Related papers: Least Squares Importance Sampling for Libor Market…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function,…
Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expression of the sum distribution is usually intractable and presents an open problem. A crude Monte…
The importance sampling (IS) method lies at the core of many Monte Carlo-based techniques. IS allows the approximation of a target probability distribution by drawing samples from a proposal (or importance) distribution, different from the…
Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model with the integrand as response and the control…
Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of…
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
Evaluating expectations on an Ising model (or Boltzmann machine) is essential for various applications, including statistical machine learning. However, in general, the evaluation is computationally difficult because it involves intractable…
Variational inference consists in finding the best approximation of a target distribution within a certain family, where `best' means (typically) smallest Kullback-Leiber divergence. We show that, when the approximation family is…
The quasi-Monte Carlo method is widely used in computational finance, whose efficiency strongly depends on the smoothness and effective dimension of the integrand. In this work, we investigate the combination of importance sampling and the…
We propose bandit importance sampling (BIS), a powerful importance sampling framework tailored for settings in which evaluating the target density is computationally expensive. BIS facilitates accurate sampling while minimizing the required…
In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic…
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates…
Multiple importance sampling (MIS) is employed to reduce variance of estimators, but when sampling and weighting are not suitable to the integrand, the estimators would have extra variance. Therefore, robust light transport simulation…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…