How was dQi and dri calculated in EP-stan?

Modeling
1

Hi I am almost done figuring out the entire EP-stan code. there is this last lingering question in the Worker.tilted() code. I understand how you can obtain the new tilted distribution Q and r using stan sampling. But in the process of deriving dQi and dri to pass back to the master, I am lost on two points

  1. why is both dgeqrf_routine and invert_normal_params called? my understanding is they both do conversion between normalized and unnormalized precision and location parameters.

  2. The sampling process should be creating the new Qi and ri. But I am not sure how the code ends up with dQi, and dri. I don’t see a subtraction taking place against the original Qi and ri.

2

Hello,

Thank you for the questions. I’ll gladly explain.

  1. samp contains collection of samples of phi for the tilted distribution. We need to invert the scatter matrix. We do that with QR decomposition.
    dgeqrf_routine is used to obtain QR-decomposition of the samples (in-place) of which we only need the R matrix. invert_normal_params then computes the inverse and precision mean vector estimate given R. See appendix A.2 in https://arxiv.org/abs/1412.4869

  2. There is the following code block which calculates the difference. Before this block, dQi, dri contains estimated tilted distribution natural parameters. After this block, they contain the change in the site distribution parameters.

# Calculate the difference into the output arrays
np.subtract(dQi, self.Q, out=dQi)
np.subtract(dri, self.r, out=dri)

Regards,
Tuomas Sivula

3

Ah, now I see those subtract lines. Thank you.