我正在实现高斯朴素贝叶斯算法：
# importing modules
import pandas as pd
import numpy as np
# create an empty dataframe
data = pd.DataFrame()
# create our target variable
data["gender"] = ["male","male","male","male",
"female","female","female","female"]
# create our feature variables
data["height"] = [6,5.92,5.58,5.92,5,5.5,5.42,5.75]
data["weight"] = [180,190,170,165,100,150,130,150]
data["foot_size"] = [12,11,12,10,6,8,7,9]
# view the data
print(data)
# create an empty dataframe
person = pd.DataFrame()
# create some feature values for this single row
person["height"] = [6]
person["weight"] = [130]
person["foot_size"] = [8]
# view the data
print(person)
# Priors can be calculated either constants or probability distributions.
# In our example, this is simply the probability of being a gender.
# calculating prior now
# number of males
n_male = data["gender"][data["gender"] == "male"].count()
# number of females
n_female = data["gender"][data["gender"] == "female"].count()
# total people
total_ppl = data["gender"].count()
print ("Male count =",n_male,"and Female count =",n_female)
print ("Total number of persons =",total_ppl)
# number of males divided by the total rows
p_male = n_male / total_ppl
# number of females divided by the total rows
p_female = n_female / total_ppl
print ("Probability of MALE =",p_male,"and FEMALE =",p_female)
# group the data by gender and calculate the means of each feature
data_means = data.groupby("gender").mean()
# view the values
data_means
# group the data by gender and calculate the variance of each feature
data_variance = data.groupby("gender").var()
# view the values
data_variance
data_variance = data.groupby("gender").var()
data_variance["foot_size"][data_variance.index == "male"].values[0]
# means for male
male_height_mean=data_means["height"][data_means.index=="male"].values[0]
male_weight_mean=data_means["weight"][data_means.index=="male"].values[0]
male_footsize_mean=data_means["foot_size"][data_means.index=="male"].values[0]
print (male_height_mean,male_weight_mean,male_footsize_mean)
# means for female
female_height_mean=data_means["height"][data_means.index=="female"].values[0]
female_weight_mean=data_means["weight"][data_means.index=="female"].values[0]
female_footsize_mean=data_means["foot_size"][data_means.index=="female"].values[0]
print (female_height_mean,female_weight_mean,female_footsize_mean)
# variance for male
male_height_var=data_variance["height"][data_variance.index=="male"].values[0]
male_weight_var=data_variance["weight"][data_variance.index=="male"].values[0]
male_footsize_var=data_variance["foot_size"][data_variance.index=="male"].values[0]
print (male_height_var,male_weight_var,male_footsize_var)
# variance for female
female_height_var=data_variance["height"][data_variance.index=="female"].values[0]
female_weight_var=data_variance["weight"][data_variance.index=="female"].values[0]
female_footsize_var=data_variance["foot_size"][data_variance.index=="female"].values[0]
print (female_height_var,female_weight_var,female_footsize_var)
# create a function that calculates p(x | y):
def p_x_given_y(x,mean_y,variance_y):
# input the arguments into a probability density function
p = 1 / (np.sqrt(2 * np.pi * variance_y)) * \
np.exp((-(x - mean_y) ** 2) / (2 * variance_y))
# return p
return p
# numerator of the posterior if the unclassified observation is a male
posterior_numerator_male = p_male * \
p_x_given_y(person["height"][0],male_height_mean,male_height_var) * \
p_x_given_y(person["weight"][0],male_weight_mean,male_weight_var) * \
p_x_given_y(person["foot_size"][0],male_footsize_mean,male_footsize_var)
# numerator of the posterior if the unclassified observation is a female
posterior_numerator_female = p_female * \
p_x_given_y(person["height"][0],female_height_mean,female_height_var) * \
p_x_given_y(person["weight"][0],female_weight_mean,female_weight_var) * \
p_x_given_y(person["foot_size"][0],female_footsize_mean,female_footsize_var)
print ("Numerator of Posterior MALE =",posterior_numerator_male)
print ("Numerator of Posterior FEMALE =",posterior_numerator_female)
if (posterior_numerator_male >= posterior_numerator_female):
print ("Predicted gender is MALE")
else:
print ("Predicted gender is FEMALE")
当我们计算概率时，我们使用高斯概率密度函数进行计算： $$ P(x) = \frac{1}{\sqrt {2 \pi {\sigma}^2}} e^{\frac{-(x- \mu)^2}{2 {\sigma}^2}} $$
我的问题是上述方程式是概率密度函数。要计算概率，我们必须在dx区域内对其进行积分。 $ \int_{x0}^{x1} P(x)dx $
但在上面的程序中，我们插入x的值并计算概率。这正确吗？为什么？我已经看到大多数文章以相同的方式计算概率。
如果这是朴素贝叶斯分类器中计算概率的错误方法，则正确的方法是什么？