The problem considered here is a generalization of the Kalman smoothing problem with non-Markov priors on the signal dynamics and/or the measurements obey an arbitrary log-concave likelihood model. For example, a group-sparsity prior on the dynamics could be used to promote estimates where only a few elements of the latent signal vary, or Bernoulli likelihoods could be used to model binary observations. We show that the alternating direction method of multipliers enables an iterative solution wherein the observations and dynamics can be optimized for separately and subsequently merged using a standard Kalman smoother.

Relevant Publications:

• G Schamberg, D Ba, and TP Coleman, “A Modularized Efficient Framework for Non-Markov Time Series Estimation,” IEEE Transactions on Signal Processing, Volume 66, Issue 12, June 2018. [IEEE Xplore] [arXiv] [Code Ocean]
• A Allegra, A Gharibans, G Schamberg, D Kunkel, and TP Coleman, “Bayesian Inverse Methods for Spatiotemporal Characterization of Gastric Electrical Activity from Cutaneous Multi-Electrode Recording,” PLOS ONE, Volume 14, Issue 10, October 2019. [pdf]
• G Schamberg, M Wagner, D Ba, and TP Coleman, “Efficient Low-Rank Spectrotemporal Decomposition using ADMM,” IEEE Statistical Signal Processing Workshop, June 2016. [IEEE Xplore]