数据挖掘组队学习之建模调参

同DataWhale一起组队学习：https://tianchi.aliyun.com/notebook-ai/detail?spm=5176.12281978.0.0.6802593a2HCrSE&postId=95460

线性回归模型：
- 线性回归对于特征的要求；
- 处理长尾分布；
- 理解线性回归模型；
模型性能验证：
- 评价函数与目标函数；
- 交叉验证方法；
- 留一验证方法；
- 针对时间序列问题的验证；
- 绘制学习率曲线；
- 绘制验证曲线；
嵌入式特征选择：
- Lasso回归；
- Ridge回归；
- 决策树；
模型对比：
- 常用线性模型；
- 常用非线性模型；
模型调参：
- 贪心调参方法；
- 网格调参方法；
- 贝叶斯调参方法；

4.3 相关原理介绍与推荐

由于相关算法原理篇幅较长，本文推荐了一些博客与教材供初学者们进行学习。

4.4 代码示例

4.4.1 读取数据

import pandas as pd
import numpy as np
import warnings
warnings.filterwarnings('ignore')

reduce_mem_usage 函数通过调整数据类型，帮助我们减少数据在内存中占用的空间

def reduce_mem_usage(df):
    """ iterate through all the columns of a dataframe and modify the data type
        to reduce memory usage.        
    """
    start_mem = df.memory_usage().sum() 
    print('Memory usage of dataframe is {:.2f} MB'.format(start_mem))
    
    for col in df.columns:
        col_type = df[col].dtype
        
        if col_type != object:
            c_min = df[col].min()
            c_max = df[col].max()
            if str(col_type)[:3] == 'int':
                if c_min > np.iinfo(np.int8).min and c_max < np.iinfo(np.int8).max:
                    df[col] = df[col].astype(np.int8)
                elif c_min > np.iinfo(np.int16).min and c_max < np.iinfo(np.int16).max:
                    df[col] = df[col].astype(np.int16)
                elif c_min > np.iinfo(np.int32).min and c_max < np.iinfo(np.int32).max:
                    df[col] = df[col].astype(np.int32)
                elif c_min > np.iinfo(np.int64).min and c_max < np.iinfo(np.int64).max:
                    df[col] = df[col].astype(np.int64)  
            else:
                if c_min > np.finfo(np.float16).min and c_max < np.finfo(np.float16).max:
                    df[col] = df[col].astype(np.float16)
                elif c_min > np.finfo(np.float32).min and c_max < np.finfo(np.float32).max:
                    df[col] = df[col].astype(np.float32)
                else:
                    df[col] = df[col].astype(np.float64)
        else:
            df[col] = df[col].astype('category')

    end_mem = df.memory_usage().sum() 
    print('Memory usage after optimization is: {:.2f} MB'.format(end_mem))
    print('Decreased by {:.1f}%'.format(100 * (start_mem - end_mem) / start_mem))
    return df

sample_feature = reduce_mem_usage(pd.read_csv('data_for_tree.csv'))

Memory usage of dataframe is 62099672.00 MB
Memory usage after optimization is: 16520303.00 MB
Decreased by 73.4%

continuous_feature_names = [x for x in sample_feature.columns if x not in ['price','brand','model','brand']]
continuous_feature_names

['SaleID',
 'bodyType',
 'fuelType',
 'gearbox',
 'kilometer',
 'name',
 'notRepairedDamage',
 'offerType',
 'power',
 'seller',
 'train',
 'v_0',
 'v_1',
 'v_10',
 'v_11',
 'v_12',
 'v_13',
 'v_14',
 'v_2',
 'v_3',
 'v_4',
 'v_5',
 'v_6',
 'v_7',
 'v_8',
 'v_9',
 'used_time',
 'city',
 'brand_amount',
 'brand_price_max',
 'brand_price_median',
 'brand_price_min',
 'brand_price_sum',
 'brand_price_std',
 'brand_price_average',
 'power_bin']

4.4.2 线性回归 & 五折交叉验证 & 模拟真实业务情况

sample_feature = sample_feature.dropna().replace('-', 0).reset_index(drop=True)
sample_feature['notRepairedDamage'] = sample_feature['notRepairedDamage'].astype(np.float32)
train = sample_feature[continuous_feature_names + ['price']]

train_X = train[continuous_feature_names]
train_y = train['price']

4.4.2 - 1 简单建模

from sklearn.linear_model import LinearRegression

model = LinearRegression(normalize=True)

model = model.fit(train_X, train_y)

查看训练的线性回归模型的截距（intercept）与权重(coef)

print('intercept:'+ str(model.intercept_))

sorted(dict(zip(continuous_feature_names, model.coef_)).items(), key=lambda x:x[1], reverse=True)

intercept:-110670.68276350443

[('v_6', 3367064.3416419127),
 ('v_8', 700675.5609398747),
 ('v_9', 170630.27723219778),
 ('v_7', 32322.66193202066),
 ('v_12', 20473.670796956518),
 ('v_3', 17868.079541495277),
 ('v_11', 11474.93899667472),
 ('v_13', 11261.764560013775),
 ('v_10', 2683.920090636247),
 ('gearbox', 881.8225039248076),
 ('fuelType', 363.9042507217425),
 ('bodyType', 189.60271012071334),
 ('city', 44.94975120521506),
 ('power', 28.553901616753308),
 ('brand_price_median', 0.5103728134078945),
 ('brand_price_std', 0.4503634709263306),
 ('brand_amount', 0.1488112039506502),
 ('brand_price_max', 0.0031910186703142654),
 ('SaleID', 5.355989919859153e-05),
 ('seller', 1.7292331904172897e-05),
 ('offerType', -3.609340637922287e-06),
 ('train', -8.841510862112045e-06),
 ('brand_price_sum', -2.1750068681876416e-05),
 ('name', -0.0002980012713070219),
 ('used_time', -0.0025158943328975666),
 ('brand_price_average', -0.4049048451011582),
 ('brand_price_min', -2.2467753486897433),
 ('power_bin', -34.42064411727693),
 ('v_14', -274.78411807745636),
 ('kilometer', -372.8975266607184),
 ('notRepairedDamage', -495.1903844630634),
 ('v_0', -2045.0549573528133),
 ('v_5', -11022.986240572642),
 ('v_4', -15121.731109855522),
 ('v_2', -26098.299920511883),
 ('v_1', -45556.18929722599)]

分析结果

from matplotlib import pyplot as plt

subsample_index = np.random.randint(low=0, high=len(train_y), size=50)

绘制特征v_9的值与标签的散点图，图片发现模型的预测结果（蓝色点）与真实标签（黑色点）的分布差异较大，且部分预测值出现了小于0的情况，说明我们的模型存在一些问题

plt.scatter(train_X['v_9'][subsample_index], train_y[subsample_index], color='black')
plt.scatter(train_X['v_9'][subsample_index], model.predict(train_X.loc[subsample_index]), color='blue')
plt.xlabel('v_9')
plt.ylabel('price')
plt.legend(['True Price','Predicted Price'],loc='upper right')
print('The predicted price is obvious different from true price')
plt.show()

The predicted price is obvious different from true price

数据挖掘之建模调参_20_1.png

通过作图我们发现数据的标签（price）呈现长尾分布，不利于我们的建模预测。原因是很多模型都假设数据误差项符合正态分布，而长尾分布的数据违背了这一假设。参考博客：https://blog.csdn.net/Noob_daniel/article/details/76087829，一般来说特征得符合正太分布，其结果也要服从正太分布

import seaborn as sns
print('It is clear to see the price shows a typical exponential distribution')
plt.figure(figsize=(15,5))
plt.subplot(1,2,1)
sns.distplot(train_y)
plt.subplot(1,2,2)
sns.distplot(train_y[train_y < np.quantile(train_y, 0.9)])

It is clear to see the price shows a typical exponential distribution

数据挖掘之建模调参_22_2.png

在这里我们对标签进行了 $log(x+1)$ 变换，使标签贴近于正态分布

train_y_ln = np.log(train_y + 1)

import seaborn as sns
print('The transformed price seems like normal distribution')
plt.figure(figsize=(15,5))
plt.subplot(1,2,1)
sns.distplot(train_y_ln)
plt.subplot(1,2,2)
sns.distplot(train_y_ln[train_y_ln < np.quantile(train_y_ln, 0.9)])

The transformed price seems like normal distribution

数据挖掘之建模调参_25_2.png

model = model.fit(train_X, train_y_ln)

print('intercept:'+ str(model.intercept_))
sorted(dict(zip(continuous_feature_names, model.coef_)).items(), key=lambda x:x[1], reverse=True)

intercept:18.750749465596538

[('v_9', 8.052409900567598),
 ('v_5', 5.764236596653164),
 ('v_12', 1.6182081236790842),
 ('v_1', 1.479831058297348),
 ('v_11', 1.1669016563604946),
 ('v_13', 0.9404711296033863),
 ('v_7', 0.7137273083565177),
 ('v_3', 0.6837875771083749),
 ('v_0', 0.00850051800990644),
 ('power_bin', 0.00849796930289138),
 ('gearbox', 0.007922377278334032),
 ('fuelType', 0.006684769706830405),
 ('bodyType', 0.004523520092703996),
 ('power', 0.0007161894205359879),
 ('brand_price_min', 3.334351114751914e-05),
 ('brand_amount', 2.8978797042783603e-06),
 ('brand_price_median', 1.2571172872987556e-06),
 ('brand_price_std', 6.659176363456033e-07),
 ('brand_price_max', 6.194956307516954e-07),
 ('brand_price_average', 5.999345965077057e-07),
 ('SaleID', 2.11941700396436e-08),
 ('seller', 3.923616986867273e-11),
 ('train', -1.5702994460298214e-11),
 ('offerType', -2.2708945834892802e-11),
 ('brand_price_sum', -1.5126504215939166e-10),
 ('name', -7.015512588894369e-08),
 ('used_time', -4.122479372349444e-06),
 ('city', -0.0022187824810420242),
 ('v_14', -0.004234223418117319),
 ('kilometer', -0.013835866226884267),
 ('notRepairedDamage', -0.27027942349846545),
 ('v_4', -0.8315701200994575),
 ('v_2', -0.9470842241619425),
 ('v_10', -1.6261466689774864),
 ('v_8', -40.343007487616305),
 ('v_6', -238.79036385506956)]

再次进行可视化，发现预测结果与真实值较为接近，且未出现异常状况

plt.scatter(train_X['v_9'][subsample_index], train_y[subsample_index], color='black')
plt.scatter(train_X['v_9'][subsample_index], np.exp(model.predict(train_X.loc[subsample_index])), color='blue')
plt.xlabel('v_9')
plt.ylabel('price')
plt.legend(['True Price','Predicted Price'],loc='upper right')
print('The predicted price seems normal after np.log transforming')
plt.show()

The predicted price seems normal after np.log transforming

数据挖掘之建模调参_28_1.png

4.4.2 - 2 五折交叉验证

from sklearn.model_selection import cross_val_score
from sklearn.metrics import mean_absolute_error,  make_scorer

def log_transfer(func):
    def wrapper(y, yhat):
        result = func(np.log(y), np.nan_to_num(np.log(yhat)))
        return result
    return wrapper

scores = cross_val_score(model, X=train_X, y=train_y, verbose=1, cv = 5, scoring=make_scorer(log_transfer(mean_absolute_error)))

[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    1.0s finished

使用线性回归模型，对未处理标签的特征数据进行五折交叉验证（Error 1.36）

print('AVG:', np.mean(scores))

AVG: 1.3658023920314064

使用线性回归模型，对处理过标签的特征数据进行五折交叉验证（Error 0.19）

scores = cross_val_score(model, X=train_X, y=train_y_ln, verbose=1, cv = 5, scoring=make_scorer(mean_absolute_error))

[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    1.1s finished

print('AVG:', np.mean(scores))

AVG: 0.19325301837047434

scores = pd.DataFrame(scores.reshape(1,-1))
scores.columns = ['cv' + str(x) for x in range(1, 6)]
scores.index = ['MAE']
scores

4.4.2 - 3 模拟真实业务情况

但在事实上，由于我们并不具有预知未来的能力，五折交叉验证在某些与时间相关的数据集上反而反映了不真实的情况。通过2018年的二手车价格预测2017年的二手车价格，这显然是不合理的，因此我们还可以采用时间顺序对数据集进行分隔。在本例中，我们选用靠前时间的4/5样本当作训练集，靠后时间的1/5当作验证集，最终结果与五折交叉验证差距不大

import datetime

sample_feature = sample_feature.reset_index(drop=True)

# 这是划分成五份后，选取了最近那一份的点
split_point = len(sample_feature) // 5 * 4

train = sample_feature.loc[:split_point].dropna()
val = sample_feature.loc[split_point:].dropna()

train_X = train[continuous_feature_names]
train_y_ln = np.log(train['price'] + 1)
val_X = val[continuous_feature_names]
val_y_ln = np.log(val['price'] + 1)

model = model.fit(train_X, train_y_ln)

mean_absolute_error(val_y_ln, model.predict(val_X))

0.19577667270300955

4.4.2 - 4 绘制学习率曲线与验证曲线

from sklearn.model_selection import learning_curve, validation_curve

? learning_curve

def plot_learning_curve(estimator, title, X, y, ylim=None, cv=None,n_jobs=1, train_size=np.linspace(.1, 1.0, 5 )):  
    plt.figure()  
    plt.title(title)  
    if ylim is not None:  
        plt.ylim(*ylim)  
    plt.xlabel('Training example')  
    plt.ylabel('score')  
    train_sizes, train_scores, test_scores = learning_curve(estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_size, scoring = make_scorer(mean_absolute_error))  
    train_scores_mean = np.mean(train_scores, axis=1)  
    train_scores_std = np.std(train_scores, axis=1)  
    test_scores_mean = np.mean(test_scores, axis=1)  
    test_scores_std = np.std(test_scores, axis=1)  
    plt.grid()#区域  
    plt.fill_between(train_sizes, train_scores_mean - train_scores_std,  
                     train_scores_mean + train_scores_std, alpha=0.1,  
                     color="r")  
    plt.fill_between(train_sizes, test_scores_mean - test_scores_std,  
                     test_scores_mean + test_scores_std, alpha=0.1,  
                     color="g")  
    plt.plot(train_sizes, train_scores_mean, 'o-', color='r',  
             label="Training score")  
    plt.plot(train_sizes, test_scores_mean,'o-',color="g",  
             label="Cross-validation score")  
    plt.legend(loc="best")  
    return plt

plot_learning_curve(LinearRegression(), 'Liner_model', train_X[:1000], train_y_ln[:1000], ylim=(0.0, 0.5), cv=5, n_jobs=1)

数据挖掘之建模调参_52_1.png

4.4.3 多种模型对比

train = sample_feature[continuous_feature_names + ['price']].dropna()

train_X = train[continuous_feature_names]
train_y = train['price']
train_y_ln = np.log(train_y + 1)

4.4.3 - 1 线性模型 & 嵌入式特征选择

本章节默认，学习者已经了解关于过拟合、模型复杂度、正则化等概念。否则请寻找相关资料或参考如下连接：

用简单易懂的语言描述「过拟合 overfitting」？ https://www.zhihu.com/question/32246256/answer/55320482
模型复杂度与模型的泛化能力 http://yangyingming.com/article/434/
正则化的直观理解 https://blog.csdn.net/jinping_shi/article/details/52433975

在过滤式和包裹式特征选择方法中，特征选择过程与学习器训练过程有明显的分别。而嵌入式特征选择在学习器训练过程中自动地进行特征选择。嵌入式选择最常用的是L1正则化与L2正则化。在对线性回归模型加入两种正则化方法后，他们分别变成了岭回归与Lasso回归。

from sklearn.linear_model import LinearRegression
from sklearn.linear_model import Ridge
from sklearn.linear_model import Lasso

models = [LinearRegression(),
          Ridge(),
          Lasso()]

result = dict()
for model in models:
    model_name = str(model).split('(')[0]
    scores = cross_val_score(model, X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error))
    result[model_name] = scores
    print(model_name + ' is finished')

LinearRegression is finished
Ridge is finished
Lasso is finished

对三种方法的效果对比

result = pd.DataFrame(result)
result.index = ['cv' + str(x) for x in range(1, 6)]
result

model = LinearRegression().fit(train_X, train_y_ln)
print('intercept:'+ str(model.intercept_))
sns.barplot(abs(model.coef_), continuous_feature_names)

intercept:18.750417086915647

数据挖掘之建模调参_63_2.png

L2正则化在拟合过程中通常都倾向于让权值尽可能小，最后构造一个所有参数都比较小的模型。因为一般认为参数值小的模型比较简单，能适应不同的数据集，也在一定程度上避免了过拟合现象。可以设想一下对于一个线性回归方程，若参数很大，那么只要数据偏移一点点，就会对结果造成很大的影响；但如果参数足够小，数据偏移得多一点也不会对结果造成什么影响，专业一点的说法是『抗扰动能力强』

model = Ridge().fit(train_X, train_y_ln)
print('intercept:'+ str(model.intercept_))
sns.barplot(abs(model.coef_), continuous_feature_names)

intercept:4.671709787512927

数据挖掘之建模调参_65_2.png

L1正则化有助于生成一个稀疏权值矩阵，进而可以用于特征选择。如下图，我们发现power与userd_time特征非常重要。

model = Lasso().fit(train_X, train_y_ln)
print('intercept:'+ str(model.intercept_))
sns.barplot(abs(model.coef_), continuous_feature_names)

intercept:8.672182402894254

数据挖掘之建模调参_67_2.png

除此之外，决策树通过信息熵或GINI指数选择分裂节点时，优先选择的分裂特征也更加重要，这同样是一种特征选择的方法。XGBoost与LightGBM模型中的model_importance指标正是基于此计算的

4.4.3 - 2 非线性模型

除了线性模型以外，还有许多我们常用的非线性模型如下，在此篇幅有限不再一一讲解原理。我们选择了部分常用模型与线性模型进行效果比对。

from sklearn.linear_model import LinearRegression
from sklearn.svm import SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
from sklearn.ensemble import GradientBoostingRegressor
from sklearn.neural_network import MLPRegressor
from xgboost.sklearn import XGBRegressor
from lightgbm.sklearn import LGBMRegressor

models = [LinearRegression(),
          DecisionTreeRegressor(),
          RandomForestRegressor(),
          GradientBoostingRegressor(),
          MLPRegressor(solver='lbfgs', max_iter=100), 
          XGBRegressor(n_estimators = 100, objective='reg:squarederror'), 
          LGBMRegressor(n_estimators = 100)]

result = dict()
for model in models:
    model_name = str(model).split('(')[0]
    scores = cross_val_score(model, X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error))
    result[model_name] = scores
    print(model_name + ' is finished')

LinearRegression is finished
DecisionTreeRegressor is finished
RandomForestRegressor is finished
GradientBoostingRegressor is finished
MLPRegressor is finished
XGBRegressor is finished
LGBMRegressor is finished

result = pd.DataFrame(result)
result.index = ['cv' + str(x) for x in range(1, 6)]
result

	LinearRegression	DecisionTreeRegressor	RandomForestRegressor	GradientBoostingRegressor	MLPRegressor	XGBRegressor	LGBMRegressor
cv1	0.191642	0.184566	0.136266	0.168626	124.299426	0.168698	0.141159
cv2	0.194986	0.187029	0.139693	0.171905	257.886236	0.172258	0.143363
cv3	0.192737	0.184839	0.136871	0.169553	236.829589	0.168604	0.142137
cv4	0.195329	0.182605	0.138689	0.172299	130.197264	0.172474	0.143461
cv5	0.194450	0.186626	0.137420	0.171206	268.090236	0.170898	0.141921

可以看到随机森林模型在每一个fold中均取得了更好的效果

4.4.4 模型调参

在此我们介绍了三种常用的调参方法如下：

贪心算法 https://www.jianshu.com/p/ab89df9759c8
网格调参 https://blog.csdn.net/weixin_43172660/article/details/83032029
贝叶斯调参 https://blog.csdn.net/linxid/article/details/81189154

## LGB的参数集合：

objective = ['regression', 'regression_l1', 'mape', 'huber', 'fair']

num_leaves = [3,5,10,15,20,40, 55]
max_depth = [3,5,10,15,20,40, 55]
bagging_fraction = []
feature_fraction = []
drop_rate = []

4.4.4 - 1 贪心调参

best_obj = dict()
for obj in objective:
    model = LGBMRegressor(objective=obj)
    score = np.mean(cross_val_score(model, X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error)))
    best_obj[obj] = score
    
best_leaves = dict()
for leaves in num_leaves:
    model = LGBMRegressor(objective=min(best_obj.items(), key=lambda x:x[1])[0], num_leaves=leaves)
    score = np.mean(cross_val_score(model, X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error)))
    best_leaves[leaves] = score
    
best_depth = dict()
for depth in max_depth:
    model = LGBMRegressor(objective=min(best_obj.items(), key=lambda x:x[1])[0],
                          num_leaves=min(best_leaves.items(), key=lambda x:x[1])[0],
                          max_depth=depth)
    score = np.mean(cross_val_score(model, X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error)))
    best_depth[depth] = score

sns.lineplot(x=['0_initial','1_turning_obj','2_turning_leaves','3_turning_depth'], y=[0.143 ,min(best_obj.values()), min(best_leaves.values()), min(best_depth.values())])

数据挖掘之建模调参_81_1.png

4.4.4 - 2 Grid Search 调参

from sklearn.model_selection import GridSearchCV

parameters = {'objective': objective , 'num_leaves': num_leaves, 'max_depth': max_depth}
model = LGBMRegressor()
clf = GridSearchCV(model, parameters, cv=5)
clf = clf.fit(train_X, train_y)

clf.best_params_

{'max_depth': 15, 'num_leaves': 55, 'objective': 'regression'}

model = LGBMRegressor(objective='regression',
                          num_leaves=55,
                          max_depth=15)

np.mean(cross_val_score(model, X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error)))

0.13754820909576437

4.4.4 - 3 贝叶斯调参

from bayes_opt import BayesianOptimization

def rf_cv(num_leaves, max_depth, subsample, min_child_samples):
    val = cross_val_score(
        LGBMRegressor(objective = 'regression_l1',
            num_leaves=int(num_leaves),
            max_depth=int(max_depth),
            subsample = subsample,
            min_child_samples = int(min_child_samples)
        ),
        X=train_X, y=train_y_ln, verbose=0, cv = 5, scoring=make_scorer(mean_absolute_error)
    ).mean()
    return 1 - val

rf_bo = BayesianOptimization(
    rf_cv,
    {
    'num_leaves': (2, 100),
    'max_depth': (2, 100),
    'subsample': (0.1, 1),
    'min_child_samples' : (2, 100)
    }
)

rf_bo.maximize()

1 - rf_bo.max['target']

0.1305927066054554