Related papers: Concentration Inequalities from Likelihood Ratio M…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…
Variational inequalities as an effective tool for solving applied problems, including machine learning tasks, have been attracting more and more attention from researchers in recent years. The use of variational inequalities covers a wide…
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration results and local semicircular laws for weighted random matrices.…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the…
It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets,…
Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work…
We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for…
We derive concentration inequalities for empirical means $\frac{1}{t} \int_0^t f(X_s) ds$ where $X_s$ is an irreducible Markov jump process on a finite state space and $f$ some observable. Using a Feynman-Kac semigroup we first derive a…
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.
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…
The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also…
This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely…
We develop concentration inequalities for the $l_\infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-$h$…
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely…