computational (time) cost

[xinyueshen]

Thanks for sharing this very interesting package! I'm trying to use it on some very simple objective functions such as \frac{1}{N}\sum_{i=1}^N\log(x_i^T \theta + \epsilon), but the time cost seems to be high. The dimension of the variable \theta is about 100, and the number of samples N is about 1e6. To get the top 50 eigenvalues, it took about 45 seconds on a GPU. Could you please give some comments on whether such timing is as expected? Thanks!

[yaozhewei]

Hi Xinyue,

Yes, it is expected. The top50 eigenvalues will be very cost using hessian.eigenvalues(). Since your problem is only about 100, I would suggest you use hessian.density(), set the niter to be exactly like your problem dimension, that should be finished very fast and give you the distribution of the full eigenvalues.

[xinyueshen]

Thanks for the response! But does hessian.density() compute and return the eigenvectors at the same time?

[xinyueshen]

I see that hessian.density() computes the eigenvalues, not the eigenvectors, but it is much faster. Thanks!