Related papers: Angular Synchronization by Eigenvectors and Semide…
This paper presents a new approach, based on polynomial optimization and the method of moments, to the problem of anomaly detection. The proposed technique only requires information about the statistical moments of the normal-state…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous…
This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…
We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
Anomaly detection is to recognize samples that differ in some respect from the training observations. These samples which do not conform to the distribution of normal data are called outliers or anomalies. In real-world anomaly detection…
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and…
We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in\mathbb{R}^{d\times d}$ where $W_{ij}$ is a Gaussian random matrix…
We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…
Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps.…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
We address the problem of solving mixed random linear equations. We have unlabeled observations coming from multiple linear regressions, and each observation corresponds to exactly one of the regression models. The goal is to learn the…
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…