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
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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。
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数据集描述（Dataset Description）
- train.csv
- test_no_label.csv
- x_train.csv
- Y_train.csv
- X_test.csv
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参考链接
https://colab.research.google.com/drive/1JaMKJU7hvnDoUfZjvUKzm9u-JLeX6B2C
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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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