Related papers: On Exponential Convergence of Random Variables
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
In the context of stability of the extremes of a random variable X with respect to a positive integer valued random variable N we discuss the cases (i) X is exponential (ii) non-geometric laws for N (iii) identifying N for the stability of…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted…
Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work…
We estimate density and regression functions for weak dependant datas. Using an exponential inequality obtained by Dedecker and Prieur and in a previous article of the author, we control the deviation between the estimator and the function…
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
In this paper it is shown that adaptive importance sampling algorithms converge at exponential rate for Markov chain expectation problems that admit a combination of a filtered estimator and a Markov zero-variance measure. It extends a…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…