Related papers: Performance Analysis of Regularized Convex Relaxat…
Common clustering methods, such as $k$-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics,…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
Optimal symbol detection in multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Recently, there has been a growing interest to get reasonably close to the optimal solution using neural networks while keeping the…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
We establish risk bounds for Regularized Empirical Risk Minimizers (RERM) when the loss is Lipschitz and convex and the regularization function is a norm. In a first part, we obtain these results in the i.i.d. setup under subgaussian…
Massive MIMO systems can greatly increase spectral and energy efficiency over traditional MIMO systems by exploiting large antenna arrays. However, increasing the number of antennas at the base station (BS) makes the uplink non-coherent…
In this paper, we study a nonconvex continuous relaxation of MAP inference in discrete Markov random fields (MRFs). We show that for arbitrary MRFs, this relaxation is tight, and a discrete stationary point of it can be easily reached by a…
Low-complexity near-optimal signal detection in large dimensional communication systems is a challenge. In this paper, we present a reactive tabu search (RTS) algorithm, a heuristic based combinatorial optimization technique, to achieve…
Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…
Detection for one-bit massive MIMO systems presents several challenges especially for higher order constellations. Recent advances in both model-based analysis and deep learning frameworks have resulted in several robust one-bit detector…
The existence of multipath brings extra "looks" of targets. This paper considers the extended target detection problem with a narrow band Multiple-Input Multiple-Output(MIMO) radar in the presence of multipath from the view of…
Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER,…
In this paper, we consider the decentralized, stochastic nonconvex strongly-concave (NCSC) minimax problem with nonsmooth regularization terms on both primal and dual variables, wherein a network of $m$ computing agents collaborate via…
To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…
Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized…
In modern data analysis, one is frequently faced with statistical inference problems involving massive datasets. Processing such large datasets is usually viewed as a substantial computational challenge. However, if data are a…
In this paper, we investigate the design of statistically robust detectors for multi-input multi-output (MIMO) systems subject to imperfect channel state information (CSI). A robust maximum likelihood (ML) detection problem is formulated by…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…