is proposed as a novel non-orthogonal multiple access (NOMA)
scheme. In the proposed scheme, pattern is designed in both beam domain and
power domain in a joint manner. At the transmitter, pattern mapping utilizes
power allocation to improve the system sum rate and beam allocation to enhance
the access connectivity and realize the integration of LSA into multiple access
spontaneously. At the receiver, hybrid detection of spatial filter (SF) and
successive interference cancellation (SIC) is employed to separate the
superposed multiple-domain signals. Furthermore, we formulate the sum rate
maximization problem to obtain the optimal pattern mapping policy, and the
optimization problem is proved to be convex through proper mathematical
manipulations. Simulation results show that the proposed LSA-PDMA scheme
achieves significant performance gain on system sum rate compared to both the
orthogonal multiple access scheme and the power-domain NOMA scheme.Comment: 6 pages, 5 figures, this paper has been accepted by IEEE VTC
2017-Sprin
System Level Synthesis
This article surveys the System Level Synthesis framework, which presents a
novel perspective on constrained robust and optimal controller synthesis for
linear systems. We show how SLS shifts the controller synthesis task from the
design of a controller to the design of the entire closed loop system, and
highlight the benefits of this approach in terms of scalability and
transparency. We emphasize two particular applications of SLS, namely
large-scale distributed optimal control and robust control. In the case of
distributed control, we show how SLS allows for localized controllers to be
computed, extending robust and optimal control methods to large-scale systems
under practical and realistic assumptions. In the case of robust control, we
show how SLS allows for novel design methodologies that, for the first time,
quantify the degradation in performance of a robust controller due to model
uncertainty -- such transparency is key in allowing robust control methods to
interact, in a principled way, with modern techniques from machine learning and
statistical inference. Throughout, we emphasize practical and efficient
computational solutions, and demonstrate our methods on easy to understand case
studies.Comment: To appear in Annual Reviews in Contro
Compressed matched filter for non-Gaussian noise
We consider estimation of a deterministic unknown parameter vector in a
linear model with non-Gaussian noise. In the Gaussian case, dimensionality
reduction via a linear matched filter provides a simple low dimensional
sufficient statistic which can be easily communicated and/or stored for future
inference. Such a statistic is usually unknown in the general non-Gaussian
case. Instead, we propose a hybrid matched filter coupled with a randomized
compressed sensing procedure, which together create a low dimensional
statistic. We also derive a complementary algorithm for robust reconstruction
given this statistic. Our recovery method is based on the fast iterative
shrinkage and thresholding algorithm which is used for outlier rejection given
the compressed data. We demonstrate the advantages of the proposed framework
using synthetic simulations
Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication
The adoption of a Reconfigurable Intelligent Surface (RIS) for downlink
multi-user communication from a multi-antenna base station is investigated in
this paper. We develop energy-efficient designs for both the transmit power
allocation and the phase shifts of the surface reflecting elements, subject to
individual link budget guarantees for the mobile users. This leads to
non-convex design optimization problems for which to tackle we propose two
computationally affordable approaches, capitalizing on alternating
maximization, gradient descent search, and sequential fractional programming.
Specifically, one algorithm employs gradient descent for obtaining the RIS
phase coefficients, and fractional programming for optimal transmit power
allocation. Instead, the second algorithm employs sequential fractional
programming for the optimization of the RIS phase shifts. In addition, a
realistic power consumption model for RIS-based systems is presented, and the
performance of the proposed methods is analyzed in a realistic outdoor
environment. In particular, our results show that the proposed RIS-based
resource allocation methods are able to provide up to higher energy
efficiency, in comparison with the use of regular multi-antenna
amplify-and-forward relaying.Comment: Accepted by IEEE TWC; additional materials on the topic are included
in the 2018 conference publications at ICASSP
(https://ieeexplore.ieee.org/abstract/document/8461496) and GLOBECOM 2018
(arXiv:1809.05397
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