- E. Xing, Scribes Jing Chen, Yulan Huang, Yu-Fang, V. ary. 2016. 12 : Variational Inference I. Abstract: From last lecture, we have introduced Kalman Filtering as a recursive procedure to update the belief state. In each iteration, there are two steps: Predict Step and Update Step. In Predict Step, we compute latent state distribution P (X t+1|y1:t) from prior belief P (Xt|y1:t) and dynamic model p(Xt+1|Xt). This step is also called time update. In Update Step, we compute new belief of the latent state distribution p(X t+1|y1:t+1) from prediction p(X t+1|y1:t) and observation yt+1 by using the observation model p(yt+1|Xt+1). The step is also called measurement update since its using the measured information y t+1. The reason for doing so is that under a joint multivariant gaussian distribution, we can compute the conditional influences, marginal influences easily. Since all distributions are gaussian, their linear combinations are also gaussian. Hence we just need the mean and covariance, which can be computed easily in this case, to describe the influence.
