Brief Explanation or Pseudocode for Factorial Sampler

[tamlhp]

Dear Dr. Matthew J. Johnson,

I am very interested in your work, especially time series models. Hopefully you can find some time to help me with this issue.

This repository refers to the paper https://arxiv.org/pdf/1203.1365v2.pdf. Unfortunately, I can't find a description of sampler for the factorial structure (Section 4.3 only explains the sampler for HDP-HSMM). Experiments in Section 5.2 refers to other baselines for factorial HMM but they use EM method. Another factorial HMM is [1], but the factorial structure appears on the state level rather than the emission level.

I understand that you are busy with the new research. But I really appreciate if you can give me some hints or brief workflows to understand the code (e.g. I cant map equation 27 to the code).

Thank you very much for your time and consideration.

Best Regards,
Tam

[1] Ghahramani, Z., & Jordan, M. I. (1997). Factorial hidden Markov models. Machine Learning, 29, 245–273. http://doi.org/10.1023/A:1007425814087

[mattjj]

Hey Tam,

Thanks for your interest!

The factorial structure is the same in the two cases; it's just a minor difference in how the graphical models are drawn, and more precisely in what variables are shown. In Fig 5 of my paper, the factorial structure is still over the states, but we also show the individual component chains' emissions (denoted by y_t^{(k)}) in addition to their sum (denoted y_t).

Eq. (27) is an equation describing the model and so it doesn't appear explicitly in the inference code, but it does influence several parts of the inference code. For example, in the _sample_component_emissions_python function, the component emissions are sampled using their diagonal Gaussian prior distribution and the likelihood that arises from Eq. (27) (i.e. that at each time step the sum over component emissions is the observed data).

I'm not sure if it has any more info, but you might want to look at my thesis, which had a revised version of this paper as an early chapter.

Sorry I can't be of more help, but let me know if you're still stuck.