The problem of estimating the phases (angles) of a complex unit-modulus vector z from their
noisy pairwise relative measurements C=zz^*+σW, where W is a complex-valued Gaussian …

Maximum likelihood estimation problems are, in general, intractable optimization problems.
As a result, it is common to approximate the maximum likelihood estimator (MLE) using …

The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry.
We show that for a class of random Laplacian matrices with independent off-diagonal …

We study exact recovery conditions for convex relaxations of point cloud clustering
problems, focusing on two of the most common optimization problems for unsupervised …

Let G be a compact group and let fij∈ C (G). We define the non-unique games (NUG)
problem as finding g1,..., gn∈ G to minimize∑ ni, j= 1 fij (gig− 1 j). We introduce a convex …

De nombreux problèmes d'optimisation, bien qu'ils soient difficiles à traiter dans les cas les
plus compliqués, peuvent souvent être résolus de manière efficace par des heuristiques …

We study the inverse problem of estimating n locations t_1,t_2,...,t_n (up to global scale,
translation, and negation) in R^d from noisy measurements of a subset of the (unsigned) …

In this paper, we consider a fundamental problem in modern digital communications known
as multiple-input multiple-output (MIMO) detection, which can be formulated as a complex …

These are notes from a course I gave at MIT on the Fall of 2015 entitled:“18. S096: Topics in
Mathematics of Data Science”. These notes are not in final form and will be continuously …

We study the phase synchronization problem with noisy measurements, where is an-
dimensional complex unit-modulus vector and is a complex-valued Gaussian random …