lapras 0.0.23

scorecard,logistical regression

LAPRAS

Lapras is designed to make the model developing job easily and conveniently. It contains these functions below in one key operation: data exploratory analysis, feature selection, feature binning, data visualization, scorecard modeling(a logistic regression model with excellent interpretability), performance measure.

Let's get started.

Usage

1.Exploratory Data Analysis lapras.detect() lapras.eda() lapras.quality() lapras.IV() lapras.VIF() lapras.PSI()

2.Feature Selection lapras.select() lapras.stepwise()

3.Binning lapras.Combiner() lapras.WOETransformer() lapras.bin_stats() lapras.bin_plot()

4.Modeling lapras.ScoreCard()

5.Performance Measure lapras.perform() lapras.LIFT() lapras.score_plot() lapras.KS_bucket() lapras.PPSI() lapras.KS() lapras.AUC()

6.One Key Auto Modeling Lapras also provides a function which runs all the steps above automatically: lapras.auto_model()

Install

via pip

pip install lapras --upgrade -i https://pypi.org/simple

via source code

python setup.py install

install_requires = [ 'numpy >= 1.18.4', 'pandas >= 0.25.1', 'scipy >= 1.3.2', 'scikit-learn =0.22.2', 'seaborn >= 0.10.1', 'statsmodels >= 0.13.1', 'tensorflow >= 2.2.0', 'hyperopt >= 0.2.7', 'pickle >= 4.0', 'plotly >= 5.9.0', ]

Documents

import lapras

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
import matplotlib as mpl
import matplotlib.pyplot as plt

pd.options.display.max_colwidth = 100
import math
%matplotlib inline

# Read in data file
df = pd.read_csv('data/demo.csv',encoding="utf-8")

to_drop = ['id'] # exclude the features which not being used， eg:id
target = 'bad' # Y label name
train_df, test_df, _, _ = train_test_split(df, df[[target]], test_size=0.3, random_state=42) # to divide the training set and testing set, strongly recommended

# EDA(Exploratory Data Analysis)
# Parameter details：
# dataframe=None 
lapras.detect(train_df).sort_values("missing")

	type	size	missing	unique	mean_or_top1	std_or_top2	min_or_top3	1%_or_top4	10%_or_top5	50%_or_bottom5	75%_or_bottom4	90%_or_bottom3	99%_or_bottom2	max_or_bottom1
id	int64	5502	0.0000	5502	3947.266630	2252.395671	2.0	87.03	820.1	3931.5	5889.25	7077.8	7782.99	7861.0
bad	int64	5502	0.0000	2	0.073246	0.260564	0.0	0.00	0.0	0.0	0.00	0.0	1.00	1.0
score	int64	5502	0.0000	265	295.280625	66.243181	0.0	0.00	223.0	303.0	336.00	366.0	416.00	461.0
age	float64	5502	0.0002	34	27.659880	4.770299	19.0	21.00	23.0	27.0	30.00	34.0	43.00	53.0
wealth	float64	5502	0.0244	18	4.529806	1.823149	1.0	1.00	3.0	4.0	5.00	7.0	10.00	22.0
education	float64	5502	0.1427	5	3.319483	1.005660	1.0	1.00	2.0	4.0	4.00	4.0	5.00	5.0
period	float64	5502	0.1714	5	7.246326	1.982060	4.0	4.00	6.0	6.0	10.00	10.0	10.00	14.0
max_unpay_day	float64	5502	0.9253	11	185.476886	22.339647	28.0	86.00	171.0	188.0	201.00	208.0	208.00	208.0

# Exploratory Data Analysis
# feature_list = ['age', 'education', 'score']
# exclude_list = ['id']
# bins_map = {'age':[-1,20,30,99]}
# data_type_map = {'education':'discrete'}
# labels_map = {'education':{'1.0':'111','2.0':'222','3.0':'333','4.0':'444','5.0':'555'}}
# lapras.eda(df,feature_list=feature_list , exclude_list = exclude_list, bins_map=bins_map,
#            labels_map=labels_map, data_type_map=data_type_map, max_bins=6)
lapras.eda(df)

# Calculate IV value of features（Calculate by default decision tree binning）
# Parameter details：
# dataframe=None original data
# target = 'target' Y label name
lapras.quality(train_df.drop(to_drop,axis=1),target = target)

	iv	unique
score	0.758342	265.0
age	0.504588	35.0
wealth	0.275775	19.0
education	0.230553	6.0
max_unpay_day	0.170061	12.0
period	0.073716	6.0

# Calculate PSI betweet features
# Parameter details：
# actual=None actual feature
# predict=None prediction feature
# bins=10 count of binning
# return_frame=False return the dataframe of binning if set to true
cols = list(lapras.quality(train_df,target = target).reset_index()['index'])
for col in cols:
    if col not in [target]:
        print("%s: %.4f" % (col,lapras.PSI(train_df[col], test_df[col])))

score: 0.1500
age: 0.0147
wealth: 0.0070
education: 0.0010
max_unpay_day: 0.0042
id: 0.0000
period: 0.0030

# Calculate VIF
# Parameter details：
# dataframe=None 
lapras.VIF(train_df.drop(['id','bad'],axis=1))

wealth            1.124927
max_unpay_day     2.205619
score            18.266471
age              17.724547
period            1.193605
education         1.090158
dtype: float64

# Calculate IV value
# Parameter details：
# feature=None feature data
# target=None Y label data
lapras.IV(train_df['age'],train_df[target])

0.5045879202656338

# Features filtering
# Parameter details：
# frame=None original data
# target=None Y label name
# empty=0.9 empty feature filtering， feature will be removed if data missing ratio greater than the threshold
# iv=0.02 IV value filtering， feature will be removed if IV value lesser than the threshold
# corr=0.7 correlation filtering， feature will be removed if correlation value greater than the threshold
# vif=False multicollinearity filtering， feature will be removed if multicollinearity value greater than the threshold, default False due to a large number of calculations 
# return_drop=False reture the removed features if set to true
# exclude=None features will be remained if set into this parameter
train_selected, dropped = lapras.select(train_df.drop(to_drop,axis=1),target = target, empty = 0.95, \
                                                iv = 0.05, corr = 0.9, vif = False, return_drop=True, exclude=[])
print(dropped)
print(train_selected.shape)
train_selected

{'empty': array([], dtype=float64), 'iv': array([], dtype=object), 'corr': array([], dtype=object)}
(5502, 7)

	bad	wealth	max_unpay_day	score	age	period	education
4168	0	4.0	NaN	288	23.0	6.0	4.0
605	0	4.0	NaN	216	32.0	6.0	4.0
3018	0	5.0	NaN	250	23.0	6.0	2.0
4586	0	7.0	171.0	413	31.0	NaN	2.0
1468	0	5.0	NaN	204	29.0	6.0	2.0
...	...	...	...	...	...	...	...
5226	0	4.0	171.0	346	23.0	NaN	3.0
5390	0	5.0	NaN	207	32.0	NaN	3.0
860	0	6.0	NaN	356	42.0	4.0	3.0
7603	0	3.0	NaN	323	34.0	NaN	3.0
7270	0	4.0	NaN	378	24.0	10.0	4.0

5502 rows × 7 columns

# Feature Binning， following methods are supported: monotonous binning， decision tree binning， Kmeans binning， equal frequency binning， equal step size binning
# Parameter details：
# X=None original data
# y=None Y label name
# method='dt' Binning method：'dt':decision tree binning(default),'mono':monotonous binning,'kmeans':Kmeans binning,'quantile':equal frequency binning,'step':equal step size binning
# min_samples=1 the least sample numbers in each binning， represent the count of numbers when greater than 1， represent the ratio of total count when between 0 and 1
# n_bins=10 maximun binning count
# c.load(dict) adjust the binning by loading a customized dict
# c.export() export current binning information by dict format
c = lapras.Combiner()
c.fit(train_selected, y = target,method = 'mono', min_samples = 0.05,n_bins=8) #empty_separate = False
# # c.load({'age': [22.5, 23.5, 24.5, 25.5, 28.5,36.5],
# #  'education': [ 3.5],
# #  'max_unpay_day': [59.5],
# #  'period': [5.0, 9.0],
# #  'score': [205.5, 236.5, 265.5, 275.5, 294.5, 329.5, 381.5],
# #  'wealth': [2.5, 3.5, 6.5]})
c.export()

{'age': [23.0, 24.0, 25.0, 26.0, 28.0, 29.0, 37.0],
'education': [3.0, 4.0],
'max_unpay_day': [171.0],
'period': [6.0, 10.0],
'score': [237.0, 272.0, 288.0, 296.0, 330.0, 354.0, 384.0],
'wealth': [3.0, 4.0, 5.0, 7.0]}

# To transform the original data into binning data
# Parameter details：
# X=None original data
# labels=False binning label will be shown when set to true
c.transform(train_selected, labels=True).iloc[0:10,:]

	bad	wealth	max_unpay_day	score	age	period	education
4168	0	02.[4.0,5.0)	00.[-inf,171.0)	03.[288.0,296.0)	01.[23.0,24.0)	01.[6.0,10.0)	02.[4.0,inf)
605	0	02.[4.0,5.0)	00.[-inf,171.0)	00.[-inf,237.0)	06.[29.0,37.0)	01.[6.0,10.0)	02.[4.0,inf)
3018	0	03.[5.0,7.0)	00.[-inf,171.0)	01.[237.0,272.0)	01.[23.0,24.0)	01.[6.0,10.0)	00.[-inf,3.0)
4586	0	04.[7.0,inf)	01.[171.0,inf)	07.[384.0,inf)	06.[29.0,37.0)	00.[-inf,6.0)	00.[-inf,3.0)
1468	0	03.[5.0,7.0)	00.[-inf,171.0)	00.[-inf,237.0)	06.[29.0,37.0)	01.[6.0,10.0)	00.[-inf,3.0)
6251	0	03.[5.0,7.0)	00.[-inf,171.0)	01.[237.0,272.0)	01.[23.0,24.0)	02.[10.0,inf)	00.[-inf,3.0)
3686	0	00.[-inf,3.0)	00.[-inf,171.0)	00.[-inf,237.0)	01.[23.0,24.0)	01.[6.0,10.0)	00.[-inf,3.0)
3615	0	02.[4.0,5.0)	00.[-inf,171.0)	03.[288.0,296.0)	06.[29.0,37.0)	02.[10.0,inf)	02.[4.0,inf)
5338	0	00.[-inf,3.0)	00.[-inf,171.0)	04.[296.0,330.0)	03.[25.0,26.0)	02.[10.0,inf)	00.[-inf,3.0)
3985	0	03.[5.0,7.0)	00.[-inf,171.0)	01.[237.0,272.0)	01.[23.0,24.0)	01.[6.0,10.0)	02.[4.0,inf)

# To output bin_stats and bin_plot
# Parameter details：
# frame=None data transformed by Combiner, keeping binning labels
# col=None features to be outputed
# target='target' Y label name

# Note：The binning details may be different between traning set and testing set due to Population Stability. 
cols = list(lapras.quality(train_selected,target = target).reset_index()['index'])
for col in cols:
    if col != target:
        print(lapras.bin_stats(c.transform(train_selected[[col, target]], labels=True), col=col, target=target))
        lapras.bin_plot(c.transform(train_selected[[col,target]], labels=True), col=col, target=target)

          score  bad_count  total_count  bad_rate     ratio       woe  \
0   00.[-inf,237.0)        136          805  0.168944  0.146310  0.944734
1  01.[237.0,272.0)        101          832  0.121394  0.151218  0.558570
2  02.[272.0,288.0)         46          533  0.086304  0.096874  0.178240
3  03.[288.0,296.0)         20          295  0.067797  0.053617 -0.083176
4  04.[296.0,330.0)         73         1385  0.052708  0.251727 -0.350985
5  05.[330.0,354.0)         18          812  0.022167  0.147583 -1.248849
6  06.[354.0,384.0)          8          561  0.014260  0.101963 -1.698053
7    07.[384.0,inf)          1          279  0.003584  0.050709 -3.089758

     iv  total_iv  
0  0.194867  0.735116
1  0.059912  0.735116
2  0.003322  0.735116
3  0.000358  0.735116
4  0.026732  0.735116
5  0.138687  0.735116
6  0.150450  0.735116
7  0.160788  0.735116

          age  bad_count  total_count  bad_rate     ratio       woe  \
0  00.[-inf,23.0)         90          497  0.181087  0.090331  1.028860
1  01.[23.0,24.0)         77          521  0.147793  0.094693  0.785844
2  02.[24.0,25.0)         57          602  0.094684  0.109415  0.280129
3  03.[25.0,26.0)         38          539  0.070501  0.097964 -0.041157
4  04.[26.0,28.0)         58          997  0.058175  0.181207 -0.246509
5  05.[28.0,29.0)         20          379  0.052770  0.068884 -0.349727
6  06.[29.0,37.0)         57         1657  0.034400  0.301163 -0.796844
7   07.[37.0,inf)          6          310  0.019355  0.056343 -1.387405

     iv  total_iv  
0  0.147647   0.45579
1  0.081721   0.45579
2  0.009680   0.45579
3  0.000163   0.45579
4  0.009918   0.45579
5  0.007267   0.45579
6  0.137334   0.45579
7  0.062060   0.45579

      wealth  bad_count  total_count  bad_rate     ratio       woe  \
0  00.[-inf,3.0)        106          593  0.178752  0.107779  1.013038
1   01.[3.0,4.0)         84         1067  0.078725  0.193929  0.078071
2   02.[4.0,5.0)         88         1475  0.059661  0.268084 -0.219698
3   03.[5.0,7.0)         99         1733  0.057126  0.314976 -0.265803
4   04.[7.0,inf)         26          634  0.041009  0.115231 -0.614215

     iv  total_iv  
0  0.169702  0.236205
1  0.001222  0.236205
2  0.011787  0.236205
3  0.019881  0.236205
4  0.033612  0.236205

   education  bad_count  total_count  bad_rate     ratio       woe  \
0  00.[-inf,3.0)        225         2123  0.105982  0.385860  0.405408
1   01.[3.0,4.0)         61          648  0.094136  0.117775  0.273712
2   02.[4.0,inf)        117         2731  0.042841  0.496365 -0.568600

     iv  total_iv  
0  0.075439  0.211775
1  0.009920  0.211775
2  0.126415  0.211775

 max_unpay_day  bad_count  total_count  bad_rate     ratio       woe  \
0  00.[-inf,171.0)        330         5098  0.064731  0.926572 -0.132726
1   01.[171.0,inf)         73          404  0.180693  0.073428  1.026204

     iv  total_iv  
0  0.015426  0.134699
1  0.119272  0.134699

      period  bad_count  total_count  bad_rate     ratio       woe  \
0  00.[-inf,6.0)         52         1158  0.044905  0.210469 -0.519398
1  01.[6.0,10.0)        218         2871  0.075932  0.521810  0.038912
2  02.[10.0,inf)        133         1473  0.090292  0.267721  0.227787

     iv  total_iv  
0  0.045641  0.061758
1  0.000803  0.061758
2  0.015314  0.061758

# WOE value transformation
# transer.fit()：
# X=None data transformed by Combiner
# y=None Y label
# exclude=None features exclude from transformation

# transer.transform()：
# X=None 

# transer.export()：

# Note： Only training set need to be fit
transfer = lapras.WOETransformer()
transfer.fit(c.transform(train_selected), train_selected[target], exclude=[target])

train_woe = transfer.transform(c.transform(train_selected))
transfer.export()

{'age': {0: 1.0288596439961428,
1: 0.7858440185299318,
2: 0.2801286322797789,
3: -0.041156782250006324,
4: -0.24650930955337075,
5: -0.34972695582581514,
6: -0.7968444812848496,
7: -1.387405073069694},
'education': {0: 0.4054075821430197,
1: 0.27371220345368763,
2: -0.5685998002779383},
'max_unpay_day': {0: -0.13272639517618706, 1: 1.026204224879801},
'period': {0: -0.51939830439238,
1: 0.0389118677598222,
2: 0.22778739438526965},
'score': {0: 0.9447339847162963,
1: 0.5585702161999536,
2: 0.17824043251497793,
3: -0.08317566500410743,
4: -0.3509853692471706,
5: -1.2488485442424984,
6: -1.6980533007340262,
7: -3.089757954582164},
'wealth': {0: 1.01303813013795,
1: 0.0780708378046198,
2: -0.21969844672815222,
3: -0.2658032661768855,
4: -0.6142151848362123}}

# Features filtering could be done once more after transformed into WOE value. This is optional.
train_woe, dropped = lapras.select(train_woe,target = target, empty = 0.9, \
                                                iv = 0.02, corr = 0.9, vif = False, return_drop=True, exclude=[])
print(dropped)
print(train_woe.shape)
train_woe.head(10)

{'empty': array([], dtype=float64), 'iv': array([], dtype=object), 'corr': array([], dtype=object)}
(5502, 7)

	bad	wealth	max_unpay_day	score	age	period	education
4168	0	-0.219698	-0.132726	-0.083176	0.785844	0.038912	-0.568600
605	0	-0.219698	-0.132726	0.944734	-0.796844	0.038912	-0.568600
3018	0	-0.265803	-0.132726	0.558570	0.785844	0.038912	0.405408
4586	0	-0.614215	1.026204	-3.089758	-0.796844	-0.519398	0.405408
1468	0	-0.265803	-0.132726	0.944734	-0.796844	0.038912	0.405408
6251	0	-0.265803	-0.132726	0.558570	0.785844	0.227787	0.405408
3686	0	1.013038	-0.132726	0.944734	0.785844	0.038912	0.405408
3615	0	-0.219698	-0.132726	-0.083176	-0.796844	0.227787	-0.568600
5338	0	1.013038	-0.132726	-0.350985	-0.041157	0.227787	0.405408
3985	0	-0.265803	-0.132726	0.558570	0.785844	0.038912	-0.568600

# stepwise regression, to select best features, this is optional
# Parameter details：
# frame=None original data
# target='target' Y label name
# estimator='ols' model for regression, supporting 'ols', 'lr', 'lasso', 'ridge'
# direction='both' direction for stepwise, supporting 'forward', 'backward', 'both' 
# criterion='aic' metric, supporting 'aic', 'bic', 'ks', 'auc'
# max_iter=None max iteration times
# return_drop=False return cols being removed if set to true
# exclude=None exclude features
final_data = lapras.stepwise(train_woe,target = target, estimator='ols', direction = 'both', criterion = 'aic', exclude = [])
final_data

	bad	wealth	max_unpay_day	score	age
4168	0	-0.219698	-0.132726	-0.083176	0.785844
605	0	-0.219698	-0.132726	0.944734	-0.796844
3018	0	-0.265803	-0.132726	0.558570	0.785844
4586	0	-0.614215	1.026204	-3.089758	-0.796844
1468	0	-0.265803	-0.132726	0.944734	-0.796844
...	...	...	...	...	...
5226	0	-0.219698	1.026204	-1.248849	0.785844
5390	0	-0.265803	-0.132726	0.944734	-0.796844
860	0	-0.265803	-0.132726	-1.698053	-1.387405
7603	0	0.078071	-0.132726	-0.350985	-0.796844
7270	0	-0.219698	-0.132726	-1.698053	0.280129

5502 rows × 5 columns

# Scorecard modeling
# Parameter details：
# base_odds=1/60,base_score=600 When base_odds is 1/60, the corresponding base_score will be 600
# pdo=40,rate=2 If the base_odds decrease by half, the corresponding pdo will increase by 40, these are the default parameters
# combiner=None Combiner, input the fitted object
# transfer=None WOETransformer, input the fitted object
# model_type='lr' enumerate:'lr':sklearn LR   'ols':statsmodels ols
# ScoreCard.fit()：
# X=None WOE value
# y=None Y label
card = lapras.ScoreCard(
    combiner = c,
    transfer = transfer
)
col = list(final_data.drop([target],axis=1).columns)
card.fit(final_data[col], final_data[target])

ScoreCard(base_odds=0.016666666666666666, base_score=600, card=None,
combiner=<lapras.transform.Combiner object at 0x000001EC0FB72438>,
pdo=40, rate=2,
transfer=<lapras.transform.WOETransformer object at 0x000001EC0FDAEF98>)

# ScoreCard class method expaination
# ScoreCard.predict() predict score for each sample：
# X=None 

# ScoreCard.predict_prob() predict prob for each sample：
# X=None 

# ScoreCard.export() output the details of scorecard by dict format

# ScoreCard.get_params() to get the parameters of scorecard by dict format, usually used in deployment

# card.intercept_  intercept of logical regression
# card.coef_  coefficient of logical regression

final_result = final_data[[target]].copy()
score = card.predict(final_data[col])
prob = card.predict_prob(final_data[col])

final_result['score'] = score
final_result['prob'] = prob

print("card.intercept_:%s" % (card.intercept_))
print("card.coef_:%s" % (card.coef_))
card.get_params()['combiner']
card.get_params()['transfer']
card.export()

card.intercept_:-2.5207582925622476
card.coef_:[0.32080944 0.3452988  0.68294643 0.66842902]

{'age': {'[-inf,23.0)': -39.69,
'[23.0,24.0)': -30.31,
'[24.0,25.0)': -10.81,
'[25.0,26.0)': 1.59,
'[26.0,28.0)': 9.51,
'[28.0,29.0)': 13.49,
'[29.0,37.0)': 30.74,
'[37.0,inf)': 53.52},
'intercept': {'[-inf,inf)': 509.19},
'max_unpay_day': {'[-inf,171.0)': 2.64, '[171.0,inf)': -20.45},
'score': {'[-inf,237.0)': -37.23,
'[237.0,272.0)': -22.01,
'[272.0,288.0)': -7.02,
'[288.0,296.0)': 3.28,
'[296.0,330.0)': 13.83,
'[330.0,354.0)': 49.22,
'[354.0,384.0)': 66.92,
'[384.0,inf)': 121.77},
'wealth': {'[-inf,3.0)': -18.75,
'[3.0,4.0)': -1.45,
'[4.0,5.0)': 4.07,
'[5.0,7.0)': 4.92,
'[7.0,inf)': 11.37}}

# model performance metrics, including KS, AUC, ROC curve, KS curve, PR curve
# Parameter details
# feature=None predicted value
# target=None actual label
lapras.perform(prob,final_result[target])

KS: 0.4160
AUC: 0.7602

# Parameter details
# frame=None original dataframe
# score='score' score label name
# target='target' Y label name
# score_bond=None score boundary, default by 30, customized by list, e.g. [100,200,300]
lapras.score_plot(final_result,score='score', target=target)

bad: [42, 78, 70, 104, 61, 28, 18, 1, 1, 0]
good: [129, 249, 494, 795, 1075, 972, 825, 282, 164, 114]
all: [171, 327, 564, 899, 1136, 1000, 843, 283, 165, 114]
all_rate: ['3.11%', '5.94%', '10.25%', '16.34%', '20.65%', '18.18%', '15.32%', '5.14%', '3.00%', '2.07%']
bad_rate: ['24.56%', '23.85%', '12.41%', '11.57%', '5.37%', '2.80%', '2.14%', '0.35%', '0.61%', '0.00%']

# LIFT show
# feature=None predicted value
# target=None actual label
# recall_list=[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1] default
lapras.LIFT(prob,final_data[target])

	recall	precision	improve
0	0.1	0.240000	3.202779
1	0.2	0.261290	3.486897
2	0.3	0.240964	3.215642
3	0.4	0.189535	2.529327
4	0.5	0.179170	2.391013
5	0.6	0.174352	2.326707
6	0.7	0.161622	2.156831
7	0.8	0.126972	1.694425
8	0.9	0.113936	1.520466
9	1.0	0.074935	1.000000

Automatical modeling

# auto_model parameters  df,target,to_drop are necessary, others are optional
# bins_show=False showing the binning graphs when set to true
# iv_rank=False feature IV values will be ranked when set to true
# perform_show=False showing performance(training set)
# coef_negative=True coefficient can be negative if set to true
# return: ScoreCard object
auto_card = lapras.auto_model(df=train_df,target=target,to_drop=to_drop,bins_show=False,iv_rank=False,perform_show=False,
                              coef_negative = False, empty = 0.95, iv = 0.02, corr = 0.9, vif = False, method = 'mono',
                              n_bins=8, min_samples=0.05, pdo=40, rate=2, base_odds=1 / 60, base_score=600)

——data filtering——
original feature：6  filtered features：6

——feature binning——

——WOE value transformation——

——feature filtering once more——
original feature：6  filtered features：6

——scorecard modeling——
intercept: -2.520670026708529
coef: [0.66928671 0.59743968 0.31723278 0.22972838 0.28750881 0.26435224]

——model performance metrics——
KS: 0.4208
AUC: 0.7626
   recall  precision   improve
0     0.1   0.238095  3.188586
1     0.2   0.254777  3.411990
2     0.3   0.239521  3.207679
3     0.4   0.193742  2.594611
4     0.5   0.182805  2.448141
5     0.6   0.171510  2.296866
6     0.7   0.160501  2.149437
7     0.8   0.130259  1.744435
8     0.9   0.110603  1.481206
9     1.0   0.074671  1.000000

Automatic modeling finished, time costing： 0 second