Efficiency of constrained Poisson regression

Modeling
,
1

I have a large model (~100k parameters, ~1.6M observations) with a Poisson GLM likelihood. The relevant bits are:

...
parameters {
    vector[n_coeffs] gamma_raw;
    ...
}

transformed parameters {
    vector[n_coeffs] gamma = 0.1*gamma_raw;
    ...
}

model {
  ...
  y ~ poisson_log_glm(X, alpha, gamma);
}

The scaling is so that gamma_raw are on the unit scale. n_coeffs is small (~40), the high-dimensional part is alpha, and there is a lot of work going on in transformed parameters to set it up.

This model fits well enough, but a couple of gammas are not as expected. I realised that domain knowledge implies that some of them should be greater than others or than 0. I have therefore imposed constraints as follows:

parameters {
    positive_ordered[2] zeta_euro;
    ordered[4]          zeta_intl;
    vector[2]           zeta_rest;
    vector[n_coeffs-8]  gamma_raw;
    ...
}

transformed parameters {
    vector[8]          zeta;
    vector[n_coeffs-8] gamma = 0.1*gamma_raw;


    zeta = 0.1*append_row(append_row(zeta_euro, zeta_intl), zeta_rest);
    ...
}

model {
  ...
  y ~ poisson_log_glm(X, alpha, append_row(zeta, gamma));
}

This fits well and zetas are as expected, but it takes 2-3x longer in wall clock time, even though treedepth, acceptance rate and step size are all pretty much the same (treedepth exactly equal). I know that append_row copies things, but it’s not that much at the end of the day. This leaves the constraints – are they inherently costly, or can I do something clever here to get back close to previous fitting times?

2

My apologies to anyone who spent time thinking about it. The problem was with my local hardware. In the cloud, the constrained model runs as gingerly as the unconstrained one.