- 分类模型的预测目标是：类别编号
- 回归模型的预测目标是：实数变量
回归模型种类
- 线性模型
- 最小二乘回归模型
- 应用L2正则化时--岭回归(ridge regression)
- 应用L1正则化时--LASSO(Least Absolute Shrinkage and Selection Operator)
- 决策树
- 不纯度度量方法：方差
0 准备数据
archive.ics.uci.edu/ml/machine-learning-databases/00275/Bike-Sharing-Dataset.zip
sed 1d hour.csv > hour_noheader.csv
0 运行环境
export SPARK_HOME=/Users/erichan/garden/spark-1.5.1-bin-hadoop2.6
export PYTHONPATH=${SPARK_HOME}/python/:${SPARK_HOME}/python/lib/py4j-0.8.2.1-src.zip
cd $SPARK_HOME
IPYTHON=1 IPYTHON_OPTS="--pylab" ./bin/pyspark --driver-memory 4G --executor-memory 4G --driver-cores 2
from pyspark.mllib.regression import LabeledPoint
from pyspark.mllib.regression import LinearRegressionWithSGD
from pyspark.mllib.tree import DecisionTree
import numpy as np
1 抽取特征
PATH = "/Users/erichan/sourcecode/book/Spark机器学习"
raw_data = sc.textFile("%s/Bike-Sharing-Dataset/hour_noheader.csv" % PATH)
num_data = raw_data.count()
records = raw_data.map(lambda x: x.split(","))
first = records.first()
print first
print num_data
[u'1', u'2011-01-01', u'1', u'0', u'1', u'0', u'0', u'6', u'0', u'1', u'0.24', u'0.2879', u'0.81', u'0', u'3', u'13', u'16']
17379
1.1 转换为二元向量
# cache the dataset to speed up subsequent operations
records.cache()
def get_mapping(rdd, idx):
return rdd.map(lambda fields: fields[idx]).distinct().zipWithIndex().collectAsMap()
print "Mapping of first categorical feasture column: %s" % get_mapping(records, 2)
Mapping of first categorical feasture column: {u'1': 0, u'3': 1, u'2': 2, u'4': 3}
mappings = [get_mapping(records, i) for i in range(2,10)]
cat_len = sum(map(len, mappings))
num_len = len(records.first()[11:15])
total_len = num_len + cat_len
print "Feature vector length for categorical features: %d" % cat_len
print "Feature vector length for numerical features: %d" % num_len
print "Total feature vector length: %d" % total_len
Feature vector length for categorical features: 57
Feature vector length for numerical features: 4
Total feature vector length: 61
1.2 创建线性模型特征向量
# 提取特征
def extract_features(record):
cat_vec = np.zeros(cat_len)
i = 0
step = 0
for field in record[2:9]:
m = mappings[i]
idx = m[field]
cat_vec[idx + step] = 1
i = i + 1
step = step + len(m)
num_vec = np.array([float(field) for field in record[10:14]])
return np.concatenate((cat_vec, num_vec))
# 提取标签
def extract_label(record):
return float(record[-1])
data = records.map(lambda r: LabeledPoint(extract_label(r), extract_features(r)))
first_point = data.first()
print "Raw data: " + str(first[2:])
print "Label: " + str(first_point.label)
print "Linear Model feature vector:
" + str(first_point.features)
print "Linear Model feature vector length: " + str(len(first_point.features))
Raw data: [u'1', u'0', u'1', u'0', u'0', u'6', u'0', u'1', u'0.24', u'0.2879', u'0.81', u'0', u'3', u'13', u'16']
Label: 16.0
Linear Model feature vector:
[1.0,0.0,0.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.24,0.2879,0.81,0.0]Linear Model feature vector length: 61
1.3 创建决策树模型特征向量
def extract_features_dt(record):
return np.array(map(float, record[2:14]))
data_dt = records.map(lambda r: LabeledPoint(extract_label(r), extract_features_dt(r)))
first_point_dt = data_dt.first()
print "Decision Tree feature vector: " + str(first_point_dt.features)
print "Decision Tree feature vector length: " + str(len(first_point_dt.features))
Decision Tree feature vector: [1.0,0.0,1.0,0.0,0.0,6.0,0.0,1.0,0.24,0.2879,0.81,0.0]
Decision Tree feature vector length: 12
2 训练
2.1 帮助
help(LinearRegressionWithSGD.train)
help(DecisionTree.trainRegressor)
2.2 训练线性模型并测试预测效果
linear_model = LinearRegressionWithSGD.train(data, iterations=10, step=0.1, intercept=False)
true_vs_predicted = data.map(lambda p: (p.label, linear_model.predict(p.features)))
print "Linear Model predictions: " + str(true_vs_predicted.take(5))
Linear Model predictions: [(16.0, 117.89250386724845), (40.0, 116.2249612319211), (32.0, 116.02369145779234), (13.0, 115.67088016754433), (1.0, 115.56315650834317)]
2.3 训练决策树模型并测试预测效果
dt_model = DecisionTree.trainRegressor(data_dt, {})
preds = dt_model.predict(data_dt.map(lambda p: p.features))
actual = data.map(lambda p: p.label)
true_vs_predicted_dt = actual.zip(preds)
print "Decision Tree predictions: " + str(true_vs_predicted_dt.take(5))
print "Decision Tree depth: " + str(dt_model.depth())
print "Decision Tree number of nodes: " + str(dt_model.numNodes())
Decision Tree predictions: [(16.0, 54.913223140495866), (40.0, 54.913223140495866), (32.0, 53.171052631578945), (13.0, 14.284023668639053), (1.0, 14.284023668639053)]
Decision Tree depth: 5
Decision Tree number of nodes: 63
3 评估性能
评估回归模型的方法：
- 均方误差(MSE, Mean Sequared Error)
- 均方根误差(RMSE, Root Mean Squared Error)
- 平均绝对误差(MAE, Mean Absolute Error)
- R-平方系数(R-squared coefficient)
- 均方根对数误差(RMSLE)
3.1 均方误差&均方根误差
def squared_error(actual, pred):
return (pred - actual)**2
mse = true_vs_predicted.map(lambda (t, p): squared_error(t, p)).mean()
mse_dt = true_vs_predicted_dt.map(lambda (t, p): squared_error(t, p)).mean()
cat_features = dict([(i - 2, len(get_mapping(records, i)) + 1) for i in range(2,10)])
# train the model again
dt_model_2 = DecisionTree.trainRegressor(data_dt, categoricalFeaturesInfo=cat_features)
preds_2 = dt_model_2.predict(data_dt.map(lambda p: p.features))
actual_2 = data.map(lambda p: p.label)
true_vs_predicted_dt_2 = actual_2.zip(preds_2)
# compute performance metrics for decision tree model
mse_dt_2 = true_vs_predicted_dt_2.map(lambda (t, p): squared_error(t, p)).mean()
print "Linear Model - Mean Squared Error: %2.4f" % mse
print "Decision Tree - Mean Squared Error: %2.4f" % mse_dt
print "Categorical feature size mapping %s" % cat_features
print "Decision Tree [Categorical feature]- Mean Squared Error: %2.4f" % mse_dt_2
Linear Model - Mean Squared Error: 30679.4539
Decision Tree - Mean Squared Error: 11560.7978
Decision Tree [Categorical feature]- Mean Squared Error: 7912.5642
3.2 平均绝对误差
def abs_error(actual, pred):
return np.abs(pred - actual)
mae = true_vs_predicted.map(lambda (t, p): abs_error(t, p)).mean()
mae_dt = true_vs_predicted_dt.map(lambda (t, p): abs_error(t, p)).mean()
mae_dt_2 = true_vs_predicted_dt_2.map(lambda (t, p): abs_error(t, p)).mean()
print "Linear Model - Mean Absolute Error: %2.4f" % mae
print "Decision Tree - Mean Absolute Error: %2.4f" % mae_dt
print "Decision Tree [Categorical feature]- Mean Absolute Error: %2.4f" % mae_dt_2
Linear Model - Mean Absolute Error: 130.6429
Decision Tree - Mean Absolute Error: 71.0969
Decision Tree [Categorical feature]- Mean Absolute Error: 59.4409
3.3 均方根对数误差
def squared_log_error(pred, actual):
return (np.log(pred + 1) - np.log(actual + 1))**2
rmsle = np.sqrt(true_vs_predicted.map(lambda (t, p): squared_log_error(t, p)).mean())
rmsle_dt = np.sqrt(true_vs_predicted_dt.map(lambda (t, p): squared_log_error(t, p)).mean())
rmsle_dt_2 = np.sqrt(true_vs_predicted_dt_2.map(lambda (t, p): squared_log_error(t, p)).mean())
print "Linear Model - Root Mean Squared Log Error: %2.4f" % rmsle
print "Decision Tree - Root Mean Squared Log Error: %2.4f" % rmsle_dt
print "Decision Tree [Categorical feature]- Root Mean Squared Log Error: %2.4f" % rmsle_dt_2
Linear Model - Root Mean Squared Log Error: 1.4653
Decision Tree - Root Mean Squared Log Error: 0.6259
Decision Tree [Categorical feature]- Root Mean Squared Log Error: 0.6192
4 改进和调优
targets = records.map(lambda r: float(r[-1])).collect()
hist(targets, bins=40, color='lightblue', normed=True)
fig = matplotlib.pyplot.gcf()
fig.set_size_inches(16, 10)
因为**不符合正态分布**，所以**对数变换**（用目标值的对数代替原始数值）或者平方根
4.1 对数变换
log_targets = records.map(lambda r: np.log(float(r[-1]))).collect()
hist(log_targets, bins=40, color='lightblue', normed=True)
fig = matplotlib.pyplot.gcf()
fig.set_size_inches(16, 10)
4.2 平方根变换
sqrt_targets = records.map(lambda r: np.sqrt(float(r[-1]))).collect()
hist(sqrt_targets, bins=40, color='lightblue', normed=True)
fig = matplotlib.pyplot.gcf()
fig.set_size_inches(16, 10)
4.3 对数变换的影响
data_log = data.map(lambda lp: LabeledPoint(np.log(lp.label), lp.features))
model_log = LinearRegressionWithSGD.train(data_log, iterations=10, step=0.1)
true_vs_predicted_log = data_log.map(lambda p: (np.exp(p.label), np.exp(model_log.predict(p.features))))
data_dt_log = data_dt.map(lambda lp: LabeledPoint(np.log(lp.label), lp.features))
dt_model_log = DecisionTree.trainRegressor(data_dt_log, {})
preds_log = dt_model_log.predict(data_dt_log.map(lambda p: p.features))
actual_log = data_dt_log.map(lambda p: p.label)
true_vs_predicted_dt_log = actual_log.zip(preds_log).map(lambda (t, p): (np.exp(t), np.exp(p)))
mse_log = true_vs_predicted_log.map(lambda (t, p): squared_error(t, p)).mean()
mae_log = true_vs_predicted_log.map(lambda (t, p): abs_error(t, p)).mean()
rmsle_log = np.sqrt(true_vs_predicted_log.map(lambda (t, p): squared_log_error(t, p)).mean())
mse_log_dt = true_vs_predicted_dt_log.map(lambda (t, p): squared_error(t, p)).mean()
mae_log_dt = true_vs_predicted_dt_log.map(lambda (t, p): abs_error(t, p)).mean()
rmsle_log_dt = np.sqrt(true_vs_predicted_dt_log.map(lambda (t, p): squared_log_error(t, p)).mean())
print "Mean Squared Error: %2.4f" % mse_log
print "Mean Absolute Error: %2.4f" % mae_log
print "Root Mean Squared Log Error: %2.4f" % rmsle_log
print "Non log-transformed predictions:
" + str(true_vs_predicted.take(3))
print "Log-transformed predictions:
" + str(true_vs_predicted_log.take(3))
print "Mean Squared Error: %2.4f" % mse_log_dt
print "Mean Absolute Error: %2.4f" % mae_log_dt
print "Root Mean Squared Log Error: %2.4f" % rmsle_log_dt
print "Non log-transformed predictions:
" + str(true_vs_predicted_dt.take(3))
print "Log-transformed predictions:
" + str(true_vs_predicted_dt_log.take(3))
Mean Squared Error: 50685.5559
Mean Absolute Error: 155.2955
Root Mean Squared Log Error: 1.5411
Non log-transformed predictions:
[(16.0, 117.89250386724845), (40.0, 116.2249612319211), (32.0, 116.02369145779234)]Log-transformed predictions:
[(15.999999999999998, 28.080291845456237), (40.0, 26.959480191001784), (32.0, 26.654725629458031)]Mean Squared Error: 14781.5760
Mean Absolute Error: 76.4131
Root Mean Squared Log Error: 0.6406
Non log-transformed predictions:
[(16.0, 54.913223140495866), (40.0, 54.913223140495866), (32.0, 53.171052631578945)]Log-transformed predictions:
[(15.999999999999998, 37.530779787154522), (40.0, 37.530779787154522), (32.0, 7.2797070993907287)]
4.4 为交叉验证创建训练集和测试集
data_with_idx = data.zipWithIndex().map(lambda (k, v): (v, k))
test = data_with_idx.sample(False, 0.2, 42)
train = data_with_idx.subtractByKey(test)
train_data = train.map(lambda (idx, p): p)
test_data = test.map(lambda (idx, p) : p)
data_with_idx_dt = data_dt.zipWithIndex().map(lambda (k, v): (v, k))
test_dt = data_with_idx_dt.sample(False, 0.2, 42)
train_dt = data_with_idx_dt.subtractByKey(test_dt)
train_data_dt = train_dt.map(lambda (idx, p): p)
test_data_dt = test_dt.map(lambda (idx, p) : p)
train_size = train_data.count()
test_size = test_data.count()
print "Training data size: %d" % train_size
print "Test data size: %d" % test_size
print "Total data size: %d " % num_data
print "Train + Test size : %d" % (train_size + test_size)
Training data size: 13934
Test data size: 3445
Total data size: 17379
Train + Test size : 17379
4.5 线性模型调优
1 评估函数
def evaluate(train, test, iterations, step, regParam, regType, intercept):
model = LinearRegressionWithSGD.train(train, iterations, step, regParam=regParam, regType=regType, intercept=intercept)
tp = test.map(lambda p: (p.label, model.predict(p.features)))
rmsle = np.sqrt(tp.map(lambda (t, p): squared_log_error(t, p)).mean())
return rmsle
2 迭代次数
params = [1, 5, 10, 20, 50, 100]
metrics = [evaluate(train_data, test_data, param, 0.01, 0.0, 'l2', False) for param in params]
print params
print metrics
[1, 5, 10, 20, 50, 100]
[2.8779465130028199, 2.0390187660391499, 1.7761565324837874, 1.5828778102209105, 1.4382263191764473, 1.4050638054019446]
plot(params, metrics)
fig = matplotlib.pyplot.gcf()
pyplot.xscale('log')
迭代次数与RMSLE关系图
3 步长
params = [0.01, 0.025, 0.05, 0.1, 1.0]
metrics = [evaluate(train_data, test_data, 10, param, 0.0, 'l2', False) for param in params]
print params
print metrics
[0.01, 0.025, 0.05, 0.1, 1.0]
[1.7761565324837874, 1.4379348243997032, 1.4189071944747715, 1.5027293911925559, nan]
plot(params, metrics)
fig = matplotlib.pyplot.gcf()
pyplot.xscale('log')
步长对预测结果的影响
4 L2正则化
params = [0.0, 0.01, 0.1, 1.0, 5.0, 10.0, 20.0]
metrics = [evaluate(train_data, test_data, 10, 0.1, param, 'l2', False) for param in params]
print params
print metrics
plot(params, metrics)
fig = matplotlib.pyplot.gcf()
pyplot.xscale('log')
[0.0, 0.01, 0.1, 1.0, 5.0, 10.0, 20.0]
[1.5027293911925559, 1.5020646031965639, 1.4961903335175231, 1.4479313176192781, 1.4113329999970989, 1.5379824584440471, 1.8279564444985839]
5 L1正则化
params = [0.0, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]
metrics = [evaluate(train_data, test_data, 10, 0.1, param, 'l1', False) for param in params]
print params
print metrics
plot(params, metrics)
fig = matplotlib.pyplot.gcf()
pyplot.xscale('log')
[0.0, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]
[1.5027293911925559, 1.5026938950690176, 1.5023761634555699, 1.499412856617814, 1.4713669769550108, 1.7596682962964318, 4.7551250073268614]
model_l1 = LinearRegressionWithSGD.train(train_data, 10, 0.1, regParam=1.0, regType='l1', intercept=False)
model_l1_10 = LinearRegressionWithSGD.train(train_data, 10, 0.1, regParam=10.0, regType='l1', intercept=False)
model_l1_100 = LinearRegressionWithSGD.train(train_data, 10, 0.1, regParam=100.0, regType='l1', intercept=False)
print "L1 (1.0) number of zero weights: " + str(sum(model_l1.weights.array == 0))
print "L1 (10.0) number of zeros weights: " + str(sum(model_l1_10.weights.array == 0))
print "L1 (100.0) number of zeros weights: " + str(sum(model_l1_100.weights.array == 0))
L1 (1.0) number of zero weights: 4
L1 (10.0) number of zeros weights: 33
L1 (100.0) number of zeros weights: 58
6 截距
# Intercept
params = [False, True]
metrics = [evaluate(train_data, test_data, 10, 0.1, 1.0, 'l2', param) for param in params]
print params
print metrics
bar(params, metrics, color='lightblue')
fig = matplotlib.pyplot.gcf()
[False, True]
[1.4479313176192781, 1.4798261513419801]
4.6 决策树调优
1 评估函数
def evaluate_dt(train, test, maxDepth, maxBins):
model = DecisionTree.trainRegressor(train, {}, impurity='variance', maxDepth=maxDepth, maxBins=maxBins)
preds = model.predict(test.map(lambda p: p.features))
actual = test.map(lambda p: p.label)
tp = actual.zip(preds)
rmsle = np.sqrt(tp.map(lambda (t, p): squared_log_error(t, p)).mean())
return rmsle
2 树深度
params = [1, 2, 3, 4, 5, 10, 20]
metrics = [evaluate_dt(train_data_dt, test_data_dt, param, 32) for param in params]
print params
print metrics
plot(params, metrics)
fig = matplotlib.pyplot.gcf()
[1, 2, 3, 4, 5, 10, 20]
[1.0280339660196287, 0.92686672078778276, 0.81807794023407532, 0.74060228537329209, 0.63583503599563096, 0.4276659008415965, 0.45481197001756291]
3 最大划分数
params = [2, 4, 8, 16, 32, 64, 100]
metrics = [evaluate_dt(train_data_dt, test_data_dt, 5, param) for param in params]
print params
print metrics
plot(params, metrics)
fig = matplotlib.pyplot.gcf()
[2, 4, 8, 16, 32, 64, 100]
[1.3076555360778914, 0.81721457107308615, 0.75651792347650992, 0.63786761731722474, 0.63583503599563096, 0.63583503599563096, 0.63583503599563096]
