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Concept

Chebyshev's inequality

Related publications (23)

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

Matteo Raphael Tacchi

This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...

IEEE2023

Heuristic Estimation of the Vacuum Energy Density of the Universe: Part I—Analysis Based on Time Domain Electromagnetic Radiation

Farhad Rachidi-Haeri, Marcos Rubinstein

In this paper, an inequality satisfied by the vacuum energy density of the universe is derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant ...

2023

Pollution mask for the continuous corrected particle number concentration data in 1 min time resolution measured in the Swiss aerosol container using a whole air inlet during MOSAiC 2019/2020

Julia Schmale, Andrea Baccarini, Ivo Fabio Beck, Hélène Paule Angot

This dataset contains particle number concentrations and a pollution flag in 1 min time resolution. It is derived by the pollution detection algorithm (PDA, doi:10.5281/zenodo.5761101) based on the corrected particle number concentration data of the CPC377 ...

Zenodo2023

Closed form approximation methods for portfolio valuation and risk management

Lotfi Boudabsa

In this thesis we present three closed form approximation methods for portfolio valuation and risk management. The first chapter is titled ``Kernel methods for portfolio valuation and risk management'', and is a joint work with Damir Filipovi'c (SFI and ...

EPFL2023

Pollution mask for the continuous corrected particle number concentration data in 1 min resolution, measured in the Swiss aerosol container during MOSAiC 2019/2020

Julia Schmale, Andrea Baccarini, Ivo Fabio Beck, Hélène Paule Angot

This dataset contains a pollution flag in 1 min time resolution. It is derived by the pollution detection algorithm (PDA) based on the corrected particle number concentration data (DOI upcoming) measured during the year long MOSAiC expedition from October ...

Zenodo2022

A note on universal inference

Anthony Christopher Davison, Timmy Rong Tian Tse

Universal inference enables the construction of confidence intervals and tests without regularity conditions by splitting the data into two parts and appealing to Markov's inequality. Previous investigations have shown that the cost of this generality is a ...

WILEY2022

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Daniel Kressner, Alice Cortinovis

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

2022

KPC: Learning-Based Model Predictive Control with Deterministic Guarantees

Colin Neil Jones, Yuning Jiang, Emilio Maddalena, Paul Scharnhorst

We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-pa ...

2021

Deterministic error bounds for kernel-based learning techniques under bounded noise

Colin Neil Jones, Emilio Maddalena, Paul Scharnhorst

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...

2021

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Alejandro Rivera

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

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

Michel Bierlaire

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

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

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, Wolfram Wiesemann, Napat Rujeerapaiboon

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

Generalized Gauss Inequalities via Semidefinite Programming

Daniel Kuhn

A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...

Springer Verlag2016

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

APPROXIMATING k-MEDIAN VIA PSEUDO-APPROXIMATION

Ola Nils Anders Svensson

We present a novel approximation algorithm for k-median that achieves an approximation guarantee of 1 + root 3 + epsilon, improving upon the decade-old ratio of 3 + epsilon. Our improved approximation ratio is achieved by exploiting the power of pseudo-app ...

Siam Publications2016

A Distributionally Robust Perspective on Uncertainty Quantification and Chance Constrained Programming

Daniel Kuhn, Wolfram Wiesemann, Grani Adiwena Hanasusanto

The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and mai ...

Springer Verlag2015