Related papers: Computational barriers in minimax submatrix detect…
We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…
We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix…
We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
We obtain the minimax rate for a mean location model with a bounded star-shaped set $K \subseteq \mathbb{R}^n$ constraint on the mean, in an adversarially corrupted data setting with Gaussian noise. We assume an unknown fraction $\epsilon…
Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been…
The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $\mu$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a…
We consider the high-dimensional inference problem where the signal is a low-rank 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 dimension…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known)…
Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
We study estimation and detection of high-order moment and cumulant tensors from $n$ i.i.d.\ observations of a $p$-dimensional random vector, with performance measured in tensor spectral norm. Under sub-Gaussianity, we show that the minimax…
In a distinguishing problem, the input is a sample drawn from one of two distributions and the algorithm is tasked with identifying the source distribution. The performance of a distinguishing algorithm is measured by its advantage, i.e.,…
Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best…
We consider the detection problem of correlations in a $p$-dimensional Gaussian vector, when we observe $n$ independent, identically distributed random vectors, for $n$ and $p$ large. We assume that the covariance matrix varies in some…
We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a…