Related papers: Importance sampling for weighted binary random mat…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…
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…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
Importance Sampling (IS) is a method for approximating expectations under a target distribution using independent samples from a proposal distribution and the associated importance weights. In many applications, the target distribution is…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We consider $N$ Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion $L_N$ of variables in a given…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…
We consider an evolving system for which a sequence of observations is being made, with each observation revealing additional information about current and past states of the system. We suppose each observation is made without error, but…
When the weights in a particle filter are not available analytically, standard resampling methods cannot be employed. To circumvent this problem state-of-the-art algorithms replace the true weights with non-negative unbiased estimates. This…
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…
This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More…
Deep generative networks can simulate from a complex target distribution, by minimizing a loss with respect to samples from that distribution. However, often we do not have direct access to our target distribution - our data may be subject…
We introduce and implement an importance-sampling Monte Carlo algorithm to study systems of globally-coupled oscillators. Our computational method efficiently obtains estimates of the tails of the distribution of various measures of…
The Bernoulli sieve is a random allocation scheme obtained by placing independent points with the uniform [0,1] law into the intervals made up by successive positions of a multiplicative random walk with factors taking values in the…