Related papers: Sharp Concentration of Simple Random Tensors
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…
We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration…
We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove…
This paper develops sharp bounds on moments of sums of k-wise independent bounded random variables, under constrained average variance. The result closes the problem addressed in part in the previous works of Schmidt et al. and Bellare,…
In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with…
Analyzing probabilistic programs and randomized algorithms are classical problems in computer science. The first basic problem in the analysis of stochastic processes is to consider the expectation or mean, and another basic problem is to…
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…
One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability.…
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…
In this short note, we provide a sample complexity lower bound for learning linear predictors with respect to the squared loss. Our focus is on an agnostic setting, where no assumptions are made on the data distribution. This contrasts with…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but rather an intrinsic notion of it. Our analysis leads to…
A random ensemble of cusp forms for the full modular group is introduced. For a weight-$k$ cusp form, restricted to a compact subdomain of the modular surface, the true order of magnitude of its expected supremum is determined to be $\asymp…
We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N…
We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…
In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes and then we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic…
We prove a tight upper bound on the variance of the priority sampling method (aka sequential Poisson sampling). Our proof is significantly shorter and simpler than the original proof given by Mario Szegedy at STOC 2006, which resolved a…
We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…