相关论文: Discrepancy Bounds for a Class of Negatively Depen…
We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved…
We study the notion of $\gamma$-negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to $1$-negative dependence), but nevertheless it still ensures…
We study some notions of negative dependence of a sampling scheme that can be used to derive variance bounds for the corresponding estimator or discrepancy bounds for the underlying random point set that are at least as good as the…
In this paper, we consider the upper bound of the probabilistic star discrepancy based on Hilbert space filling curve sampling. This problem originates from the multivariate integral approximation, but the main result removes the strict…
By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\'z}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}} s \ve^{-2}$. This is equivalent to the fact that for any…
Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…
Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…
We investigate the expected star discrepancy under a newly designed class of convex equivolume partition models. The main contributions are two-fold. First, we establish a strong partition principle for the star discrepancy, showing that…
The star discrepancy $D_N^*(\mathcal{P})$ is a quantitative measure for the irregularity of distribution of a finite point set $\mathcal{P}$ in the multi-dimensional unit cube which is intimately related to the integration error of…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
Overlap between two neural quantum states can be computed through Monte Carlo sampling by evaluating the unnormalized probability amplitudes on a subset of basis configurations. Due to the presence of probability amplitude ratios in the…
Given a real symmetric positive semi-definite matrix E, and an approximation S that is a sum of n independent matrix-valued random variables, we present bounds on the relative error in S due to randomization. The bounds do not depend on the…
We establish sharp non-asymptotic probabilistic bounds for the star discrepancy of double-infinite random matrices -- a canonical model for sequences of random point sets in high dimensions. By integrating the recently proved…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
We consider the problem of approximating a function in a general nonlinear subset of $L^2$, when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…
The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…
Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy between the empirical distribution of the samples…
By a result of Heinrich, Novak, Wasilkowski and Wo\'zniakowski the inverse of the star discrepancy $n(d,\varepsilon)$ satisfies $n(d,\varepsilon)\leq c_{\abs}d\varepsilon^{-2}$. Equivalently for any $N$ and $d$ there exists a set of $N$…
We extend the notion of jittered sampling to arbitrary partitions and study the discrepancy of the related point sets. Let $\mathbf{\Omega}=(\Omega_1,\ldots,\Omega_N)$ be a partition of $[0,1]^d$ and let the $i$th point in $\mathcal{P}$ be…
Quantifying the effect of uncertainties in systems where only point evaluations in the stochastic domain but no regularity conditions are available is limited to sampling-based techniques. This work presents an adaptive sequential…