Related papers: Computational lower bounds for multi-frequency gro…
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…
In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…
Finding group elements from noisy measurements of their pairwise ratios is also known as the group synchronization problem, first introduced in the context of the group SO(2) of planar rotations, whose usefulness has been demonstrated…
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…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
Group synchronization is the problem of determining reliable global estimates from noisy local measurements on networks. The typical task for group synchronization is to assign elements of a group to the nodes of a graph in a way that…
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…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
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…
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…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…
We study here the so-called spiked Wigner and Wishart models, where one observes a low-rank matrix perturbed by some Gaussian noise. These models encompass many classical statistical tasks such as sparse PCA, submatrix localization,…
Group synchronization plays a crucial role in global pipelines for Structure from Motion (SfM). Its formulation is nonconvex and it is faced with highly corrupted measurements. Cycle consistency has been effective in addressing these…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…