Related papers: On Concentration Inequalities for Random Matrix Pr…
Suppose $\{ X_k \}_{k \in \mathbb{Z}}$ is a sequence of bounded independent random matrices with common dimension $d\times d$ and common expectation $\mathbb{E}[ X_k ]= X$. Under these general assumptions, the normalized random matrix…
This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of…
We present a non-asymptotic concentration inequality for the random matrix product \begin{equation}\label{eq:Zn} Z_n = \left(I_d-\alpha X_n\right)\left(I_d-\alpha X_{n-1}\right)\cdots \left(I_d-\alpha X_1\right), \end{equation} where…
Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\ldots, Z_m$, this article provides an expression of the concentration of functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each variable…
We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This…
This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to…
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…
Let ${\cal X }=XX^{\prime}$ be a random matrix associated with a centered $r$-column centered Gaussian vector $X$ with a covariance matrix $P$. In this article we compute expectations of matrix-products of the form $\prod_{1\leq i\leq…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks…
Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis. We present a set of concentration inequalities…
Analyzing concentration of large random matrices is a common task in a wide variety of fields. Given independent random variables, many tools are available to analyze random matrices whose entries are linear in the variables, e.g. the…
This paper deduces exponential matrix concentration from a Poincar\'e inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…
In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies…