Related papers: Bounds on restricted isometry constants of random …
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
Compressed sensing (CS) theory considers the restricted isometry property (RIP) as a sufficient condition for measurement matrix which guarantees the recovery of any sparse signal from its compressed measurements. The RIP condition also…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
We study the Restricted Isometry Property of a random matrix $\Gamma$ with independent isotropic log-concave rows. To this end, we introduce a parameter $\Gamma_{k,m}$ that controls uniformly the operator norm of sub-matrices with $k$ rows…
In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
The class of Fourier matrices is of special importance in compressed sensing (CS). This paper concerns deterministic construction of compressed sensing matrices from Fourier matrices. By using Katz' character sum estimation, we are able to…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Statistical modeling often involves identifying an optimal estimate to some underlying probability distribution known to satisfy some given constraints. I show here that choosing as estimate the centroid, or center of mass, of the set…
A practical limitation of cluster randomized controlled trials (cRCTs) is that the number of available clusters may be small, resulting in an increased risk of baseline imbalance under simple randomization. Constrained randomization…
In this paper, we analyze the performance of the estimation of Laplacian matrices under general observation models. Laplacian matrix estimation involves structural constraints, including symmetry and null-space properties, along with matrix…
The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the…
Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L)…