Publications related to Dynamic Average Diffusion With Randomized Coordinate Updates

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

Characterization of Real-World Power System Signals in Non-Stationary Conditions using a Dictionary Approach

Mario Paolone, Asja Derviskadic, Guglielmo Frigo, Alexandra Cameron Karpilow

As power grids transition towards low-inertia net-works based on converter-interfaced renewable energy resources, they become increasingly vulnerable to extreme dynamics. Currently, the most advanced methods for signal processing in power systems are embed ...

IEEE2021

DiffuserCam Project

William Cappelletti, Jonathan Philippe Reymond, Matteo Pariset

We test the reconstruction power of a lensless cam- era on a custom dataset. We define a linear inverse problem on the raw image, based on a PSF estimation of the the sensing device and the actual captures. We implement various regularizations to enforce s ...

2021

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Volkan Cevher, Ali Kavis, Shaul Nadav Hallak

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

2020

Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization

Ali H. Sayed, Kun Yuan

This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

Cover: A Cluster-Based Variance Reduced Method For Online Learning

Ali H. Sayed, Bicheng Ying, Kun Yuan

In this paper, we develop a stochastic-gradient learning algorithm for situations involving streaming data that arise from an underlying clustered structure. In such settings, the variance of gradient noise can be decomposed into the in-cluster variance si ...

IEEE2019

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

Armin Eftekhari

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 ...

SIAM PUBLICATIONS2019

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

Matthieu Claude Martin

This thesis work focuses on optimal control of partial differential equations (PDEs) with uncertain parameters, treated as a random variables. In particular, we assume that the random parameters are not observable and look for a deterministic control which ...

EPFL2019

Dynamic Average Diffusion With Randomized Coordinate Updates

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Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Characterization of Real-World Power System Signals in Non-Stationary Conditions using a Dictionary Approach

DiffuserCam Project

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Strong convergence of multivariate maxima

Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization

A Local Law for Singular Values from Diophantine Equations

Cover: A Cluster-Based Variance Reduced Method For Online Learning

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

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Characterization of Real-World Power System Signals in Non-Stationary Conditions using a Dictionary Approach

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization

DiffuserCam Project

A Local Law for Singular Values from Diophantine Equations

Cover: A Cluster-Based Variance Reduced Method For Online Learning

Strong convergence of multivariate maxima

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

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters