Related papers: Exact bounds on epsilon processes
We give strong bounds for the rate of convergence of the regenerative process distribution to the stationary distribution in the total variation metric. These bounds are obtained by using coupling method. We propose this method for…
The harmonizable Piranashvili-type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed.
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent copies of a random process $\{X(t), t\ge0\}$. For a given positive constant $u$, define the set of $r$th conjunctions $C_r(u):=\{t\in[0,1]: X_{r:n}(t)>u\}$ with $ X_{r:n}$ the $r$th largest…
This paper focuses on the further development of the Lie bracket approximation approach for extremum seeking systems. Classical results in this area provide extremum seeking algorithms with exponential convergence rates for quadratic-like…
We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained…
Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…
Let $\{\xi(k), k \in \mathbb{Z} \}$ be a stationary sequence of random variables and let $\{S_n, n \in \mathbb{N}_+ \}$ be a transient random walk in the domain of attraction of a stable law. In the previous work \cite{Nicolas_Ahmad}, under…
We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of first-order and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
A new recalibration post-processing method is presented to improve the quality of the posterior approximation when using Approximate Bayesian Computation (ABC) algorithms. Recalibration may be used in conjunction with existing…
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
In the problem called single resource constraint scheduling, we are given $m$ identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource $R$. A schedule of these jobs is…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$…
Neural oscillators, originating from second-order ordinary differential equations (ODEs), have demonstrated strong performance in stably learning causal mappings between long-term sequences or continuous temporal functions, as well as in…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…