Related papers: A baby steps/giant steps Monte Carlo algorithm for…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…
We show that the VC-dimension of a graph can be computed in time $n^{\log d+1} d^{O(d)}$, where $d$ is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the O(N_pix^N) barrier, and yet, they are fast enough…
Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
For the vast majority of local graph problems standard dynamic programming techniques give c^tw V^O(1) algorithms, where tw is the treewidth of the input graph. On the other hand, for problems with a global requirement (usually…
We develop new approximation algorithms for classical graph and set problems in the RAM model under space constraints. As one of our main results, we devise an algorithm for d-Hitting Set that runs in time n^{O(d^2 + d/\epsilon})}, uses…
The worst-case fastest known algorithm for the Set Cover problem on universes with $n$ elements still essentially is the simple $O^*(2^n)$-time dynamic programming algorithm, and no non-trivial consequences of an $O^*(1.01^n)$-time…
Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let $f$ be an $n$-variate polynomial given by a straight-line program, which has…
We present the first algorithm for finding holes in high dimensional data that runs in polynomial time with respect to the number of dimensions. Previous algorithms are exponential. Finding large empty rectangles or boxes in a set of points…
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…
Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role…
We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on…