Related papers: Performance Analysis of Regularized Convex Relaxat…
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
In multiple-input multiple-output (MIMO) spatially multiplexing (SM) systems, achievable error rate performance is determined by signal detection strategy. The optimal maximum-likelihood detection (MLD) that exhaustively examines all symbol…
Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
This paper concerns with a noisy structured low-rank matrix recovery problem which can be modeled as a structured rank minimization problem. We reformulate this problem as a mathematical program with a generalized complementarity constraint…
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…
Practical data detectors for future wireless systems with hundreds of antennas at the base station must achieve high throughput and low error rate at low complexity. Since the complexity of maximum-likelihood (ML) data detection is…
This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…
In this paper, we consider recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding,…
This paper addresses robust waveform design for multiple-input-multiple-output (MIMO) radar detection. A probabilistic model is proposed to describe the target uncertainty. Considering that waveform design based on maximizing the…
Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
For a regularized least squares estimation of discrete-valued signals, we propose a Linearly involved Generalized Moreau Enhanced (LiGME) regularizer, as a nonconvex regularizer, of designated isolated minimizers. The proposed regularizer…
Many neural network (NN) verification systems represent the network's input-output relation as a constraint program. Sound and complete, representations involve integer constraints, for simulating the activations. Recent works convexly…
Optimal data detection in massive multiple-input multiple-output (MIMO) systems requires prohibitive computational complexity. A variety of detection algorithms have been proposed in the literature, offering different trade-offs between…
Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…
Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several ML-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO…