Wrong LDA hyperparameter offset (downweighting factor tau0)?

[jonaschn]

I observed that the hyperparameter offset (introduced as downweighting factor in aa56561) which corresponds to tau_0 from Hoffman et al. is set differently compared to the original algorithm proposed by Hoffman.

    self._tau0 = tau0 + 1

When passing tau0 to his algorithm, tau0 + 1 is actually used in the calculation of rhot:

    rhot = pow(self._tau0 + self._updatect, -self._kappa)

This line is used here and here.

The commit edc3ce5 in gensim further changes the computation of rho (in order to pay attention to multi-pass algorithm as discussed in #298:

https://github.com/RaRe-Technologies/gensim/blob/351456b4f7d597e5a4522e71acedf785b2128ca1/gensim/models/ldamodel.py#L963-L967

I wonder if there is any rationale behind this decision to deviate from Hoffman's tau0 or if this was unintended?

[jonaschn]

I find this resource helpful: https://vb-learning-rate-demo.herokuapp.com to see how the parameters offset (tau) and decay (kappa) affect the learning rate of the online VB method

The source code by @ecoronado92 could be found here.