李宏毅（2020）作业2-hw2_classification
2024-05-22 17:48:11
数据集：https://wwr.lanzoui.com/ibnAxud394j
密码:bvf8
文章目录
- Logistic Regression
- Preparing Data
- Some Useful Functions
- Functions about gradient and loss
- Training
- Plotting Loss and accuracy curve
- Predicting testing labels
- Porbabilistic generative model
- Preparing Data
- Mean and Covariance
- Computing weights and bias
- Predicting testing labels
!tar -zxvf data.tar.gz
!ls
data/
data/sample_submission.csv
data/test_no_label.csv
data/train.csv
data/X_test
data/X_train
data/Y_train
acc.png data data.tar.gz loss.png output_logistic.csv hw2.ipynb
Logistic Regression
Preparing Data
下载数据，并且对每个属性做正则化，处理过后再将其切分为训练集与验证集。
import numpy as npnp.random.seed(0)
X_train_fpath = './data/X_train'
Y_train_fpath = './data/Y_train'
X_test_fpath = './data/X_test'
output_fpath = './output_{}.csv'# Parse csv files to numpy array
with open(X_train_fpath) as f:next(f)X_train = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)
with open(Y_train_fpath) as f:next(f)Y_train = np.array([line.strip('\n').split(',')[1] for line in f], dtype = float)
with open(X_test_fpath) as f:next(f)X_test = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)def _normalize(X, train = True, specified_column = None, X_mean = None, X_std = None):# 此函数用于规范化X的特定列。# 训练数据的均值和标准方差将在处理测试数据时重复使用。## Arguments:# X: 待处理的数据# train: 'True' when processing training data, 'False' for testing data# specific_column: 将被规范化的列的索引。如果参数为“None”，则所有列都将标准化。# 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 dataif specified_column == None:specified_column = np.arange(X.shape[1])if train:X_mean = np.mean(X[:, specified_column] ,0).reshape(1, -1)X_std = np.std(X[:, specified_column], 0).reshape(1, -1)X[:,specified_column] = (X[:, specified_column] - X_mean) / (X_std + 1e-8)return X, X_mean, X_stddef _train_dev_split(X, Y, dev_ratio = 0.25):# This function spilts data into training set and development set.train_size = int(len(X) * (1 - dev_ratio))return X[:train_size], Y[:train_size], X[train_size:], Y[train_size:]# Normalize training and testing data
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)# Split data into training set and development set
dev_ratio = 0.1
X_train, Y_train, X_dev, Y_dev = _train_dev_split(X_train, Y_train, dev_ratio = dev_ratio)train_size = X_train.shape[0]
dev_size = X_dev.shape[0]
test_size = X_test.shape[0]
data_dim = X_train.shape[1]
print('Size of training set: {}'.format(train_size))
print('Size of development set: {}'.format(dev_size))
print('Size of testing set: {}'.format(test_size))
print('Dimension of data: {}'.format(data_dim))
Size of training set: 48830
Size of development set: 5426
Size of testing set: 27622
Dimension of data: 510
X_train.shape
(48830, 510)
Some Useful Functions
这几个函数可能会在训练循环中被重复使用到。
def _shuffle(X, Y):# 此函数将两个等长的列表/数组X和Y混合在一起。randomize = np.arange(len(X))np.random.shuffle(randomize)return (X[randomize], Y[randomize])def _sigmoid(z):# Sigmoid function can be used to calculate probability.return np.clip(1 / (1.0 + np.exp(-z)), 1e-8, 1 - (1e-8)) # 为避免溢出，设置了最小/最大输出值。def _f(X, w, b):# 逻辑回归函数, parameterized by w and b## Arguements:# X: input data, shape = [batch_size, data_dimension]# w: weight vector, shape = [data_dimension, ]# b: bias, scalar# Output:# X的每一行被正标记的预测概率, shape = [batch_size, ]return _sigmoid(np.matmul(X, w) + b)def _predict(X, w, b):# 此函数通过对逻辑回归函数的结果进行四舍五入，为X的每一行返回真值预测。return np.round(_f(X, w, b)).astype(np.int)def _accuracy(Y_pred, Y_label):# This function calculates prediction accuracyacc = 1 - np.mean(np.abs(Y_pred - Y_label))return acc
Functions about gradient and loss
Cross entropy:
C(f(xn),y^n)=−[y^nlnf(xn)+(1−y^n)ln(1−f(xn))]C\left(f\left(x^{n}\right), \hat{y}^{n}\right)=-\left[\hat{y}^{n} \ln f\left(x^{n}\right)+\left(1-\hat{y}^{n}\right) \ln \left(1-f\left(x^{n}\right)\right)\right]C(f(xn),y^n)=−[y^nlnf(xn)+(1−y^n)ln(1−f(xn))]
def _cross_entropy_loss(y_pred, Y_label):# This function computes the cross entropy.## Arguements:# y_pred: probabilistic predictions, float vector# Y_label: ground truth labels, bool vector# Output:# cross entropy, scalarcross_entropy = -np.dot(Y_label, np.log(y_pred)) - np.dot((1 - Y_label), np.log(1 - y_pred))return cross_entropydef _gradient(X, Y_label, w, b):# This function computes the gradient of cross entropy loss with respect to weight w and bias b.y_pred = _f(X, w, b)pred_error = Y_label - y_predw_grad = -np.sum(pred_error * X.T, 1)b_grad = -np.sum(pred_error)return w_grad, b_grad
Training
我们使用小批次梯度下降法来训练。训练数据被分为许多小批次，针对每一个小批次，我们分别计算其梯度以及损失，并根据该批次来更新模型的参数。当一次循环完成，也就是整个训练集的所有小批次都被使用过一次以后，我们将所有训练数据打散并且重新分成新的小批次，进行下一个循环，直到事先设定的循环数量达成为止。
# 权重和偏差的初始化为0
w = np.zeros((data_dim,))
b = np.zeros((1,))# Some parameters for training
max_iter = 10
batch_size = 8
learning_rate = 0.2# 在每次迭代时保存损失和精度，以便绘图
train_loss = []
dev_loss = []
train_acc = []
dev_acc = []# Calcuate the number of parameter updates
step = 1# Iterative training
for epoch in range(max_iter):# 在每个epoch开始时进行随机混合X_train, Y_train = _shuffle(X_train, Y_train)# Mini-batch trainingfor idx in range(int(np.floor(train_size / batch_size))):X = X_train[idx*batch_size:(idx+1)*batch_size]Y = Y_train[idx*batch_size:(idx+1)*batch_size]# Compute the gradientw_grad, b_grad = _gradient(X, Y, w, b)# gradient descent update# learning rate decay with timew = w - learning_rate/np.sqrt(step) * w_gradb = b - learning_rate/np.sqrt(step) * b_gradstep = step + 1# Compute loss and accuracy of training set and development sety_train_pred = _f(X_train, w, b)Y_train_pred = np.round(y_train_pred)#四舍五入train_acc.append(_accuracy(Y_train_pred, Y_train))train_loss.append(_cross_entropy_loss(y_train_pred, Y_train) / train_size)y_dev_pred = _f(X_dev, w, b)Y_dev_pred = np.round(y_dev_pred)dev_acc.append(_accuracy(Y_dev_pred, Y_dev))dev_loss.append(_cross_entropy_loss(y_dev_pred, Y_dev) / dev_size)print('Training loss: {}'.format(train_loss[-1]))
print('Development loss: {}'.format(dev_loss[-1]))
print('Training accuracy: {}'.format(train_acc[-1]))
print('Development accuracy: {}'.format(dev_acc[-1]))
Training loss: 0.271355435246406
Development loss: 0.2896359675026286
Training accuracy: 0.8836166291214418
Development accuracy: 0.8733873940287504
print(w)
[ 5.92915192e-01 1.24074857e-01 1.83630863e-01 -7.70052933e-021.01394159e-01 3.20603386e-02 -4.03196028e+00 3.65554831e-028.69717534e-02 -3.20047799e-02 -3.03096235e-01 1.94064135e-02-3.85584310e-02 7.00523961e-02 2.73524545e-02 2.04627379e-021.09724785e-02 -9.36514029e-03 -2.00279580e-03 -6.09131082e-022.43449989e-02 3.14315744e-02 -3.11362963e-02 2.62313688e-026.41679870e-02 -2.59866508e-02 -4.58250689e-02 1.53066552e-025.03107399e-03 3.15076844e-02 -3.99684936e-02 -3.84093140e-02-3.88026206e-02 5.78755912e-02 -2.99634188e-02 1.43790145e-027.34378526e-02 1.90405432e-03 5.09819666e-03 -1.75756429e-03-1.93598360e-02 5.19897751e-02 2.66014738e-02 2.21600062e-02-7.12755653e-02 -4.38964656e-02 -1.00193950e-02 -5.54453739e-033.73557951e-02 -1.35260617e-02 3.79730351e-02 4.06755762e-02-3.52166616e-02 -3.73820684e-02 -3.08406773e-02 -9.06102046e-03-4.22869883e-02 5.45105197e-02 -1.84837645e-02 -9.73816178e-042.35096290e-02 4.36160353e-03 -5.22678316e-03 6.56595626e-02-3.96729095e-02 2.34134376e-02 -2.33975169e-02 5.87461431e-027.36327176e-02 8.38750350e-02 -1.30694593e-02 -2.91644238e-021.42799260e-02 -1.40928226e-01 -7.22504366e-02 -3.07968494e-026.18218957e-03 -1.93561165e-02 -1.77971010e-02 -1.53469573e-028.26096958e-02 -1.04483810e-02 -7.93838732e-02 -2.90085757e-02-3.62440449e-02 -3.47261797e-02 -1.25102172e-01 2.46400252e-02-3.49167611e-03 -8.78659553e-02 3.86936104e-02 1.49035447e-032.32374232e-02 -5.74477020e-02 -1.36891742e-01 1.36123979e-02-4.88133865e-02 -5.74810409e-02 1.77515908e-01 -5.23769256e-034.06755762e-02 -9.04404090e-03 -6.34098078e-03 1.54080695e-018.85118474e-02 3.36738814e-03 8.23197488e-02 -4.97083063e-032.35096290e-02 -4.80790235e-02 -1.16362870e-02 -1.74476376e-018.02275522e-02 3.67902632e-01 -1.70801496e-01 -1.06224464e-012.83182527e-01 2.57067335e-01 2.95422914e-02 -1.55890413e-012.86382860e-01 3.78936970e-02 -1.01663872e-01 -4.88765495e-01-1.53292684e-01 -1.45762205e-01 -3.74187655e-02 7.27300522e-03-7.57582232e-02 6.80128902e-02 -9.93414482e-03 -5.80535623e-02-1.23798193e-02 -3.13483910e-03 2.27974344e-01 -2.69272900e-02-2.03951860e-01 3.79730351e-02 2.66014738e-02 -3.88026206e-02-6.09131082e-02 2.44176324e-02 -9.06102046e-03 -4.58250689e-025.21858719e-03 -3.11362963e-02 2.43449989e-02 3.14315744e-024.06755762e-02 -9.73816178e-04 2.21600062e-02 -4.38964656e-02-2.00279580e-03 -3.05408583e-02 3.73557951e-02 5.22790699e-02-5.54453739e-03 1.78015408e-02 -7.12755653e-02 2.70737039e-032.35096290e-02 -1.59047546e-01 9.15192919e-03 -9.31798486e-02-3.47261797e-02 1.05507312e-01 1.36123979e-02 -3.24444325e-028.94897505e-02 4.06755762e-02 -1.37699304e-02 -8.69028761e-02-1.31838624e-02 -1.44602158e-01 2.35096290e-02 1.49838911e-012.42577307e-02 3.43031737e-02 2.50531873e-02 -2.78316196e-02-6.15983620e-02 3.30344036e-02 2.31681547e-03 -2.51053434e-02-4.40556137e-02 5.57076208e-02 -3.63960679e-02 -8.69624995e-022.00569516e-02 -8.57990684e-04 5.35089606e-02 2.87088021e-01-2.87088021e-01 8.95978968e-03 3.45749147e-02 -2.56327505e-02-2.59273404e-02 -3.16117225e-02 -2.03838303e-02 2.57507332e-028.69717534e-02 -1.74139681e-02 -2.49845413e-02 -2.34973847e-011.18355195e-01 1.49699481e-01 1.72561102e-02 3.95507939e-02-1.45467260e-02 4.65258485e-02 1.17125583e+00 2.66533224e-016.63525864e-01 -7.27827630e-01 -5.07667170e-02 -4.98233485e-023.39861659e-01 1.97761640e-01 2.48696844e-01 -5.82757947e-036.48555493e-02 8.79573597e-03 -1.30352193e-01 -5.50644196e-034.56574410e-02 3.52357383e-02 1.26392843e-02 -1.45606838e-022.26005503e-02 -3.70668567e-02 6.17429857e-03 6.23984329e-03-6.37739438e-03 -1.26999656e-03 2.70265911e-02 4.07870314e-021.75550803e-02 4.88231677e-02 2.47230063e-02 3.41322946e-02-8.00533358e-03 -2.33559829e-02 4.48247183e-02 -1.59850017e-021.04536247e-03 1.47047168e-02 -4.07252943e-02 6.14464901e-02-1.56271527e-02 -5.20450618e-02 1.72157416e-02 -2.34973759e-015.45197343e-04 -4.45609679e-03 4.06560403e-02 8.79573597e-03-4.57926861e-03 2.48132054e-02 3.39024037e-02 6.35446089e-047.53157026e-04 2.90646964e-02 1.85728920e-02 -2.99027909e-028.22948962e-04 -6.51020747e-01 -1.99112025e-02 6.21244989e-021.65282739e-02 5.70440732e-02 -1.34075287e-02 2.84760273e-024.99995700e-02 -1.43149285e-02 -1.55062812e-02 5.77329914e-02-3.69292506e-01 1.85185705e-01 -1.62540396e+00 -6.10308780e-021.90180669e-03 -4.04372675e-02 5.61635933e-02 1.09464402e-011.95775552e-02 -1.41957598e+00 0.00000000e+00 1.52638296e-011.51874586e-01 -3.35707151e-01 2.10206942e-02 -8.88917872e-031.49249708e-01 2.08298466e-02 1.81110355e-01 6.04814282e-023.95429998e-02 -2.45003137e-02 1.37817961e-01 -4.82220155e-02-5.67961117e-01 -1.83616676e-02 0.00000000e+00 8.16848461e-02-1.63960438e-01 2.52193554e-02 -1.29585721e+00 1.20071731e-02-2.34232528e-02 -1.92393043e-02 2.97280736e-02 1.32905137e-011.50310263e-01 1.69551084e-02 -1.16779181e+00 -5.78850347e-011.82971161e-01 -1.89815872e-02 2.57564229e-02 4.14126041e-022.77022159e-01 -2.39123563e-01 -1.10876152e-01 -7.35060996e-011.38831593e-02 4.28625899e-02 -1.19294741e-02 6.30333266e-021.03028112e-03 -3.50181242e-02 -7.23435726e-03 -2.48613475e-031.05123678e-02 -1.72779241e-02 -7.35060996e-01 3.85574950e-02-6.53372808e-03 6.30333266e-02 -1.19474000e-02 -5.50644196e-03-2.48613475e-03 4.19392113e-02 -1.72779241e-02 -7.35060996e-01-1.65351730e-02 7.62270772e-03 6.30333266e-02 -1.19474000e-028.68768714e-03 -5.50644196e-03 -2.48613475e-03 -5.67461262e-026.30333266e-02 -8.79573597e-03 7.83747806e-03 -2.48613475e-032.01469636e-02 -4.07393974e-02 3.66672040e-01 9.38992277e-01-5.11948249e-01 -1.17099133e-01 -7.98523467e-01 3.11488704e-023.18128110e-02 -2.66613114e-02 1.11889429e-01 -1.79139718e-01-8.02663810e-02 -5.60761108e-03 -1.40482455e-02 3.03537826e-02-1.19358442e-02 8.01655241e-02 -1.07307290e-01 -9.81331256e-032.74842494e-04 7.57205724e-02 1.57883850e-02 2.44127053e-021.60225360e-02 1.84400447e-02 2.20798953e-02 2.07603753e-02-1.06303656e+00 -2.68607668e-02 9.87097940e-02 3.61727162e-039.17383247e-02 -9.48509683e-02 -5.39205127e-03 7.72450470e-021.05271766e-02 -1.13628793e-02 6.68173269e-02 -1.85428803e-023.04033958e-02 2.83028233e-02 -5.33805724e-01 -2.60507241e-02-1.71841724e-02 -1.70909119e-02 -3.64454160e-02 5.74614270e-021.61836314e-01 -1.17644747e-02 4.01201859e-02 4.25922863e-022.24045782e-02 -9.01743750e-02 6.99669105e-04 -2.71684652e-03-3.86347376e-02 4.01499594e-03 1.86945941e-02 6.05694714e-02-3.15348183e-02 3.99132207e-02 2.91947040e-02 2.49551591e-02-5.86622605e-02 3.60658476e-02 7.84888374e-04 5.02475053e-02-9.46789071e-02 3.33914878e-02 2.62680076e-02 3.20750525e-02-5.94337201e-01 1.08208228e-01 -1.53157252e-02 2.14145748e-02-6.50727785e-02 8.32744213e-02 -6.04723054e-03 -3.97474836e-025.62623026e-02 -2.11583861e-03 5.94678753e-03 3.60987927e-02-3.67392667e-02 -1.53115476e-02 -1.09345814e+00 5.78387804e-03-3.49596972e-04 8.32295952e-02 -3.78016197e-02 1.66456045e-01-2.75717539e-02 -1.22802640e-02 -1.86061772e-01 -2.41814902e-02-9.50519553e-03 7.43952479e-02 6.96787657e-02 -2.90360728e-022.80817919e-02 6.00474195e-02 -6.38743060e-02 -7.49832513e-023.36176183e-02 9.16755527e-03 -4.55444360e-02 8.08578673e-022.25488387e-02 2.17729754e-02 2.75659487e-02 7.55106467e-02-1.23013676e-01 -1.13212007e-01 -9.00521884e-02 -7.22166756e-012.76286610e-03 -1.46307816e-02 7.45215701e-02 1.65937294e-02-1.64732342e-02 -7.48207181e-03 -1.57432618e-02 7.50349338e-03-3.54804751e-02 6.72622789e-02 -1.58077957e-03 -2.00818661e-027.05419732e-02 5.56183347e-02 4.35683709e-02 -1.51234264e-02-5.16263909e-02 4.48685948e-02 -3.25668703e-01 7.63067239e-031.02488270e-02 -1.67080754e-02 -1.15820085e-02 -2.86029040e-025.34047963e-02 -3.72715378e-02 -3.42018332e-02 -2.63880779e-021.32741848e-01 -7.14347815e-02 3.02172395e-02 6.45711463e-024.12247244e-01 -4.90592028e-01 7.14347815e-02 8.22661492e-012.48613475e-03 -2.48613475e-03]
Plotting Loss and accuracy curve
import matplotlib.pyplot as plt# Loss curve
plt.plot(train_loss)
plt.plot(dev_loss)
plt.title('Loss')
plt.legend(['train', 'dev'])
plt.savefig('loss.png')
plt.show()# Accuracy curve
plt.plot(train_acc)
plt.plot(dev_acc)
plt.title('Accuracy')
plt.legend(['train', 'dev'])
plt.savefig('acc.png')
plt.show()
Predicting testing labels
预测测试集的数据标签并且存在output_logistic.csv中。
# Predict testing labels
predictions = _predict(X_test, w, b)
with open(output_fpath.format('logistic'), 'w') as f:f.write('id,label\n')for i, label in enumerate(predictions):f.write('{},{}\n'.format(i, label))# Print out the most significant weights
ind = np.argsort(np.abs(w))[::-1]
with open(X_test_fpath) as f:content = f.readline().strip('\n').split(',')
features = np.array(content)
for i in ind[0:10]:print(features[i], w[i])
Not in universe -4.031960278019252Spouse of householder -1.6254039587051405Other Rel <18 never married RP of subfamily -1.4195759775765422Child 18+ ever marr Not in a subfamily -1.2958572076664725Unemployed full-time 1.1712558285885906Other Rel <18 ever marr RP of subfamily -1.1677918072962385Italy -1.0934581438006181Vietnam -1.0630365633146415
num persons worked for employer 0.938992277356651 0.8226614922117186
Porbabilistic generative model
基于generative model的二元分类器
Preparing Data
训练集与测试集的处理方法跟logistic regression一模一样，然而因为generative model有可解析的最佳解，因此不必使用到development set。
# Parse csv files to numpy array
with open(X_train_fpath) as f:next(f)X_train = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)
with open(Y_train_fpath) as f:next(f)Y_train = np.array([line.strip('\n').split(',')[1] for line in f], dtype = float)
with open(X_test_fpath) as f:next(f)X_test = np.array([line.strip('\n').split(',')[1:] for line in f], dtype = float)# Normalize training and testing data
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)
Mean and Covariance
在generative model中，我们需要分别计算两个类别内的数据平均与协方差
# Compute in-class mean
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])mean_0 = np.mean(X_train_0, axis = 0)
mean_1 = np.mean(X_train_1, axis = 0) # Compute in-class covariance
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]
for x in X_train_1:cov_1 += np.dot(np.transpose([x - mean_1]), [x - mean_1]) / X_train_1.shape[0]# 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])
Computing weights and bias
# 计算协方差矩阵的逆
# 由于协方差矩阵可能几乎是奇异的，因此np.linalg.inv（）可能会给出较大的数值误差.
# 通过奇异值分解，可以高效、准确地得到矩阵逆。
u, s, v = np.linalg.svd(cov, full_matrices=False)
inv = np.matmul(v.T * 1 / s, u.T)# Directly compute weights and 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]) # Compute accuracy on training set
Y_train_pred = 1 - _predict(X_train, w, b)
print('Training accuracy: {}'.format(_accuracy(Y_train_pred, Y_train)))
Training accuracy: 0.871885137127691
Predicting testing labels
预测测试集的数据标签并且存在output_generative.csv中。
# Predict testing labels
predictions = 1 - _predict(X_test, w, b)
with open(output_fpath.format('generative'), 'w') as f:f.write('id,label\n')for i, label in enumerate(predictions):f.write('{},{}\n'.format(i, label))# Print out the most significant weights
ind = np.argsort(np.abs(w))[::-1]
with open(X_test_fpath) as f:content = f.readline().strip('\n').split(',')
features = np.array(content)
for i in ind[0:10]:print(features[i], w[i])
Retail trade 8.179687534 -6.2187537 -5.7890625Other service -5.328125Other professional services -4.51562544 4.23437529 -3.125Same county 3.078125Different state in West -3.0546875Forestry and fisheries 2.90625
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