Publications related to Chebyshev's inequality

Inequality in genetic cancer risk suggests bad genes rather than bad luck

Heritability is often estimated by decomposing the variance of a trait into genetic and other factors. Interpreting such variance decompositions, however, is not straightforward. In particular, there is an ongoing debate on the importance of genetic factor ...

2017

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Assyr Abdulle, Gilles Vilmart

A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or Chebyshev method) for ...

MATHICSE2017

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Assyr Abdulle, Gilles Vilmart

A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or Chebyshev method) for ...

MATHICSE2017

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

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces

P_\Lambda := span\{y \mapsto y^\nu | \nu \in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma := [-1,1]^d

, based on the sa ...

MATHICSE2015

A Distributionally Robust Perspective on Uncertainty Quantification and Chance Constrained Programming

Daniel Kuhn, Grani Adiwena Hanasusanto, Wolfram Wiesemann

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

Distributionally Robust Logistic Regression

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ...

2015

A New Entropy Power Inequality for Integer-Valued Random Variables

Emmanuel Abbé, Saeid Haghighatshoar

The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for spe ...

Institute of Electrical and Electronics Engineers2014

Chebyshev's inequality

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Inequality in genetic cancer risk suggests bad genes rather than bad luck

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Generalized Gauss Inequalities via Semidefinite Programming

Dimensionality Reduction in Dynamic Optimization under Uncertainty

APPROXIMATING k-MEDIAN VIA PSEUDO-APPROXIMATION

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

A Distributionally Robust Perspective on Uncertainty Quantification and Chance Constrained Programming

Distributionally Robust Logistic Regression

A New Entropy Power Inequality for Integer-Valued Random Variables

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Distributionally Robust Logistic Regression

Inequality in genetic cancer risk suggests bad genes rather than bad luck

Generalized Gauss Inequalities via Semidefinite Programming

Dimensionality Reduction in Dynamic Optimization under Uncertainty

APPROXIMATING k-MEDIAN VIA PSEUDO-APPROXIMATION

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

A Distributionally Robust Perspective on Uncertainty Quantification and Chance Constrained Programming

A New Entropy Power Inequality for Integer-Valued Random Variables