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add example of learning a directed graphical model #113

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murphyk opened this issue Feb 12, 2022 · 1 comment
Open

add example of learning a directed graphical model #113

murphyk opened this issue Feb 12, 2022 · 1 comment
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documentation Improvements or additions to documentation

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@murphyk
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murphyk commented Feb 12, 2022

It would be cool to show how to fit an HMM with Gaussian local evidence potentials.
The model would be

p(z(1:T)) = 1/Z prod_{t=1} Psi(z(t), z(t-1)) Phi(z(t))
 Psi(z(t), z(t-1)) = p(z(t)|z(t-1))
Phi(z(t)) = gauss(x(t) | mu_{z(t)}, sigma I)

You use LBP to compute the (exact!) marginal likelihood and then do gradient descent for the params.
Or you could recreate our discrete HMM example at https://github.com/probml/JSL/blob/main/jsl/demos/hmm_casino_sgd_train.py

@nathanielvirgo
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It would be great also just to have an example of inference in a directed graphical model. e.g. just the standard sprinkler example would be really useful for getting a handle on how to use the package.

@StannisZhou StannisZhou added the documentation Improvements or additions to documentation label Feb 14, 2022
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