Local Adaptive Importance Sampling for Multivariate Densities With Strong Nonlinear Relationships

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Abstract
We consider adaptive importance sampling techniques that use kernel density estimates at each iteration as importance sampling functions. These can provide more nearly constant importance weights and more precise estimates of quantities of interest than the sampling importance resampling algorithm when the initial importance sampling function is diffuse relative to the target. We propose a new method that adapts to the varying local structure of the target. When the target has unusual structure, such as strong nonlinear relationships between variables, this method provides estimates with smaller mean squared error than alternative methods.

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