1 理論
EM算法通過迭代求解觀測數據的對數似然函數的極大化,實現極大似然估計。每次迭代包括兩步:
- 步:求期望
- 步:求極大
2 代碼
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 參考
理論:周志華《機器學習》,李航《統計學習方法》
代碼:https://github.com/fengdu78/lihang-code