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Abstract:
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Particle methods provide Monte Carlo approximations of intractable quantities, such as point-wise evaluations of the likelihood in state-space models. In many settings, the interest does not lie in the value of the estimated quantity itself, but in the comparison of quantities for various parameters or inputs. For instance, we might want to compare the likelihood for two distinct parameters, or compute the gradient of the log-likelihood for parameter estimation. Such a comparison is facilitated by introducing positive correlations between the estimators produced by particle methods. We propose coupled resampling schemes that increase the correlation between two particle systems. Some of the proposed couplings rely on recent advances in optimization for transport problems. The resulting particle filters improve the performance of gradient estimators and allow perfect estimation of integrals with respect to the smoothing distribution.
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