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We consider the problem of performing Bayesian inference for logisticregression using appropriate extensions of the ensemble Kalman filter. Twointeracting particle systems are proposed that sample from an approximateposterior and prove quantitative convergence rates of these interactingparticle systems to their mean-field limit as the number of particles tends toinfinity. Furthermore, we apply these techniques and examine theireffectiveness as methods of Bayesian approximation for quantifying predictiveuncertainty in ReLU networks.

Affine Invariant Ensemble Transform Methods to Improve Predictive Uncertainty in ReLU Networks