Related papers: A variational approach to dimension-free self-norm…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper…
In this paper, we prove a Berry--Esseen bound with optimal order for self-normalized sums of local dependent random variables under some mild dependence conditions. The proof is based on Stein's method and a randomized concentration…
Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…
When I first encountered PAC-Bayesian concentration inequalities they seemed to me to be rather disconnected from good old-fashioned results like Hoeffding's and Bernstein's inequalities. But, at least for one flavour of the PAC-Bayesian…
We study sequential mean estimation in $\mathbb{R}^d$. In particular, we derive time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of random vectors with high probability simultaneously across…
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala enforce…
In this paper we show an alternative approach to the concentration of truncated variation for stochastic processes on a real line. Our method is based on the moments control and can be used to generalize the results to the case of processes…
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
We revisit the convergence analysis of constant stepsize stochastic approximation (SA) with decision-dependent Markovian noise, with a focus on characterizing the stationary bias against the root of the mean-field equation. We first…
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by…
In this work we provide performance guarantees for hypocoercive non-reversible MCMC samplers $X_t$ with invariant measure $\mu_*$; our results apply in particular to the Langevin equation, Hamiltonian Monte-Carlo, and the bouncy particle…
We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…
We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via…
The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…
In this work, we investigate how to develop sharp concentration inequalities for sub-Weibull random variables, including sub-Gaussian and sub-exponential distributions. Although the random variables may not be sub-Guassian, the tail…
Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a…
We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…
We prove generalised concentration inequalities for a class of scaled self-bounding functions of independent random variables, referred to as ${(M,a,b)}$ self-bounding. The scaling refers to the fact that the component-wise difference is…
The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…