Affine-Invariant Ensemble Transform Methods for Logistic Regression

Abstract We investigate the application of ensemble transform approaches to Bayesian inference logistic regression problems. Our approach relies on appropriate extensions popular Kalman filter and feedback particle cross entropy loss function is based a well-established homotopy inference. The arising finite evolution equations as well their mean-field limits are affine-invariant. Furthermore, proposed methods can be implemented in gradient-free manner case nonlinear data randomly subsampled similar mini-batching stochastic gradient descent. also propose closely related SDE-based sampling method which again affine-invariant easily made gradient-free. Numerical examples demonstrate appropriateness methodologies.