相关论文: Simple Analysis of Sparse, Sign-Consistent JL

We prove essentially sharp bounds for Ramsey numbers of ordered hypergraph matchings, inroduced recently by Dudek, Grytczuk, and Ruci\'{n}ski. Namely, for any $r \ge 2$ and $n \ge 2$, we show that any collection $\mathcal H$ of $n$ pairwise…

The goal of the paper is to lay the foundation for the qualitative analogue of the classical, quantitative sparse graph limit theory. In the first part of the paper we introduce the qualitative analogues of the Benjamini-Schramm and…

We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu (1935) and Bhatia and Davis (2000) concerning measures on the line to several dimensions. This is…

The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given $N$, for any set of $N$ vectors $X \subset \mathbb{R}^n$, there exists a mapping $f : X \to \mathbb{R}^m$ such that $f(X)$…

We study a plug in least squares estimator for the change point parameter where change is in the mean of a high dimensional random vector under subgaussian or subexponential distributions. We obtain sufficient conditions under which this…

Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lov\'asz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved…

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin…

We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…

The goal of this paper is to attract attention of the reader to a dimension-free geometric inequality that can be proved using the classical needle decomposition. This inequality allows us to derive sharp dimension-free estimates for the…

We consider the adjacency matrices of sparse random graphs from the Chung-Lu model, where edges are added independently between the $N$ vertices with varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed positive…

The Lovasz Local Lemma (LLL) is a probabilistic tool which has been used to show the existence of a variety of combinatorial structures with good "local" properties. The "LLL-distribution" can be used to show that the resulting structures…

Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

The $l_2$ flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction. It has been conjectured that the target dimension bounds can be refined and bounded in terms of the intrinsic dimensionality of the…

Limit distributions of likelihood ratio statistics are well-known to be discontinuous in the presence of nuisance parameters at the boundary of the parameter space, which lead to size distortions when standard critical values are used for…

We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse. We focus on Gaussian random underdetermined…

The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidrv; the limiting rescaled spectral measure (LRSM)…

We study the oracle complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz functions, in the sense proposed by Zhang et al. [2020]. While there exist dimension-free randomized algorithms for producing such points within…

For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design,…

The Johnson-Lindenstrauss Lemma (J-L Lemma) is a cornerstone of dimension reduction techniques. We study it in the one-bit context, namely we consider the unit sphere $ \mathbb S ^{N-1}$, with normalized geodesic metric, and map a finite…