likelihood gradient acceleration computing from Sigma matrix

[YuuuXie]

This pull request adds the function to compute likelihood gradient from Sigma matrix expression, instead of Qff. It needs to be merged after #27

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The compute_likelihood_gradient method construct Qff matrix and invert it via QR decomposition. The cost is N_full^3. While compute_likelihood_stable uses the Sigma matrix which avoids the usage of Qff.

I added the method compute_likelihood_gradient_stable which computes the gradient of compute_likelihood_stable. Now the most expensive part when using compute_likelihood_gradient_stable is the QR decomposition of matrix A to get Sigma, and the cost is N_full * N_sparse^2. Therefore, the speedup and memory saving are both (N_full / N_sparse)^2.

Notes:

For NormalizedDotProduct kernel, the computational cost can be further reduced (a bit) using the fact that Kuf_grad is only a constant different from Kuf. So for this kernel, some results can be precomputed and stored, which are used repeatedly during the training and no need for re-computing. Therefore, there are options precompute... added for some functions. This part of code might be re-organized a bit for a cleaner way.

Below is a timing report from Cameron (on the warm & melt Au dataset), where the tot_time is the total time for hyperparameter optimization. Each frame selects 5 sparse envs.

This comparison is not exact, because different training sizes have different numbers of iterations. But the speedup is still significant.

Todo

The likelihood scales with n_labels, maybe we should normalize it with n_labels?