Randomized trials: repeatability, observability, uncertainty.
Conditional probability
P (B | A) = probability P (AB) / P (A ), under the conditions of occurrence of event A is event B.
Probability multiplication formula:
P (AB) = P (B | A) P (A) = P (A | B) P (B)
events independent: no effect on the occurrence of two events. P (B | A) = P (B).
P (AB) = P (B | A) P (A) = P (A) P (B)
total probability formula
if the event A1, A2, ..., An event group is complete, and has positive probability, there are P (B) = P (A1) P (B | A1) + P (A2) P (B | A2) + ... + P (An) P (B | An)
Bayesian formula, A1 for a complete set of events, A2, ..., An, to remain an event B, P (B)> 0 , there is
P (Ai | B) = P (AiB) / P (B), of P (B) formula of total probability,
P ( Ai | B) = P (Ai ) P (B | Ai) / ΣP (Ai) P (B | Ai)
an event has occurred is known, the trigger event can examine Bayesian formula possibilities for various reasons and the size of.
Bayesian inference
applied to observed phenomena subjective probability (a priori probability) be amended. An attribute of the incident support the more, the greater the likelihood that the property was established.
Prior probability: the probability of past experience and analysis obtained, as "seeking the cause and effect" problem "for" probability of occurrence. Generally separate probability, such as the probability of illness, rain probability, probability and other shopping.
The posterior probability: After getting information, "the result of" re-corrected probability, is "picking fruit Soin" in the "fruit." To calculate the posterior probability priori probability basis. And the same general form of conditional probability.
Maximum likelihood estimation: the distribution parameters for the current sample as the best estimate parameters of population.
P(H|E) 后验概率
P(H) 先验概率
P(E|H), P(E) 证据。
最大后验概率估计:融入了要估计的先验分布，是最大似然估计的规则化。
朴素贝叶斯
一种分类算法，通过计算样本归属于不同类别的概率进行分类。
贝叶斯理论:基于能获得的最好证据，来计算信念度的有效方法。信念度即为对事物真实性和正确性所具有的信心。
朴素:单纯、简单假设给定目标值时属性之间相互条件独立。如果这个条件不成立，不能用朴素贝叶斯。
朴素贝叶斯模型
m个样本，每个样本n个特征，输出为k个类。
通过样本学习得到先验概率，即分类为某个值的概率。
通过样本学习条件概率，即分类为某值时样本为某个的概率。
计算联合概率，分类为某项时样本为某个分布的概率。
一个例子
课程是用手算的，我试试用sklearn。
sklearn主要提供GaussianNB(高斯朴素贝叶斯)、MultinomialNB(多项式朴素贝叶斯)、BernoulliNB(伯努利朴素贝叶斯)。后两者主要用于离散特征分类。
手工将数据输入csv文件，读入以后再将数据数值化，最后建模，输出。
朴素贝叶斯的例子
import pandas as pd
from sklearn.naive_bayes import MultinomialNB
数据转换
def transform(data):
data.loc[data.Age == "青少年", "Age"] = 1
data.loc[data.Age == "中年", "Age"] = 2
data.loc[data.Age == "老年", "Age"] = 3
data.loc[data.Income == "高", "Income"] = 1
data.loc[data.Income == "中", "Income"] = 2
data.loc[data.Income == "低", "Income"] = 3
data.loc[data.Alone == "是", "Alone"] = 1
data.loc[data.Alone == "否", "Alone"] = 2
data.loc[data.Credit == "良好", "Credit"] = 1
data.loc[data.Credit == "一般", "Credit"] = 2
data.loc[data.Buy == "是", "Buy"] = 1
data.loc[data.Buy == "否", "Buy"] = 2
return data
if name == "main":
data = pd.read_csv("data.csv")
print(data)
data = transform(data)
print(data)
train_data = data[["Age", "Income", "Alone", "Credit"]]
test_data = data["Buy"]
test = np.array([3, 3, 2, 2])
print(test)
print("测试输出")
print(data.values)
进行朴素贝叶斯分类模型训练
clf = MultinomialNB(alpha = 2.0)
clf.fit(data.values, test_data)
print(clf.class_log_prior_)
用模型预测
print(clf.predict(test))
print(clf.predict_proba(test))运行结果
[1]
[[0.66684573 0.33315427]]
拉普拉斯平滑
有时会碰到零概率的问题，由于其中某个概率为0，相乘导致整个概率为0。拉普拉斯平滑通过在分子分母上加上调整解决这一问题。即上面程序里的alpha参数。
优点
有统计理论背书，分类效率稳定。
支持多分类任务。
对缺失数据不敏感。
算法简单，模型容易解释。
计算量小，支持海量数据。
支持增量式计算，可做在线预测。
缺点
需要有先验概率，不同值对结果有影响。
分类决策存在错误率。
对输入数据表达形式敏感。
"朴素"的假设对结果影响大。
接下来，试试用这个算法来解决泰坦尼克号问题吧。
课程也看完了，好像不全，还有其它方法没讲。再找找看有没有其它课程。
本文代码:
https://github.com/zwdnet/MyQuant/tree/master/21
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