python 機(jī)器學(xué)習(xí)之實(shí)現(xiàn)樸素貝葉斯算法的示例

from collections import defaultdict
import numpy as np
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from loguru import logger


class NaiveBayesScratch():
  """樸素貝葉斯算法Scratch實(shí)現(xiàn)"""
  def __init__(self):
    # 存儲(chǔ)先驗(yàn)概率 P(Y=ck)
    self._prior_prob = defaultdict(float)
    # 存儲(chǔ)似然概率 P(X|Y=ck)
    self._likelihood = defaultdict(defaultdict)
    # 存儲(chǔ)每個(gè)類別的樣本在訓(xùn)練集中出現(xiàn)次數(shù)
    self._ck_counter = defaultdict(float)
    # 存儲(chǔ)每一個(gè)特征可能取值的個(gè)數(shù)
    self._Sj = defaultdict(float)

  def fit(self, X, y):
    """
    模型訓(xùn)練，參數(shù)估計(jì)使用貝葉斯估計(jì)
    X:
      訓(xùn)練集，每一行表示一個(gè)樣本，每一列表示一個(gè)特征或?qū)傩?    y:
      訓(xùn)練集標(biāo)簽
    """
    n_sample, n_feature = X.shape
    # 計(jì)算每個(gè)類別可能的取值以及每個(gè)類別樣本個(gè)數(shù)
    ck, num_ck = np.unique(y, return_counts=True)
    self._ck_counter = dict(zip(ck, num_ck))
    for label, num_label in self._ck_counter.items():
      # 計(jì)算先驗(yàn)概率，做了拉普拉斯平滑處理，即計(jì)算P（y）
      self._prior_prob[label] = (num_label + 1) / (n_sample + ck.shape[0])

    # 記錄每個(gè)類別樣本對(duì)應(yīng)的索引
    ck_idx = []
    for label in ck:
      label_idx = np.squeeze(np.argwhere(y == label))
      ck_idx.append(label_idx)

    # 遍歷每個(gè)類別
    for label, idx in zip(ck, ck_idx):
      xdata = X[idx]
      # 記錄該類別所有特征對(duì)應(yīng)的概率
      label_likelihood = defaultdict(defaultdict)
      # 遍歷每個(gè)特征
      for i in range(n_feature):
        # 記錄該特征每個(gè)取值對(duì)應(yīng)的概率
        feature_val_prob = defaultdict(float)
        # 獲取該列特征可能的取值和每個(gè)取值出現(xiàn)的次數(shù)
        feature_val, feature_cnt = np.unique(xdata[:, i], return_counts=True)
        self._Sj[i] = feature_val.shape[0]
        feature_counter = dict(zip(feature_val, feature_cnt))
        for fea_val, cnt in feature_counter.items():
          # 計(jì)算該列特征每個(gè)取值的概率，做了拉普拉斯平滑，即為了計(jì)算P（x|y）
          feature_val_prob[fea_val] = (cnt + 1) / (self._ck_counter[label] + self._Sj[i])
        label_likelihood[i] = feature_val_prob
      self._likelihood[label] = label_likelihood

  def predict(self, x):
    """
    輸入樣本，輸出其類別，本質(zhì)上是計(jì)算后驗(yàn)概率
    **注意計(jì)算后驗(yàn)概率的時(shí)候?qū)Ω怕嗜?duì)數(shù)**，概率連乘可能導(dǎo)致浮點(diǎn)數(shù)下溢，取對(duì)數(shù)將連乘轉(zhuǎn)化為求和
    """
    # 保存分類到每個(gè)類別的后驗(yàn)概率，即計(jì)算P（y|x）
    post_prob = defaultdict(float)
    # 遍歷每個(gè)類別計(jì)算后驗(yàn)概率
    for label, label_likelihood in self._likelihood.items():
      prob = np.log(self._prior_prob[label])
      # 遍歷樣本每一維特征
      for i, fea_val in enumerate(x):
        feature_val_prob = label_likelihood[i]
        # 如果該特征值出現(xiàn)在訓(xùn)練集中則直接獲取概率
        if fea_val in feature_val_prob:
          prob += np.log(feature_val_prob[fea_val])
        else:
          # 如果該特征沒有出現(xiàn)在訓(xùn)練集中則采用拉普拉斯平滑計(jì)算概率
          laplace_prob = 1 / (self._ck_counter[label] + self._Sj[i])
          prob += np.log(laplace_prob)
      post_prob[label] = prob
    prob_list = list(post_prob.items())
    prob_list.sort(key=lambda v: v[1], reverse=True)
    # 返回后驗(yàn)概率最大的類別作為預(yù)測類別
    return prob_list[0][0]


def main():
  X, y = load_iris(return_X_y=True)
  xtrain, xtest, ytrain, ytest = train_test_split(X, y, train_size=0.8, shuffle=True)

  model = NaiveBayesScratch()
  model.fit(xtrain, ytrain)

  n_test = xtest.shape[0]
  n_right = 0
  for i in range(n_test):
    y_pred = model.predict(xtest[i])
    if y_pred == ytest[i]:
      n_right += 1
    else:
      logger.info("該樣本真實(shí)標(biāo)簽為：{}，但是Scratch模型預(yù)測標(biāo)簽為：{}".format(ytest[i], y_pred))
  logger.info("Scratch模型在測試集上的準(zhǔn)確率為：{}%".format(n_right * 100 / n_test))

if __name__ == "__main__":
  main()