A note on exact correspondences between adaptive learning algorithms and the Kalman filter

► The correspondence between learning algorithms and the Kalman filter is generalized. ► Both least squares and stochastic gradient are covered in the same united framework. ► Our approach derives these correspondences from the algorithms' non-recursive forms. ► The algorithms' gains are allowed to be (unrestrictedly) time-varying. ► Our correspondences hold exactly, instead of asymptotically approximated.