"Machine Learning Core Algorithm" Classification Algorithm - Naive Bayes MultinomialNB

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Naive Bayes model ( NBM for short ) is a classification method based on "Bayes' theorem" and "feature conditional independence assumption" .

"Bayes' Theorem" : Also called Bayes' formula, it is used to describe the relationship between two "conditional probabilities" . For example, if you see a person always doing good things, then this person is probably a good person.
"Feature Conditional Independence Assumption" : In order to solve the problem of excessive exponential growth of "parameters" , Naive Bayes assumes that the conditions of features are "mutually independent" based on Bayes' theorem .

1. Naive Bayes API

Naive Bayes classifier of "polynomial" model, used for classification with "discrete" features, such as word count for text classification, which requires integer feature count.

sklearn.naive_bayes.MultinomialNB()

parameter

• alpha : (optional, float) smoothing parameter, default is 1.0
• force_alpha : (optional, Boolean type) default value False, if it is False and alpha is less than 1e-10, set alpha to 1e-10; if True, aplha remains unchanged; this is to prevent alpha from being too close to 0 leading to numerical errors
• fit_prior : (optional, Boolean type) whether to learn the prior probability, the default value is True, if it is False, the unified prior is used.

function

• MultinomialNB.fit(x_train, y_train): Receive training set features and training set targets
• MultinomialNB.predict(x_test): Receives test set features and returns the class label of the data
• MultinomialNB.score(x_test, y_test): Receives test set features and test set targets, and returns the accuracy.
• MultinomialNB.get_params(): Get the received parameters (parameters such as alpha and fit_prior)
• MultinomialNB.set_params(): Set parameters
• MultinomialNB.partial_fit(): incremental test, used when the amount of data is too large to be loaded into the memory at once.

2. Practical application of Naive Bayes algorithm

2.1. Obtain data set

Here we use the "Iris" data set that comes with sklearn .

from sklearn import datasets

# 1、获取数据集
iris = datasets.load_iris()
print(iris.data)

Output:

[[5.1 3.5 1.4 0.2]
 [4.9 3.  1.4 0.2]
 ......
  [5.9 3.  5.1 1.8]]

2.2. Divide the data set

Next, we "divide" the data set , pass in the feature values ​​and target values, and divide it according to the default proportion (25% test set, 75% training set)

from sklearn import datasets
from sklearn import model_selection

# 1、获取数据集
iris = datasets.load_iris()
# 2、划分数据集
x_train, x_test, y_train, y_test = model_selection.train_test_split(iris.data, iris.target)
print('训练集特征值：', len(x_train))
print('测试集特征值：', len(x_test))
print('训练集目标值：', len(y_train))
print('测试集目标值：', len(y_test))

Output:

训练集特征值： 112
测试集特征值： 38
训练集目标值： 112
测试集目标值： 38

From the results, we can see that the training set is divided into 112 groups and the test set is divided into 38 groups, which is in line with expectations.

2.3. Feature normalization

Next, we "normalize" the feature values . It should be noted that the training set and test set must be processed exactly the same.

from sklearn import datasets
from sklearn import model_selection
from sklearn import preprocessing

# 1、获取数据集
iris = datasets.load_iris()
# 2、划分数据集
x_train, x_test, y_train, y_test = model_selection.train_test_split(iris.data, iris.target)
# 3、特征归一化
mm = preprocessing.MinMaxScaler()
x_train = mm.fit_transform(x_train)
x_test = mm.fit_transform(x_test)
print(x_train)
print(x_test)

Output:

[[0.8        0.5        0.87719298 0.70833333]
 [0.42857143 0.5        0.66666667 0.70833333]
 ......

From the results we can see that the eigenvalues ​​have changed accordingly.

2.4. Bayesian algorithm processing and evaluation

Next, instantiate the Bayesian class object and pass in the feature value target value of the training set for training.

from sklearn import datasets
from sklearn import model_selection
from sklearn import preprocessing
from sklearn import naive_bayes

# 1、获取数据集
iris = datasets.load_iris()
# 2、划分数据集
x_train, x_test, y_train, y_test = model_selection.train_test_split(iris.data, iris.target)
# 3、特征归一化
mm = preprocessing.MinMaxScaler()
x_train = mm.fit_transform(x_train)
x_test = mm.fit_transform(x_test)
# 4、贝叶斯算法处理
estimator = naive_bayes.MultinomialNB()
estimator.fit(x_train, y_train)

# 5、模型评估
y_predict = estimator.predict(x_test)
print('真实值和预测值对比', y_predict == y_test)
score = estimator.score(x_test, y_test)
print('准确率', score)

Output:

真实值和预测值对比 [ True False  True False  True False  True  True  True  True False  True
 False False False False False  True False  True False  True  True  True
  True  True  True  True  True False False False  True  True  True  True
  True False]
准确率 0.6052631578947368

3. Frequently Asked Questions

The training set data of MultinomialNB cannot be "negative" , otherwise an error will be reported: Negative values ​​in data passed to MultinomialNB.

For example, when normalizing features, negative results will appear and an error will be reported. You can use normalization instead.

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