Related papers: Limit theorems for stochastic approximation algori…

We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.

In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…

We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After…

We study a mutliscale jump process introduced in a work by Crudu, Debussche, Muller and Radulescu. Using an adequate coupling, we are able to prove the strong convergence, for the uniform topology, to a piecewise deterministic Markov…

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…

There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…

This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated…

We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.

In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can…

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…

In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…

In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…

We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…

In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been argued that the asymptotic covariance of the method is best…

Stochastic optimization naturally appear in many application areas, including machine learning. Our goal is to go further in the analysis of the Stochastic Average Gradient Accelerated (SAGA) algorithm. To achieve this, we introduce a new…