李宏毅机器学习课程笔记-4.4概率生成模型Python实战

本文为作者学习李宏毅机器学习课程时参照样例完成homework2的记录。

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代码仓库：https://github.com/chouxianyu/LHY_ML2020_Codes

• 任务描述（Task Description）

  二分类（Binary Classification）

  根据个人资料，判断每个人的年收入是否超过50000美元。

• 数据集描述（Dataset Description）

  • train.csv
  • test_no_label.csv
  • x_train.csv
  • Y_train.csv
  • X_test.csv

• 参考链接

  https://colab.research.google.com/drive/1JaMKJU7hvnDoUfZjvUKzm9u-JLeX6B2C

• 代码

  import numpy as np
  
  
  ## 文件路径
  X_train_fpath = '../data/X_train.csv'
  Y_train_fpath = '../data/Y_train.csv'
  X_test_fpath = '../data/X_test.csv'
  output_fpath = 'output.csv'
  
  
  ## 函数定义
  # 归一化
  def _normalize(X, train=True, specified_column=None, X_mean=None, X_std=None):
      # This function normalizes specific columns of X.
      # The mean and standard variance of training data will be reused when processing testing data.
      #
      # Arguments:
      #     X: data to be processed
      #     train: 'True' when processing training data, 'False' for testing data
      #     specific_column: indexes of the columns that will be normalized. If 'None', all columns
      #         will be normalized.
      #     X_mean: mean value of training data, used when train = 'False'
      #     X_std: standard deviation of training data, used when train = 'False'
      # Outputs:
      #     X: normalized data
      #     X_mean: computed mean value of training data
      #     X_std: computed standard deviation of training data
      if specified_column is None:
          specified_column = np.arange(X.shape[1])
      if train:
          X_mean = np.mean(X[:, specified_column], axis=0).reshape(1, -1)
          X_std = np.std(X[:, specified_column], axis=0).reshape(1, -1)
      X[:, specified_column] = (X[:, specified_column] - X_mean) / (X_std + 1e-8)
      return X, X_mean, X_std
  
  # 训练集划分
  def _train_valid_split(X, Y, valid_ratio=0.25):
      # This function splits data into training set and validation set.
      train_size = int(len(X) * (1 - valid_ratio))
      return X[:train_size], Y[:train_size], X[train_size:], Y[train_size:]
  
  # sigmoid函数
  def _sigmoid(z):
      # Sigmoid function can be used to calculate probability.
      # To avoid overflow, minimum/maximum output value is set.
      return np.clip(1.0 / (1.0 + np.exp(-z)), 1e-8, 1 - ( 1e-8))
  
  # forward
  def _f(X, w, b):
      # This is the logistic regression function, parameterized by w and b
      #
      # Arguements:
      #     X: input data, shape = [batch_size, data_dimension]
      #     w: weight vector, shape = [data_dimension, ]
      #     b: bias, scalar
      # Output:
      #     predicted probability of each row of X being positively labeled, shape = [batch_size, ]
      return _sigmoid(np.matmul(X, w) + b)
  
  # 预测
  def _predict(X, w, b):
      # This function returns a truth value prediction for each row of X 
      # by rounding the result of logistic regression function.
      return np.round(_f(X, w, b)).astype(np.int)
  
  # 计算精度
  def _accuracy(Y_pred, Y_label):
      # This function calculates prediction accuracy
      return 1 - np.mean(np.abs(Y_pred - Y_label))
  
  
  ## 读取数据
  with open(X_train_fpath) as f:
      next(f) # 不需要第一行的表头
      X_train = np.array([line.strip('
  ').split(',')[1:] for line in f], dtype=float) # 不要第一列的ID
      # print(X_train)
  with open(Y_train_fpath) as f:
      next(f) # 不需要第一行的表头
      Y_train = np.array([line.strip('
  ').split(',')[1] for line in f], dtype=float)# 不要第一列的ID，只取第二列
      # print(Y_train)
  with open(X_test_fpath) as f:
      next(f) # 不需要第一行的表头
      X_test = np.array([line.strip('
  ').split(',')[1:] for line in f], dtype=float)
      # print(X_test)
  
  
  ## 数据集处理
  # 训练集和测试集normalization
  X_train, X_mean, X_std = _normalize(X_train, train=True)
  X_test, _, _ = _normalize(X_test, train=False, specified_column=None, X_mean=X_mean, X_std=X_std)
  data_dim = X_train.shape[1]
  
  
  ## 计算每个类别的样本的平均值和协方差
  # 区分类别
  X_train_0 = np.array([x for x, y in zip(X_train, Y_train) if y==0])
  X_train_1 = np.array([x for x, y in zip(X_train, Y_train) if y==1])
  # 计算每个类别的样本的平均值
  mean_0 = np.mean(X_train_0, axis=0) # 计算每个维度特征的平均值
  mean_1 = np.mean(X_train_1, axis=0)
  # 计算每个类别的样本的协方差矩阵（可以研究下协方差矩阵是如何计算的以及为什么）
  cov_0 = np.zeros((data_dim, data_dim))
  cov_1 = np.zeros((data_dim, data_dim))
  for x in X_train_0:
      cov_0 += np.dot(np.transpose([x - mean_0]), [x - mean_0]) / X_train_0.shape[0] # transpose没有参数的话，就是转置，计算协方差矩阵时需要转置
  for x in X_train_1:
      cov_1 += np.dot(np.transpose([x - mean_1]), [x - mean_1]) / X_train_1.shape[0]
  # 计算共享协方差矩阵（Shared covariance is taken as a weighted average of individual in-class covariance）
  cov = (cov_0 * X_train_0.shape[0] + cov_1 * X_train_1.shape[0]) / (X_train_0.shape[0] + X_train_1.shape[0])
  
  
  ## 计算权重和偏置
  # 计算协方差矩阵的逆矩阵
  # Since covariance matrix may be nearly singular, np.linalg.inv() may give a large numerical error.
  # Via SVD decomposition, one can get matrix inverse efficiently and accurately.
  u, s, v = np.linalg.svd(cov, full_matrices=False)
  inv = np.matmul(v.T * 1 / s, u.T)
  # 计算weight和bias
  w = np.dot(inv, mean_0 - mean_1)
  b = (-0.5) * np.dot(mean_0, np.dot(inv, mean_0)) + 0.5 * np.dot(mean_1, np.dot(inv, mean_1)) + np.log(float(X_train_0.shape[0])) / X_train_1.shape[0]
  
  
  ## 计算在训练集上的准确率
  Y_train_pred = 1 - _predict(X_train, w, b)
  print('Training accuracy: {}'.format(_accuracy(Y_train_pred, Y_train)))
  
  
  ## 预测测试集结果
  predictions = 1 - _predict(X_test, w, b)
  with open(output_fpath, 'w') as f:
      f.write('id,label
  ')
      for i, label in enumerate(predictions):
          f.write('{},{}
  '.format(i, label))
  
  
  ## 寻找最重要的10个维度的特征
  index = np.argsort(np.abs(w))[::-1] # 将w按绝对值从大到小排序
  with open(X_test_fpath) as f:
      features = np.array(f.readline().strip('
  ').split(','))
      for i in index[:10]:
          print(features[i], w[i])
  
  

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