实验目的

理解和掌握朴素贝叶斯基本原理和方法，理解极大似然估计方法，理解先验概率分布和后验概率分布等概念，掌握朴素贝叶斯分类器训练方法。

实验要求

给定数据集，编程实现朴素贝叶斯分类算法，计算相应先验概率，条件概率，高斯分布均值和方差的估计值，并给出模型在测试集上的精度。

实验环境

python, numpy, scipy

实验代码

import numpy as npfrom scipy.stats import norm# 导入训练数据train_dataset_data = np.genfromtxt("experiment_07_training_set.csv", delimiter=",", skip_header=1, usecols=(1, 2, 3, 4))rowOfTrainDataset = train_dataset_data.shape[0]train_dataset_label = np.genfromtxt("experiment_07_training_set.csv", delimiter=",", skip_header=1, usecols=(5,), dtype="str")# 导入测试数据test_dataset_data = np.genfromtxt("experiment_07_testing_set.csv", delimiter=",", skip_header=1, usecols=(1, 2, 3, 4))rowOfTestDataset = test_dataset_data.shape[0]test_dataset_label = np.genfromtxt("experiment_07_testing_set.csv", delimiter=",", skip_header=1, usecols=(5,), dtype="str")# 定义种类列表和属性列表species = ["Iris-setosa", "Iris-versicolor", "Iris-virginica"]xs = ["SepalLength", "SepalWidth", "PetalLength", "PetalWidth"]# 统计先验概率prior = np.zeros(3)for i in range(3):prior[i] = np.sum(train_dataset_label == species[i], axis=0) / rowOfTrainDatasetprint("先验概率: ")for i in range(3):print(f"{species[i]}-> {prior[i]}")# 计算条件概率condition = np.zeros((3, 4, 2))# 对3个类别计算for i in range(3):# 每个类别4个属性for j in range(4):temp = train_dataset_data[train_dataset_label == species[i], j]# 存储均值condition[i, j, 0] = np.mean(temp)# 存储标准差condition[i, j, 1] = np.sqrt(np.var(temp))print(f"高斯分布参数估计:")for i in range(3):print(f"P(X|Y={species[i]})->", end='')for j in range(4):print(f"|X1={xs[j]}:均值->{condition[i, j, 0]:.4f} 标准差->{condition[i, j, 1]: .4f}|", end=' ')print("")# 计算精度pred = np.zeros_like(test_dataset_label)for i in range(rowOfTestDataset):# 将概率初始化为0probability1 = 0# 计算3种类别的概率取最大概率作为种类for j in range(3):p0 = norm.pdf(test_dataset_data[i, 0], loc=condition[j, 0, 0], scale=condition[j, 0, 1])p1 = norm.pdf(test_dataset_data[i, 1], loc=condition[j, 1, 0], scale=condition[j, 1, 1])p2 = norm.pdf(test_dataset_data[i, 2], loc=condition[j, 2, 0], scale=condition[j, 2, 1])p3 = norm.pdf(test_dataset_data[i, 3], loc=condition[j, 3, 0], scale=condition[j, 3, 1])probability2 = prior[j] * p0 * p1 * p2 * p3if probability2 > probability1:pred[i] = jprobability1 = probability2# 将类别从编号转为字符串pred_species = np.array([species[int(p)] for p in pred])# 计算精度accuracy = np.sum(pred_species == test_dataset_label) / rowOfTestDatasetprint(f"模型精度: {accuracy * 100: .2f}%")

结果分析

先验概率

类别	先验概率
P(Y=setosa)	0.4
P(Y=versicolor)	0.4
P(Y=virginica)	0.2

高斯分布参数估计精度：

类别	X1=SepalLength		X2=SepalWidth		X3=PetalLength		X4=PetalWidth
类别	均值	标准差	均值	标准差	均值	标准差	均值	标准差
P(X\|Y=setosa)	5.0375	0.3576	3.4400	0.3597	1.4625	0.1698	0.2325	0.0985
P(X\|Y=versicolor)	6.0150	0.5126	2.7875	0.3257	4.3200	0.4440	1.3500	0.2049
P(X\|Y=virginica)	6.5600	0.7130	2.9200	0.3763	5.6550	0.6241	2.0450	0.2673