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poypoyan / edhsmm

An(other) implementation of Explicit Duration Hidden Semi-Markov Models in Python 3
MIT License
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What is the selection criteria of D in HSMM? #5

Closed Wusir2018 closed 4 years ago

poypoyan commented 4 years ago

Oh sorry for late reply huhuhu

In my code, "maximum segment length" is the n_durations variable.

The duration probabilities are stored in a 2D array with n_states rows and n_durations columns. Each entry is the p_j(d), the probability that state j lasts at duration d. During the parameter estimation (the fit function), for a state that corresponds to some smaller segment than n_durations, we should expect to see p_j(d*) peaking at some d* < n_durations (and practically-zeroes at durations near n_durations). That's why we could learn states of smaller segments.

Hence, in the code, treat the "maximum segment length"/n_durations as a "memory limit" variable. Ideally, we should detect segments of any length, but for EM algorithm at least, that means looping up to infinity. So there's a trade-off: you may set n_durations as high as you want (maybe equal to the length of the training data), but of course it will be slower and takes a lot of memory.

My code is still under development. I am still studying some functionalities to add (as written in the readme). Thanks!

Wusir2018 commented 4 years ago

@poypoyan Thank you for your reply! It means that Duration (D) in HSMM is a probability distribution, so the smaller segment can transit to next state. Poisson distribution is used to denote the duration distribution. I have a question about how to chose the parameters of Poisson distribution ($\lambda$) ?

Best wishes!

poypoyan commented 4 years ago

It means that Duration (D) in HSMM is a probability distribution, so the smaller segment can transit to next state.

Yeah, there is a duration distribution for each state in (explicit-duration) hsmm. Please take note that there are many other variants of hsmm, and probably those have more (or different) parameters than explicit-duration hsmm.

Poisson distribution is used to denote the duration distribution. I have a question about how to chose the parameters of Poisson distribution ($\lambda$) ?

As of now, my code doesn't support Poisson distribution as duration distribution (yet). For now, the duration distribution for each state j is stored as the rows of the 2D array in my reply above. I call it "non-parametric" because there is no assumed "formula" for distribution: just probability values for d in range(n_durations). As for choosing the $\lambda$, I think it should be learned during the fit function, but I am still studying how to do it (along with other distributions like Negative Binomial, Geometric, etc.).

Ask questions for clarifications. Thanks!

Wusir2018 commented 4 years ago

@poypoyan Thank you very much! :)