Related papers: Derandomizing Chernoff Bound with Union Bound with…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

For the Hahn and Krawtchouk polynomials orthogonal on the set $\{0, \ldots,N\}$ new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These…

Let $\gamma_k=[x_1,\dots,x_k]$ be the $k$-th lower central group-word. Given a group $G$, we write $X_k(G)$ for the set of $\gamma_k$-values and $\gamma_k(G)$ for the $k$-th term of the lower central of $G$. This paper deals with groups in…

Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…

This paper introduces a distribution-dependent PAC-Chernoff bound that exhibits perfect tightness for interpolators, even within over-parameterized model classes. This bound, which relies on basic principles of Large Deviation Theory,…

We give a new simple proof of boundedness of the family of semistable sheaves with fixed numerical invariants on a fixed smooth projective variety. In characteristic zero our method gives a quick proof of Bogomolov's inequality for…

We describe a simple polynomial-time algorithm for the CDT problem that relies on a construction of Barvinok.

We give a new proof of VC bounds where we avoid the use of symmetrization and use a shadow sample of arbitrary size. We also improve on the variance term. This results in better constants, as shown on numerical examples. Moreover our bounds…

We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…

We obtain lower bounds for the dimension of fixed loci of diagonalizable $p$-groups acting on smooth projective varieties. Those bounds depend on the modulo $p$ Chern numbers of the ambient variety, and are expressed in a natural way by…

We investigate the size of fixed point sets of automorphisms of bounded domains in $\mathbb{C}^n$. In one complex variable, a nontrivial automorphism has at most two fixed points, but in higher dimensions fixed point sets need not be…

Isoperimetric inequalities form a very intuitive yet powerful characterization of the connectedness of a state space, that has proven successful in obtaining convergence bounds. Since the seventies they form an essential tool in…

Answering a question of Gamarnik and Smedira, we give a polynomial time algorithm that approximately computes the volume of a truncation of a relaxation of the independent set polytope, improving on their quasi-polynomial time algorithm.…

We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudo-random distribution, a k-design. k-designs have the first k moments equal to those of the Haar…

We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…

Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…

We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…

We derive bounds on the size of an independent set based on eigenvalues. This generalizes a result due to Delsarte and Hoffman. We use this to obtain new bounds on the independence number of the Erd\H{o}s-R\'{e}nyi graphs. We investigate…

We consider randomized Verblunsky parameters for orthogonal polynomials on the unit circle as they relate to the problem of Steklov, bounding the polynomials' uniform norm independent of $n$.

We prove a Chernoff-type upper variance bound for the multinomial and the negative multinomial distribution. An application is also given.