Timeline for HMM with emission depending on past states

4 events

when toggle format	what		by	license	comment
Jun 26, 2018 at 21:58	vote	accept	Gonzalo Benegas
May 12, 2018 at 0:27	comment	added	Pierrot		Well then, for exact calculation of the likelihood, it might be difficult unless you leverage model-specific information. However you can turn to simulation-based approaches. For instance, in section 6.2 of "Particle Gibbs with Ancestor Sampling" by Lindsten, Jordan and Schön (jmlr.org/papers/volume15/lindsten14a/lindsten14a.pdf), Bayesian inference is described for a model where Y_t depends on all the past states X_1, ..., X_t. In general particle filters are directly implementable in this setting and provide likelihood estimators, see e.g. the particle MCMC literature.
May 11, 2018 at 3:33	comment	added	Gonzalo Benegas		Thank you. I have talked to people who have tried this approach on the problem, and it has been useful, however, it did not scale well with the number of past states (we are considering using 20 instead of 10, for example). The space Z becomes too big, even if the transition matrix is sparse. Any suggestion on how to overcome this?
May 11, 2018 at 1:22	history	answered	Pierrot	CC BY-SA 4.0