Related papers: Importance Sampling Variance Reduction for the Fok…
We overview a series of recent works devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires solving a set of problems at the micro scale, the so-called corrector problems. In a…
Efficiently solving the Fokker-Planck equation (FPE) is crucial for understanding the probabilistic evolution of stochastic particles in dynamical systems, however, analytical solutions or density functions are only attainable in specific…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
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…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system,…
Importance sampling (IS) is an important technique to reduce the estimation variance in Monte Carlo simulations. In many practical problems, however, the use of IS method may result in unbounded variance, and thus fail to provide reliable…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
In non-linear estimations, it is common to assess sampling uncertainty by bootstrap inference. For complex models, this can be computationally intensive. This paper combines optimization with resampling: turning stochastic optimization into…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
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…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing…
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…
The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric…
Estimating the expectations of functionals applied to sums of random variables (RVs) is a well-known problem encountered in many challenging applications. Generally, closed-form expressions of these quantities are out of reach. A naive…