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