內(nèi)容介紹
- 線性回歸模型：
- 線性回歸對于特征的要求灰署；
- 處理長尾分布；
- 理解線性回歸模型局嘁；
- 模型性能驗證：
- 評價函數(shù)與目標(biāo)函數(shù)溉箕；
- 交叉驗證方法；
- 留一驗證方法悦昵；
- 針對時間序列問題的驗證肴茄；
- 繪制學(xué)習(xí)率曲線；
- 繪制驗證曲線但指；
- 嵌入式特征選擇：
- Lasso回歸寡痰；
- Ridge回歸；
- 決策樹棋凳；
- 模型對比：
- 常用線性模型拦坠；
- 常用非線性模型；
- 模型調(diào)參：
- 貪心調(diào)參方法剩岳；
- 網(wǎng)格調(diào)參方法贞滨；
- 貝葉斯調(diào)參方法；
代碼示例
1：讀取數(shù)據(jù)
import pandas as pd
import numpy as np
import warnings
warnings.filterwarnings('ignore')
reduce_mem_usage 函數(shù)通過調(diào)整數(shù)據(jù)類型拍棕，幫助我們減少數(shù)據(jù)在內(nèi)存中占用的空間,可復(fù)用
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'))
continuous_feature_names = [x for x in sample_feature.columns if x not in ['price','brand','model','brand']]
2:線性回歸 & 五折交叉驗證 & 模擬真實業(yè)務(wù)情況
sample_feature = sample_feature.dropna().replace('-', 0).reset_index(drop=True) #記得重置索引
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']
3：簡單建模
from sklearn.linear_model import LinearRegression
model = LinearRegression(normalize=True)
model = model.fit(train_X, train_y)
查看訓(xùn)練的線性回歸模型的截距（intercept）與權(quán)重(coef)
'intercept:'+ str(model.intercept_)
sorted(dict(zip(continuous_feature_names, model.coef_)).items(), key=lambda x:x[1], reverse=True)
from matplotlib import pyplot as plt
subsample_index = np.random.randint(low=0, high=len(train_y), size=50)
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()
偏差.PNG
通過作圖我們發(fā)現(xiàn)數(shù)據(jù)的標(biāo)簽（price）呈現(xiàn)長尾分布晓铆，不利于我們的建模預(yù)測。原因是很多模型都假設(shè)數(shù)據(jù)誤差項符合正態(tài)分布绰播，而長尾分布的數(shù)據(jù)違背了這一假設(shè)
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)])
標(biāo)簽price分布.PNG
我們對標(biāo)簽進行了 log(y+1)變換骄噪，使標(biāo)簽貼近于正態(tài)分布,加一防止變?yōu)?
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)])
log變換.PNG
重新預(yù)測
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)
再次進行可視化，發(fā)現(xiàn)預(yù)測結(jié)果與真實值較為接近蠢箩，且未出現(xiàn)異常狀況
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()
無偏差.PNG
4:交叉驗證
在使用訓(xùn)練集對參數(shù)進行訓(xùn)練的時候腰池，經(jīng)常會發(fā)現(xiàn)人們通常會將一整個訓(xùn)練集分為三個部分（比如mnist手寫訓(xùn)練集）尾组。一般分為：訓(xùn)練集（train_set），評估集（valid_set）示弓，測試集（test_set）這三個部分讳侨。這其實是為了保證訓(xùn)練效果而特意設(shè)置的。其中測試集很好理解奏属，其實就是完全不參與訓(xùn)練的數(shù)據(jù)跨跨，僅僅用來觀測測試效果的數(shù)據(jù)。而訓(xùn)練集和評估集則牽涉到下面的知識了囱皿。
因為在實際的訓(xùn)練中勇婴，訓(xùn)練的結(jié)果對于訓(xùn)練集的擬合程度通常還是挺好的（初始條件敏感），但是對于訓(xùn)練集之外的數(shù)據(jù)的擬合程度通常就不那么令人滿意了嘱腥。因此我們通常并不會把所有的數(shù)據(jù)集都拿來訓(xùn)練耕渴，而是分出一部分來（這一部分不參加訓(xùn)練）對訓(xùn)練集生成的參數(shù)進行測試，相對客觀的判斷這些參數(shù)對訓(xùn)練集之外的數(shù)據(jù)的符合程度齿兔。這種思想就稱為交叉驗證（Cross Validation）
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)))
使用線性回歸模型橱脸，對未處理標(biāo)簽的特征數(shù)據(jù)進行五折交叉驗證
print('AVG:', np.mean(scores))
使用線性回歸模型，對處理過標(biāo)簽的特征數(shù)據(jù)進行五折交叉驗證
scores = cross_val_score(model, X=train_X, y=train_y_ln, verbose=1, cv = 5, scoring=make_scorer(mean_absolute_error))
print('AVG:', np.mean(scores))
scores = pd.DataFrame(scores.reshape(1,-1))
scores.columns = ['cv' + str(x) for x in range(1, 6)]
scores.index = ['MAE']
scores
模擬真實業(yè)務(wù)情況
但在事實上分苇，由于我們并不具有預(yù)知未來的能力添诉，五折交叉驗證在某些與時間相關(guān)的數(shù)據(jù)集上反而反映了不真實的情況。通過2018年的二手車價格預(yù)測2017年的二手車價格医寿，這顯然是不合理的栏赴，因此我們還可以采用時間順序?qū)?shù)據(jù)集進行分隔。在本例中靖秩，我們選用靠前時間的4/5樣本當(dāng)作訓(xùn)練集须眷，靠后時間的1/5當(dāng)作驗證集，最終結(jié)果與五折交叉驗證差距不大
import datetime
sample_feature = sample_feature.reset_index(drop=True)
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))
5:繪制學(xué)習(xí)率曲線與驗證曲線
from sklearn.model_selection import learning_curve, validation_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()#區(qū)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)
學(xué)習(xí)曲線.PNG
6:多種模型對比
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)
6.1:線性模型 & 嵌入式特征選擇
在過濾式和包裹式特征選擇方法中沟突，特征選擇過程與學(xué)習(xí)器訓(xùn)練過程有明顯的分別柒爸。而嵌入式特征選擇在學(xué)習(xí)器訓(xùn)練過程中自動地進行特征選擇。嵌入式選擇最常用的是L1正則化與L2正則化事扭。在對線性回歸模型加入兩種正則化方法后，他們分別變成了嶺回歸與Lasso回歸乐横。
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')
#三種模型對比
result = pd.DataFrame(result)
result.index = ['cv' + str(x) for x in range(1, 6)]
result
模型對比.PNG
model = LinearRegression().fit(train_X, train_y_ln)
print('intercept:'+ str(model.intercept_))
sns.barplot(abs(model.coef_), continuous_feature_names)
線性回歸系數(shù)圖.PNG
L2正則化在擬合過程中通常都傾向于讓權(quán)值盡可能小求橄，最后構(gòu)造一個所有參數(shù)都比較小的模型。因為一般認為參數(shù)值小的模型比較簡單葡公，能適應(yīng)不同的數(shù)據(jù)集罐农，也在一定程度上避免了過擬合現(xiàn)象〈呤玻可以設(shè)想一下對于一個線性回歸方程涵亏，若參數(shù)很大，那么只要數(shù)據(jù)偏移一點點，就會對結(jié)果造成很大的影響气筋；但如果參數(shù)足夠小拆内，數(shù)據(jù)偏移得多一點也不會對結(jié)果造成什么影響，專業(yè)一點的說法是『抗擾動能力強』
model = Ridge().fit(train_X, train_y_ln)
print('intercept:'+ str(model.intercept_))
sns.barplot(abs(model.coef_), continuous_feature_names)
基于l2正則的Ridge.PNG
L1正則化有助于生成一個稀疏權(quán)值矩陣宠默，進而可以用于特征選擇麸恍。如下圖，我們發(fā)現(xiàn)power與userd_time特征非常重要搀矫。
model = Lasso().fit(train_X, train_y_ln)
print('intercept:'+ str(model.intercept_))
sns.barplot(abs(model.coef_), continuous_feature_names)
基于l1的lasso.PNG
除此之外抹沪，決策樹通過信息熵或GINI指數(shù)選擇分裂節(jié)點時，優(yōu)先選擇的分裂特征也更加重要瓤球，這同樣是一種特征選擇的方法融欧。XGBoost與LightGBM模型中的model_importance指標(biāo)正是基于此計算的
6.2:非線性模型
除了線性模型以外，還有許多我們常用的非線性模型如下卦羡，在此篇幅有限不再一一講解原理噪馏。我們選擇了部分常用模型與線性模型進行效果比對。
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')
result = pd.DataFrame(result)
result.index = ['cv' + str(x) for x in range(1, 6)]
result
模型比較.PNG
可以看到隨機森林模型在每一個fold中均取得了更好的效果
7：模型調(diào)參
#LGB的參數(shù)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 = []
7.1：貪心調(diào)參
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())])
貪心調(diào)參.PNG
7.2：網(wǎng)格搜索調(diào)參
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_
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)))
7.3：貝葉斯調(diào)參
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']
總結(jié)
在本章中虹茶，我們完成了建模與調(diào)參的工作逝薪，并對我們的模型進行了驗證。此外蝴罪，我們還采用了一些基本方法來提高預(yù)測的精度董济，提升如下圖所示。
plt.figure(figsize=(13,5))
sns.lineplot(x=['0_origin','1_log_transfer','2_L1_&_L2','3_change_model','4_parameter_turning'], y=[1.36 ,0.19, 0.19, 0.14, 0.13])
效果圖.PNG
