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We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…
The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…
Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work,…
We study statistical restricted isometry, a property closely related to sparse signal recovery, of deterministic sensing matrices of size $m \times N$. A matrix is said to have a statistical restricted isometry property (StRIP) of order $k$…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
Conventional correlation-based frame synchronization techniques can suffer significant performance degradation over multi-path frequency-selective channels. As a remedy, in this paper we consider joint frame synchronization and channel…
In the target tracking and its engineering applications, recursive state estimation of the target is of fundamental importance. This paper presents a recursive performance bound for dynamic estimation and filtering problem, in the framework…
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild…
Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…
As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
The co-sparse analysis model for signals assumes that the signal of interest can be multiplied by an analysis dictionary \Omega, leading to a sparse outcome. This model stands as an interesting alternative to the more classical synthesis…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning. RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work…
Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal…