A quantitative central limit theorem for the random walk among random conductances

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and ...

One major challenge in distributed learning is to efficiently learn for each client when the data across clients is heterogeneous or non iid (not independent or identically distributed). This provides a significant challenge as the data of the other client ...

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g. random utility maximisation). In the presence of outliers, ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

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 ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

There is sustained and widespread interest in understanding the limit, if there is any, to the human life span. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social security sys ...

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether higher-order approxima ...

The convergence speed of machine learning models trained with Federated Learning is significantly affected by non-independent and identically distributed (non-IID) data partitions, even more so in a fully decentralized setting without a central server. In ...

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

Peaks-over-threshold analysis using the generalised Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results. In this paper, w ...

Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then th ...

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as max ...

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

Understanding the diffusion patterns of sequences of interdependent events is a central question for a variety of disciplines. Temporal point processes are a class of elegant and powerful models of such sequences; these processes have become popular across ...

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. ...

A quantitative central limit theorem for the random walk among random conductances

Chat with Graph Search

Anthony C Davison and Igor Rodionov's contribution to the Discussion of 'Estimating means of bounded random variables by betting' by Waudby-Smith and Ramdas

Personalized Privacy-Preserving Distributed Learning on Heterogeneous Data

Unlikely intersections on the p-adic formal ball

Robust discrete choice models with t-distributed kernel errors

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Preconditioners for robust optimal control problems under uncertainty

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

A Functional Perspective on Information Measures

Is There a Cap on Longevity? A Statistical Review

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Improved Inference On Risk Measures For Univariate Extremes

D-Cliques: Compensating for Data Heterogeneity with Topology in Decentralized Federated Learning

Localization errors of the stochastic heat equation

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Functional peaks-over-threshold analysis

Sub‐asymptotic motivation for new conditional multivariate extreme models

Multivariate extremes over a random number of observations

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Learning Self-Exciting Temporal Point Processes Under Noisy Observations

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