Publications de Armin Eftekhari

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This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks, the data vectors a ...

Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient algorithm for detecti ...

We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a "continuum-of-subspaces" model, a re ...

Principal component analysis (PCA) finds the best linear representation of data and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that preserve most of its "e ...

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to t ...

We consider the problem of non-negative super-resolution, which concerns reconstructing a non-negative signal x = Sigma(k )(i=1)a(i)delta(ti) from m samples of its convolution with a window function phi(s - t), of the form y(s(j)) = Sigma(k)(i=1) a(i) phi( ...

In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the specification that a ...

Overparameterization refers to the important phenomenon where the width of a neural network is chosen such that learning algorithms can provably attain zero loss in nonconvex training. The existing theory establishes such global convergence using various i ...

We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate first- and second-order critical point which relies on the geometric formalism o ...

A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling ...

Armin Eftekhari

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MOSES: A Streaming Algorithm for Linear Dimensionality Reduction

Streaming Principal Component Analysis From Incomplete Data

Sparse Inverse Problems Over Measures: Equivalence Of The Conditional Gradient And Exchange Methods

Principal Component Analysis By Optimization Of Symmetric Functions Has No Spurious Local Optima

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Sparse non-negative super-resolution - simplified and stabilised

Fast and Provable ADMM for Learning with Generative Priors

Subquadratic Overparameterization for Shallow Neural Networks

Computing Second-Order Points Under Equality Constraints: Revisiting Fletcher's Augmented Lagrangian

Double-Loop Unadjusted Langevin Algorithm