从零开始的朴素贝叶斯分类器

Posted 2023-03-12

【中文标题】从零开始的朴素贝叶斯分类器

【英文标题】：Naive Bayes Classifier from scratch

【发布时间】：2021-11-12 20:52:42

【问题描述】：

最近发现 GaussianNaiveBayes 分类器的代码如下。

 import numpy as np
 class GaussianNaiveBayes:
     def fit(self, X, y):
         n_samples, n_features = X.shape
         self._classes = np.unique(y)
         n_classes = len(self._classes)
         self._mean = np.zeros((n_classes, n_features), dtype=np.float64)
         self._var = np.zeros((n_classes, n_features), dtype=np.float64)
         self._priors =  np.zeros(n_classes, dtype=np.float64)

         # calculating the mean, variance and prior P(H) for each class
         for i, c in enumerate(self._classes):
             X_for_class_c = X[y==c]
             self._mean[i, :] = X_for_class_c.mean(axis=0)
             self._var[i, :] = X_for_class_c.var(axis=0)
             self._priors[i] = X_for_class_c.shape[0] / float(n_samples)
#function for calculating the likelihood, P(E|H), of data X given the mean and variance
def _calculate_likelihood(self, class_idx, x):
         mean = self._mean[class_idx]
         var = self._var[class_idx]
         num = np.exp(- (x-mean)**2 / (2 * var))
         denom = np.sqrt(2 * np.pi * var)
         return num / denom 

#classifications by calculating the posterior probability, P(H|E), of the classes 
def predict(self, X):
         y_pred = [self._classify_sample(x) for x in X]
         return np.array(y_pred)

     def _classify_sample(self, x):
         posteriors = []
         # calculating posterior probability for each class
         for i, c in enumerate(self._classes):
             prior = np.log(self._priors[i])
             posterior = np.sum(np.log(self._calculate_likelihood(i, x)))
             posterior = prior + posterior
             posteriors.append(posterior)
         # return the class with highest posterior probability
         return self._classes[np.argmax(posteriors)] 

通过以下代码在 Iris 数据集上尝试上述代码，但收到错误“AttributeError: 'GaussianNaiveBayes' object has no attribute 'predict'”

iris = datasets.load_iris()
X = pd.DataFrame(iris.data, columns = iris.feature_names)
y = pd.DataFrame(iris.target, columns = ['Target'])
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2,random_state = 42)

nb = GaussianNaiveBayes()
nb.fit(X_train, y_train)
predictions = nb.predict(X_test)

请求任何指导以显示我的错误。

【问题讨论】：

predict 方法没有缩进，所以它不属于GaussianNaiveBayes 类（而fit 属于）

【参考方案1】：

您需要正确缩进代码，并且当y 是数据框时，这行子集X 数组将不起作用：

X_for_class_c = X[y==c]

同样，此函数不适用于数据框：

y_pred = [self._classify_sample(x) for x in X]

所以让我们正确缩进：

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn import datasets

class GaussianNaiveBayes:
    def fit(self, X, y):
        n_samples, n_features = X.shape
        self._classes = np.unique(y)
        n_classes = len(self._classes)
        self._mean = np.zeros((n_classes, n_features), dtype=np.float64)
        self._var = np.zeros((n_classes, n_features), dtype=np.float64)
        self._priors =  np.zeros(n_classes, dtype=np.float64)

        for i, c in enumerate(self._classes):
            X_for_class_c = X[y==c]
            self._mean[i, :] = X_for_class_c.mean(axis=0)
            self._var[i, :] = X_for_class_c.var(axis=0)
            self._priors[i] = X_for_class_c.shape[0] / float(n_samples)

    def _calculate_likelihood(self, class_idx, x):
        mean = self._mean[class_idx]
        var = self._var[class_idx]
        num = np.exp(- (x-mean)**2 / (2 * var))
        denom = np.sqrt(2 * np.pi * var)
        return num / denom 
 
    def predict(self, X):
        y_pred = [self._classify_sample(x) for x in X]
        return np.array(y_pred)

    def _classify_sample(self, x):
        posteriors = []
         
        for i, c in enumerate(self._classes):
            prior = np.log(self._priors[i])
            posterior = np.sum(np.log(self._calculate_likelihood(i, x)))
            posterior = prior + posterior
            posteriors.append(posterior)
         
        return self._classes[np.argmax(posteriors)]

首先使用您的示例运行拟合，您可以看到拟合为您的所有值返回 nan：

iris = datasets.load_iris()
X = pd.DataFrame(iris.data, columns = iris.feature_names)
y = pd.DataFrame(iris.target, columns = ['Target'])
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2,random_state = 42)

nb = GaussianNaiveBayes()
nb.fit(X_train, y_train)

nb._mean

array([[nan, nan, nan, nan],
       [nan, nan, nan, nan],
       [nan, nan, nan, nan]])

改变输入：

iris = datasets.load_iris()
X = iris.data
y = iris.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2,random_state = 42)
    
nb = GaussianNaiveBayes()
nb.fit(X_train, y_train)
nb.predict(X_test)

array([1, 0, 2, 1, 1, 0, 1, 2, 1, 1, 2, 0, 0, 0, 0, 1, 2, 1, 1, 2, 0, 2,
       0, 2, 2, 2, 2, 2, 0, 0])