importance_resampling.py

import math
import random
import matplotlib.pyplot as plt


class UniformDistribution:
    def __init__(self, a: float, b: float) -> None:
        self.a = a
        self.b = b

    def sample(self) -> float:
        return random.uniform(self.a, self.b)

    def pdf(self, x: float) -> float:
        return 1.0 / (self.b - self.a)


class SinDistribution:
    def sample(self) -> None:
        assert False, 'cannot sample from this distribution!'

    def pdf(self, x: float) -> float:
        return math.sin(x)


def draw_using_weights(candidates: list, weights: list) -> float:
    weight_sum = sum(weights)
    cumulation = 0.0
    rand = random.uniform(0.0, weight_sum)
    for i in range(len(weights)):
        cumulation += weights[i]
        if rand < cumulation:
            return candidates[i]


def sample_using_sir(num_candidates: int) -> float:
    source = UniformDistribution(0.0, math.pi)
    target = SinDistribution()

    candidates = []
    weights = []
    for _ in range(num_candidates):
        x = source.sample()
        w = target.pdf(x) / source.pdf(x)
        candidates.append(x)
        weights.append(w)

    y = draw_using_weights(candidates, weights)
    return y


if __name__ == "__main__":
    num_candidates = 4
    samples = [sample_using_sir(num_candidates) for _ in range(50000)]
    plt.hist(samples, bins=20)
    plt.title("Sampling Importance Resampling M=" + str(num_candidates))
    plt.show()
    plt.close()

SIRを使ってsin分布からランダムサンプリングした