Related papers: On the Supremum of Random Dirichlet Polynomials
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
We compute the leading asymptotics of the maximum of the (centered) logarithm of the absolute value of the characteristic polynomial, denoted $\Psi_N$, of the Ginibre ensemble as the dimension $N$ of the random matrix tends to infinity. The…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum…
This work develops algorithms for non-parametric confidence regions for samples from a univariate distribution whose support is a discrete mesh bounded on the left. We generalize the theory of Learned-Miller to preorders over the sample…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
We show that the max entropy algorithm can be derandomized (with respect to a particular objective function) to give a deterministic $3/2-\epsilon$ approximation algorithm for metric TSP for some $\epsilon > 10^{-36}$. To obtain our result,…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…