Deep Importance Sampling based on Regression for Model Inversion and Emulation
arXiv:2010.10346 · doi:10.1016/j.dsp.2021.103104
Abstract
Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and optimization. They require the choice of a suitable proposal density that is crucial for their performance. For this reason, several adaptive importance sampling (AIS) schemes have been proposed in the literature. We here present an AIS framework called Regression-based Adaptive Deep Importance Sampling (RADIS). In RADIS, the key idea is the adaptive construction via regression of a non-parametric proposal density (i.e., an emulator), which mimics the posterior distribution and hence minimizes the mismatch between proposal and target densities. RADIS is based on a deep architecture of two (or more) nested IS schemes, in order to draw samples from the constructed emulator. The algorithm is highly efficient since employs the posterior approximation as proposal density, which can be improved adding more support points. As a consequence, RADIS asymptotically converges to an exact sampler under mild conditions. Additionally, the emulator produced by RADIS can be in turn used as a cheap surrogate model for further studies. We introduce two specific RADIS implementations that use Gaussian Processes (GPs) and Nearest Neighbors (NN) for constructing the emulator. Several numerical experiments and comparisons show the benefits of the proposed schemes. A real-world application in remote sensing model inversion and emulation confirms the validity of the approach.
References in corpus (24)
- Learning graphs from data: A signal representation perspective
- Adaptive Importance Sampling in General Mixture Classes
- Effective Sample Size for Importance Sampling based on discrepancy measures
- Generalized Multiple Importance Sampling
- Cooperative Parallel Particle Filters for online model selection and applications to Urban Mobility
- Layered Adaptive Importance Sampling
- Physics-Aware Gaussian Processes in Remote Sensing
- Improved Adaptive Rejection Metropolis Sampling Algorithms
- Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes
- Bayesian Re-analysis of the Gliese 581 Exoplanet System
- Emulation of reionization simulations for Bayesian inference of astrophysics parameters using neural networks
- Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
- Marginal likelihood computation for model selection and hypothesis testing: an extensive review
- Group Importance Sampling for Particle Filtering and MCMC
- Active emulation of computer codes with Gaussian processes -- Application to remote sensing
- A Perspective on Gaussian Processes for Earth Observation
- Importance Gaussian Quadrature
- Discovery of WASP-113b and WASP-114b, two inflated hot-Jupiters with contrasting densities
- Adaptive Independent Sticky MCMC algorithms
- Two Jovian planets around the giant star HD202696. A growing population of packed massive planetary pairs around massive stars?
- Adaptive quadrature schemes for Bayesian inference via active learning
- Moving Target Monte Carlo
- Model Evidence with Fast Tree Based Quadrature
- Tree pyramidal adaptive importance sampling