Spread Spectrum for Universal Compressive Sampling

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We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we propose a novel t ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

We consider high-dimensional random optimization problems where the dynamical variables are subjected to nonconvex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints a ...

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

We address the problem of predicting aggregate vote outcomes (e.g., national) from partial outcomes (e.g., regional) that are revealed sequentially. We combine matrix factorization techniques and generalized linear models (GLMs) to obtain a flexible, effic ...

Spread Spectrum for Universal Compressive Sampling

Chattez avec Graph Search

TimeEvolver: A program for time evolution with improved error bound

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

High-dimensional optimization under nonconvex excluded volume constraints

New Results in Integer and Lattice Programming

A fast spectral divide-and-conquer method for banded matrices

Optimal radial basis for density-based atomic representations

Sub-Matrix Factorization for Real-Time Vote Prediction