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 ReLU networks.

翻译：我们考虑使用集成卡尔曼滤波器的适当扩展对逻辑回归执行贝叶斯推断的问题。提出了两种交互粒子系统，用于从近似后验分布中采样，并证明了当粒子数趋于无穷大时，这些交互粒子系统向平均场极限的定量收敛速率。此外，我们应用这些技术，并检验其作为贝叶斯逼近方法在量化ReLU网络预测不确定性方面的有效性。