混合ガウス分布のパラメータ推定

gmm.py

import numpy as np
import numpy.random as nprand
import matplotlib.pyplot as plt

def dnorm(x, m, s):
    return np.exp(-((x - m) ** 2)/(2 * s)) / np.sqrt(2 * np.pi * s)

def EM(data, init, iter):
    params = np.array(init)

    for _ in range(iter):
        w = np.array(map(lambda d: d/sum(d), [[dnorm(d, p[0], p[1]) * p[2] for p in params] for d in data])).T
        c = map(sum, w)
        for i, v in enumerate(params):
            params[i, 0] = sum([w[i, j] * d for j, d in enumerate(data)]) / c[i]
            params[i, 1] = sum([w[i, j] * (d - params[i, 0]) ** 2 for j, d in enumerate(data)]) / c[i]
            params[i, 2] = c[i] / len(data)

    return params

def main():
    params = [[-7, 2, 0.3], [-2, 1, 0.5], [4, 3, 0.2]]
    xs = np.linspace(-15, 15, 1000)
    ys = [sum([dnorm(x, m, s) * c for m, s, c in params]) for x in xs]
    plt.plot(xs, ys, label = "base")

    data = reduce(lambda r, l: r + l, [nprand.normal(m, np.sqrt(s), c * 500).tolist() for m, s, c in params], [])
    for i in map(lambda x: 2 ** x, range(5)):
        est = EM(data, [[-6, 2, 0.3], [0, 2, 0.4], [6, 2, 0.3]], i)
        ys = [sum([dnorm(x, m, s) * c for m, s, c in est]) for x in xs]
        plt.plot(xs, ys, label = "iter-%d" % i)

    plt.legend(loc = "best")
    plt.show()

if __name__ == '__main__':
    main()