Publications related to Chebyshev's inequality

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii ...

INST MATHEMATICAL STATISTICS2020

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

Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations

Michel Bierlaire, Prateek Bansal

Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substan ...

PERGAMON-ELSEVIER SCIENCE LTD2020

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

A gyrokinetic model for the plasma periphery of fusion devices

Paolo Ricci, Rogério Manuel Cabete De Jesus Jorge, Baptiste Jimmy Frei

Understanding the turbulent dynamics of the plasma in the periphery of fusion devices - the region extending from the external part of the closed flux surface region to the scrape-off layer - is of crucial importance on the way to fusion energy. Indeed, th ...

2019

Remote Source Coding Under Gaussian Noise: Dueling Roles of Power and Entropy Power

Michael Christoph Gastpar

The distributed remote source coding (the so-called CEO) problem is studied in the case where the underlying source, not necessarily Gaussian, has finite differential entropy and the observation noise is Gaussian. The main result is a new lower bound for t ...

2019

Learning and Adaptive Data Analysis via Maximal Leakage

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

There has been growing interest in studying connections between generalization error of learning algorithms and information measures. In this work, we generalize a result that employs the maximal leakage, a measure of leakage of information, and explore ho ...

IEEE2019

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

Localizing the Source of an Epidemic Using Few Observations

Brunella Marta Spinelli

Localizing the source of an epidemic is a crucial task in many contexts, including the detection of malicious users in social networks and the identification of patient zeros of disease outbreaks. The difficulty of this task lies in the strict limitation ...

EPFL2018

Chebyshev's inequality

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A Covariance Formula For Topological Events Of Smooth Gaussian Fields

A Local Law for Singular Values from Diophantine Equations

Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations

On the asymptotic behavior of the solutions to parabolic variational inequalities

Forbidden induced subposets of given height

A gyrokinetic model for the plasma periphery of fusion devices

Remote Source Coding Under Gaussian Noise: Dueling Roles of Power and Entropy Power

Learning and Adaptive Data Analysis via Maximal Leakage

Chebyshev Inequalities for Products of Random Variables

Localizing the Source of an Epidemic Using Few Observations

On the asymptotic behavior of the solutions to parabolic variational inequalities

Localizing the Source of an Epidemic Using Few Observations

Remote Source Coding Under Gaussian Noise: Dueling Roles of Power and Entropy Power

A Local Law for Singular Values from Diophantine Equations

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations

Forbidden induced subposets of given height

A gyrokinetic model for the plasma periphery of fusion devices

Learning and Adaptive Data Analysis via Maximal Leakage

Chebyshev Inequalities for Products of Random Variables