相关论文: Compressed Regression
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
We consider the compressed sensing problem, where the object $x_0 \in \bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \times N$ random matrix with iid Gaussian entries and $n < N$.…
We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models the overall number of regressors $p$ is very large, possibly larger than the sample…
In this paper, we discuss the statistical properties of the $\ell_q$ optimization methods $(0<q\leq 1)$, including the $\ell_q$ minimization method and the $\ell_q$ regularization method, for estimating a sparse parameter from noisy…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover…
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal,…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
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 regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
The goal of model compression is to reduce the size of a large neural network while retaining a comparable performance. As a result, computation and memory costs in resource-limited applications may be significantly reduced by dropping…
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…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
In this paper, we study the support recovery guarantees of underdetermined sparse regression using the $\ell_1$-norm as a regularizer and a non-smooth loss function for data fidelity. More precisely, we focus in detail on the cases of…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…