1 理论
EM算法通过迭代求解观测数据的对数似然函数的极大化,实现极大似然估计。每次迭代包括两步:
- 步:求期望
- 步:求极大
2 代码
class EM:
def __init__(self, prob):
self.pro_A, self.pro_B, self.pro_C = prob
# E步
def pmf(self, i):
pro_1 = self.pro_A * math.pow(self.pro_B, data[i]) * math.pow(
(1 - self.pro_B), 1 - data[i])
pro_2 = (1 - self.pro_A) * math.pow(self.pro_C, data[i]) * math.pow(
(1 - self.pro_C), 1 - data[i])
return pro_1 / (pro_1 + pro_2)
# M步
def fit(self, data):
count = len(data)
for d in range(count):
_ = yield
_pmf = [self.pmf(k) for k in range(count)]
pro_A = 1 / count * sum(_pmf)
pro_B = sum([_pmf[k] * data[k] for k in range(count)]) / sum(
[_pmf[k] for k in range(count)])
pro_C = sum([(1 - _pmf[k]) * data[k]
for k in range(count)]) / sum([(1 - _pmf[k])
for k in range(count)])
self.pro_A = pro_A
self.pro_B = pro_B
self.pro_C = pro_C
3 参考
理论:周志华《机器学习》,李航《统计学习方法》
代码:https://github.com/fengdu78/lihang-code