Related papers: Computational barriers in minimax submatrix detect…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…
In the general submatrix detection problem, the task is to detect the presence of a small $k \times k$ submatrix with entries sampled from a distribution $\mathcal{P}$ in an $n \times n$ matrix of samples from $\mathcal{Q}$. This…
We consider the following detection problem: given a realization of a symmetric matrix ${\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We consider the problem of detecting a planted clique of size $k$ in a random graph on $n$ vertices. When the size of the clique exceeds $\Theta(\sqrt{n})$, polynomial-time algorithms for detection proliferate. We study faster -- namely,…
In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics. While there has been success evidencing these gaps from the failure of restricted…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by…