check_mixture.py

# linearity of expectation under mixture model
# license: mit
# author: vlad niculae

from scipy.stats import norm

import numpy as np

def main():
    rng = np.random.RandomState(42)

    centers = rng.randn(3)
    w = np.array([.8, .1, .1])
    stds = np.array([.5, 1., 1.])

    dists = [norm(loc=c, scale=s) for c, s in zip(centers, stds)]

    def psi(t):
        # return (1 / 3) * t ** 3
        return np.sin(t / 3)

    # mc sampling
    n_samples = 100000

    mean_mc = 0
    for _ in range(n_samples):
        h = rng.choice(3, p=w)
        t = dists[h].rvs(random_state=rng)
        mean_mc += psi(t)
    mean_mc /= n_samples
    print(mean_mc)

    # closed form:
    means = np.array([d.expect(psi) for d in dists])
    print(w @ means)


if __name__ == '__main__':
    main()