Use quadrature rules in Owen Sampling

[janosg]

Owen sampling has roughly the following structure:

for idx in data.indices:
    for prob in np.linspace(0, 1, n_samples_outer):
        for _ in range(n_samples_inner):
            # draw samples and calculate utilites with and without index

The loop over probabilities controls the size of the samples. The fixed grid is a discrete approximation of an integral.

We should investigate the following questions:

• Can we use standard quadrature rules to approximate the integral more efficiently than with a uniform grid?
• Can we learn from other methods (e.g Truncated Permutation Sampling) which set sizes should be sampled with a lower frequency?

My rough intuition is that very small sample sizes should be avoided because they yield very noisy value estimates and very large samples should be avoided because no single data point contributes a lot of value if the sample size is large.