相关论文: Derandomizing restricted isometries via the Legend…

Many inverse problems in signal processing deal with the robust estimation of unknown data from underdetermined linear observations. Low dimensional models, when combined with appropriate regularizers, have been shown to be efficient at…

We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $\epsilon>0$ such that, conditioned on a folklore conjecture in…

This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…

This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…

Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime…

In conventional supervised pattern recognition tasks, model selection is typically accomplished by minimizing the classification error rate on a set of so-called development data, subject to ground-truth labeling by human experts or some…

We provide algorithms for isotonic regression minimizing $L_0$ error (Hamming distance). This is also known as monotonic relabeling, and is applicable when labels have a linear ordering but not necessarily a metric. There may be…

In an instrumental variable model, the score statistic can be bounded for any alternative in parts of the parameter space. These regions involve a constraint on the first-stage regression coefficients and the reduced-form covariance matrix.…

It is well known that a random q-ary code of rate \Omega(\epsilon^2) is list decodable up to radius (1 - 1/q - \epsilon) with list sizes on the order of 1/\epsilon^2, with probability 1 - o(1). However, until recently, a similar statement…

In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic,…

Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $\varepsilon=3.26\cdot 10^{-7}$, large $k$ and $k^{2-\varepsilon} \le N\le…

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…

We present a one-shot method for compressing large labeled graphs called Random Edge Coding. When paired with a parameter-free model based on P\'olya's Urn, the worst-case computational and memory complexities scale quasi-linearly and…

In Compressed Sensing the matrices that satisfy the Restricted Isometry Property (RIP) play an important role. But to date, very few results for designing such matrices are available. For applications such as multiplier-less data…

We propose a new family of label randomizers for training regression models under the constraint of label differential privacy (DP). In particular, we leverage the trade-offs between bias and variance to construct better label randomizers…

We derive near optimal performance guarantees for subsampled blind deconvolution. Blind deconvolution is an ill-posed bilinear inverse problem and additional subsampling makes the problem even more challenging. Sparsity and spectral…

Dimensional reduction of high dimensional data can be achieved by keeping only the relevant eigenmodes after principal component analysis. However, differentiating relevant eigenmodes from the random noise eigenmodes is problematic. A new…

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…

In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be…