2025/02/28 by Tronarp, Filip
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2502.21116
In this article, the two filter formula is re-examined in the setting of partially observed Gauss--Markov models. It is traditionally formulated as a filter running backward in time, where the Gaussian density is parametrized in ``information form''. However, the quantity in the backward recursion is strictly speaking not a distribution, but a likelihood. Taking this observation seriously, a recursion over log-quadratic likelihoods is formulated instead, which obviates the need for ``information'' parametrization. In particular, it greatly simplifies the square-root formulation of the algorithm. Furthermore, formulae are given for producing the forward Markov representation of the a posteriori distribution over paths from the proposed likelihood representation.