We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove quantitative convergence rates of these interacting particle systems to their mean-field limit as the number of particles tends to infinity. Furthermore, we apply these techniques and examine their effectiveness as methods of Bayesian approximation for quantifying predictive uncertainty in neural networks.

翻译：本文探讨了利用集成卡尔曼滤波的适当扩展进行逻辑回归贝叶斯推断的问题。我们提出了两种相互作用的粒子系统，这些系统能够从近似后验分布中采样，并证明了当粒子数量趋于无穷时，这些相互作用粒子系统向其平均场极限收敛的定量速率。此外，我们将这些技术应用于神经网络预测不确定性的贝叶斯近似量化，并检验其作为近似方法的有效性。