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Concept

Event (probability theory)

Related publications (22)

Mean value theorems for collections of lattices with a prescribed group of symmetries

Nihar Prakash Gargava

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

A multigrid method for PDE-constrained optimization with uncertain inputs

Fabio Nobile, Tommaso Vanzan

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

Springer Science and Business Media LLC2024

Preconditioners for robust optimal control problems under uncertainty

Fabio Nobile, Tommaso Vanzan

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2023

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

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

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

Daniel Maria Busiello

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the th ...

2020

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

Positivity of the CM line bundle for families of K-stable klt Fano varieties

Zsolt Patakfalvi, Giulio Codogni

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...

2021

Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations

Assyr Abdulle, Gilles Vilmart

In this paper, we propose a new approach for sampling from probability measures in, possibly, high-dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the invariant measure of t ...

2019

One-shot learning and behavioral eligibility traces in sequential decision making

Michael Herzog, Wulfram Gerstner, Kerstin Preuschoff, He Xu, Marco Philipp Lehmann, Vasiliki Liakoni

In many daily tasks, we make multiple decisions before reaching a goal. In order to learn such sequences of decisions, a mechanism to link earlier actions to later reward is necessary. Reinforcement learning (RL) theory suggests two classes of algorithms s ...

2019

Selection Bias in News Coverage: Learning it, Fighting it

Karl Aberer, Jérémie Rappaz

News entities must select and filter the coverage they broadcast through their respective channels since the set of world events is too large to be treated exhaustively. The subjective nature of this filtering induces biases due to, among other things, res ...

2018

Representing groups against all odds

Maxime Gheysens

We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...

EPFL2017

Probabilistic Derivation of Spatiotemporal Correlation Functions in the Hydrodynamic Limit

Sara Bonella

In this paper, we use probability theory to prove in suitable conditions the equivalence of equilibrium time correlation functions of microscopic density fields with the time correlation functions of local macroscopic density fields evolved by hydrodynamic ...

Amer Chemical Soc2016

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...

Springer2016

What’s the Frequency, Kenneth?: Sublinear Fourier Sampling Off the Grid

Volkan Cevher, Yen-Huan Li

We design a sublinear Fourier sampling algorithm for a case of sparse off-grid frequency recovery. These are signals with the form f(t)=∑kj=1ajeiωjt+ν^ , t∈Z ; i.e., exponential polynomials with a noise term. The frequencies {ω j } satisfy ω j ∈ [η,2π − η ...

Springer Verlag2015

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

Cast aluminium microwires : processing and plastic deformation

Jérôme Krebs

Plasticity size effects have been the focus of strong recent interest due to the miniaturization of devices such as actuators and different medical apparatuses. Devices with a sub-micrometre dimension have a high market potential and therefore a thorough u ...

EPFL2015

A stochastic collocation method for the second order wave equation with a discontinuous random speed

Fabio Nobile

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and ...

Springer2013

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

Choice Probability Generating Functions

Michel Bierlaire

This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (C ...

2013