Publications related to Sum of normally distributed random variables

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

2023

Common Information Components Analysis

Michael Christoph Gastpar, Erixhen Sula

Wyner's common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis ...

2021

A hybrid collocation-perturbation approach for PDEs with random domains

Fabio Nobile

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...

2021

Feedback and Common Information: Bounds and Capacity for Gaussian Networks

Erixhen Sula

Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...

EPFL2021

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021

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

On some consistent tests of mutual independence among several random vectors of arbitrary dimensions

Soham Sarkar

Testing for mutual independence among several random vectors is a challenging problem, and in recent years, it has gained significant attention in statistics and machine learning literature. Most of the existing tests of independence deal with only two ran ...

SPRINGER2020

An Operational Approach to Information Leakage

Ibrahim Issa

Given two random variables X and Y , an operational approach is undertaken to quantify the "leakage" of information from X to Y . The resulting measure L (X -> Y) is called maximal leakage, and is defined as the multiplicative increase, upon observing Y , ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Distributional Robustness in Mechanism Design

Cagil Kocyigit

Mechanism design theory examines the design of allocation mechanisms or incentive systems involving multiple rational but self-interested agents and plays a central role in many societally important problems in economics. In mechanism design problems, agen ...

EPFL2020

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

Entropic Matroids and Their Representation

Emmanuel Abbé

This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p. We draw ...

2019

A Data-Driven Approach Based on Multivariate Copulas for Quantitative Risk Assessment of Concrete Dam

Zhenzhu Meng, Yating Hu, Chenfei Shao

Risk assessment of dam's running status is an important part of dam management. A data-driven method based on monitored displacement data has been applied in risk assessment, owing to its easy operation and real-time analysis. However, previous data-driven ...

2019

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

Reconstruction using approximate message passing methods

Paul Hurley, Matthieu Martin Jean-André Simeoni, Giovanni Cherubini, Sanaz Kazemi

The present invention is notably directed to a computer-implemented method for image reconstruction. The method comprises: accessing elements that respectively correspond to measurement values, which can be respectively mapped to measurement nodes; and per ...

2017

Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

2016

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...

2016

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies

Stephan Morgenthaler

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomi ...

Wiley-Blackwell2016

Numerical Approximation of Flows in Random Porous Media

Francesco Tesei

The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coeffi ...

EPFL2016

Dimensionality Reduction in Dynamic Optimization under Uncertainty

Napat Rujeerapaiboon

Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...

EPFL2016

The Chaining Lemma and Its Application

Sebastian Faust

We present a new information-theoretic result which we call the Chaining Lemma. It considers a so-called "chain" of random variables, defined by a source distribution X-(0) with high min-entropy and a number (say, t in total) of arbitrary functions (T-1,.. ...

Springer-Verlag Berlin2015