What are Linear time MMD and Quadratic time MMD in Shogun

In this recipe, we shall learn what are Linear time MMD and Quadratic time MMD in Shogun with the help of simple examples.

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Recipe Objective: What are Linear time MMD and Quadratic time MMD in Shogun?

This recipe explains what Linear time MMD and Quadratic time MMD in Shogun are.
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Linear Time MMD

The linear time MMD implements a nonparametric statistical hypothesis test to reject the null hypothesis that to distributions p and q, only observed via n samples are the same.

# Linear Time MMD
MMD = LinearTimeMMD()
w = 1000
k = GaussianKernel(10, 1)
MMD.set_kernel(k)
MMD.set_p(p)
MMD.set_q(q)
MMD.set_num_samples_p(w)
MMD.set_num_samples_q(w)
a = 0.05

Quadratic Time MMD

The quadratic time MMD implements a nonparametric statistical hypothesis test to reject the null hypothesis that distributions p and q, only observed via n and m samples, respectively, are the same.

# Quadratic Time MMD
p = RealFeatures(f_p)
q = RealFeatures(f_q)

MMD = QuadraticTimeMMD(p, q)
k = GaussianKernel(10, 1)
MMD.set_kernel(k)

MMD.set_statistic_type(ST_BIASED_FULL)
stats = MMD.compute_statistic()

MMD.set_null_approximation_method(NAM_PERMUTATION)
MMD.set_num_null_samples(200)
val = MMD.compute_p_value(stats)

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