Question about alpha calculation in forward pass

[ncguilbeault]

Hi,

Thank you for developing this fantastic tool!

I have a question regarding the use of your package for performing online inference. Specifically, I am trying to implement the equation 𝛼hat = 𝑃(𝑧𝑛 ∣ 𝑥1, … , 𝑥𝑛) as described in Bishop (2006).

Does your package or API include a function that calculates this directly? From my review of the source code, the closest functionality I found is in the forward_pass function where the alphas are computed (this line in messages.py). Is this 𝛼 the same as 𝛼hat?

Any insights or guidance you can provide would be greatly appreciated.

Best regards,
Nick

[joacorapela]

Hello Nick,

$\hat{\alpha}_n=P(z_n|x_1,\ldots,x_n)$, in Eq. 13.55 of Bishop, 2006, is computed inside function hmm_filter in variable pz_tt, but it is not returned by this fuction. It only returns $P(z_{n+1}|x_1,\ldots,x_n)$. It would be better if hmm_filter, and function filter which calls it, returned both of these quantities.

@slinderman would a pull request changing the return values of these functions be welcomed?

Joaquin