The internals of all four logistic models are here, with some performance comparison at the end of this post. The projection trick does not extend to logistic and genotype sparsity doesn’t help much as the sample covariates are dense and used alongside in each iteration. We’ve also tried using QR and triangular solve in Newton iteration to avoid direct inversion of the Hessian (Fisher info), but found this does worse, likely because the number of covariates is tiny compared to the number of samples. If you really want to optimize single-core performance, check out the vectorization tricks in TopCoder competition. In the end, logistic regression is per variant and scales beautifully with cores, so does not seem to be a pressing computational bottleneck for Hail (though we may circle back to make it more efficient in the future).