statsmodels.genmod.bayes_mixed_glm.PoissonBayesMixedGLM.fit_vb¶
- PoissonBayesMixedGLM.fit_vb(mean=None, sd=None, fit_method='BFGS', minim_opts=None, scale_fe=False, verbose=False)¶
Fit a model using the variational Bayes mean field approximation.
- Parameters:
- meanarray_like
Starting value for VB mean vector
- sdarray_like
Starting value for VB standard deviation vector
- fit_method
str Algorithm for scipy.minimize
- minim_opts
dict Options passed to scipy.minimize
- scale_febool
If true, the columns of the fixed effects design matrix are centered and scaled to unit variance before fitting the model. The results are back-transformed so that the results are presented on the original scale.
- verbosebool
If True, print the gradient norm to the screen each time it is calculated.
Notes
The goal is to find a factored Gaussian approximation q1*q2*… to the posterior distribution, approximately minimizing the KL divergence from the factored approximation to the actual posterior. The KL divergence, or ELBO function has the form
E* log p(y, fe, vcp, vc) - E* log q
where E* is expectation with respect to the product of qj.
References
Blei, Kucukelbir, McAuliffe (2017). Variational Inference: A review for Statisticians https://arxiv.org/pdf/1601.00670.pdf