Related papers: Appendix to "Approximating perpetuities"
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…
The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect…
We use coupling into and from the past to sample perfectly in a simple and provably fast fashion from the Vervaat family of perpetuities. The family includes the Dickman distribution, which arises both in number theory and in the analysis…
We investigate the approximation for computing the sum $a_1+...+a_n$ with an input of a list of nonnegative elements $a_1,..., a_n$. If all elements are in the range $[0,1]$, there is a randomized algorithm that can compute an…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
In this paper we study the number of key exchanges required by Hoare's FIND algorithm (also called Quickselect) when operating on a uniformly distributed random permutation and selecting an independent uniformly distributed rank. After…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We consider the simulation of distributions that are a mixture of discrete and continuous components. We extend a Metropolis-Hastings-based perfect sampling algorithm of Corcoran and Tweedie to allow for a broader class of transition…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…
We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an `imperfect' alignment, in which the shorter sequence has d units without…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…