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Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

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Learning without Smoothness and Strong Convexity

Yen-Huan Li

Recent advances in statistical learning and convex optimization have inspired many successful practices. Standard theories assume smoothness---bounded gradient, Hessian, etc.---and strong convexity of the loss function. Unfortunately, such conditions may ...

EPFL2018

This paper addresses the mean-field behavior of large-scale systems of parallel servers with a processor sharing service discipline when arrivals are Poisson and jobs have general service time distributions when an SQ(d) routing policy is used. Under this ...

ELSEVIER SCIENCE BV2018

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Alexandre Caboussat, Dimitrios Gourzoulidis

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

SPRINGER/PLENUM PUBLISHERS2018

The regularized tau estimator: A robust and efficient solution to ill-posed linear inverse problems

Martin Vetterli, Benjamin Bejar Haro, Marta Martinez-Camara

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the performance of pop ...

2017

Parameter Determination of Sensor Stochastic Models under Covariate Dependency

Jan Skaloud, Stéphane Guerrier, Philipp Clausen

The proliferation of (low-cost) sensors provokes new challenges in data fusion. This is related to the correctness of stochastic characterization that is a prerequisite for optimal estimation of parameters from redundant observations. Different (statistica ...

2017

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Emeric Rolland Georges Thibaud, Raphaël Huser

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect depen ...

Elsevier Sci Ltd2017

We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving system. As a corollary we obtain easy to check necessary and sufficient condition ...

2017

Excess-Risk of Distributed Stochastic Learners

Ali H. Sayed

This paper studies the learning ability of consensus and diffusion distributed learners from continuous streams of data arising from different but related statistical distributions. Four distinctive features for diffusion learners are revealed in relation ...

IEEE2016

For studying spectral properties of a non-normal matrix A ∈ Cn×n, information about its spectrum σ(A) alone is usually not enough. Effects of perturbations on σ(A) can be studied by computing ε-pseudospectra, that is the level-sets of the resolvent norm fu ...

MATHICSE2016

Sparsity-Driven Statistical Inference for Inverse Problems

Ulugbek Kamilov

This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring sig ...

EPFL2015