机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

线性回归:

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

注:机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测为偏置项,这一项的x的值假设为[1,1,1,1,1....]

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

注:为使似然函数越大,则需要最小二乘法函数越小越好

线性回归中为什么选用平方和作为误差函数?假设模型结果与测量值 误差满足,均值为0的高斯分布,即正态分布。这个假设是靠谱的,符合一般客观统计规律。若使 模型与测量数据最接近,那么其概率积就最大。概率积,就是概率密度函数的连续积,这样,就形成了一个最大似然函数估计。对最大似然函数估计进行推导,就得出了推导后结果: 平方和最小公式

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

注:

1.x的平方等于x的转置乘以x。

2.机器学习中普遍认为函数属于凸函数(凸优化问题),函数图形如下,从图中可以看出函数要想取到最小值或者极小值,就需要使偏导等于0。

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

3.一些问题上机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测没办法直接求解,则可以在上图中选一个点,依次一步步优化,取得最小值(梯度优化)

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

R平方是多元回归中的回归平方和占总平方和的比例,它是度量多元回归方程中拟合程度的一个统计量,反映了在因变量y的变差中被估计的回归方程所解释的比例。
R平方越接近1,表明回归平方和占总平方和的比例越大,回归线与各观测点越接近,用x的变化来解释y值变差的部分就越多,回归的拟合程度就越好。

R平方取值范围是负无穷到1,越是接近于1越好。

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测没办法直接求解是:

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

 注:批量梯度下降法BGD;

   随机梯度下降法SGD;

  小批量梯度下降法MBGD(在上述的批量梯度的方式中每次迭代都要使用到所有的样本,对于数据量特别大的情况,如大规模的机器学习应用,每次迭代求解所有样本需要花费大量的计算成本。是否可以在每次的迭代过程中利用部分样本代替所有的样本呢?基于这样的思想,便出现了mini-batch的概念。 假设训练集中的样本的个数为1000,则每个mini-batch只是其一个子集,假设,每个mini-batch中含有10个样本,这样,整个训练数据集可以分为100个mini-batch。)

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

点击查看:

逻辑回归:

线性回归的应用场合大多是回归分析,一般不用在分类问题上,原因可以概括为以下两个:
1)回归模型是连续型模型,即预测出的值都是连续值(实数值),非离散值;
2)预测结果受样本噪声的影响比较大。

LR本质上还是线性回归,只是特征到结果的映射过程中加了一层函数映射,即sigmoid函数,即先把特征线性求和,然后使用sigmoid函数将线性和约束至(0,1)之间,结果值用于二分类。线性回归,采用的是平方损失函数。而逻辑回归采用的是 对数 损失函数。

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

注:Z指的是线性回归的输出

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

注:对数似然加负号为逻辑回归的损失函数,如下所示

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

sigmoid用来解决二分类问题,softmax解决多分类问题,sigmoid是softmax的特殊情况。

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

核函数的物理意义?

映射到高维,使其变得线性可分。什么是高维?如一个一维数据特征x,转换为(x,x^2, x^3),就成为了一个三维特征,且线性无关。一个一维特征线性不可分的特征,在高维,就可能线性可分了。

对于非线性问题逻辑Regression问题的常规步骤为:

  1. 寻找h函数(即hypothesis);对非线性问题的处理方式不同,LR主要靠特征构造,必须组合交叉特征,特征离散化。SVM也可以这样,还可以通过kernel
  2. 构造J函数(损失函数);
  3. 想办法使得J函数最小并求得回归参数(θ)

LR的优缺点

优点

一、预测结果是界于0和1之间的概率;
二、可以适用于连续性和类别性自变量;
三、容易使用和解释;

缺点

1)对模型中自变量多重共线性较为敏感,例如两个高度相关自变量同时放入模型,可能导致较弱的一个自变量回归符号不符合预期,符号被扭转。​需要利用因子分析或者变量聚类分析等手段来选择代表性的自变量,以减少候选变量之间的相关性;

2)预测结果呈“S”型,因此从log(odds)向概率转化的过程是非线性的,在两端随着​log(odds)值的变化,概率变化很小,边际值太小,slope太小,而中间概率的变化很大,很敏感。 导致很多区间的变量变化对目标概率的影响没有区分度,无法确定阀值。

为什么做回归分析和逻辑回归时要考虑消除多重共线性?

回归方程的解释,比如第一个beta1 意义是在保持其他自变量不变的情况下,X1每增加一个单位,y平均增加一个单位,记得是平均。我们进行回归分析需要了解每个自变量对因变量的单纯效应,多重共线性就是说自变量间存在某种函数关系,如果你的两个自变量间(X1和X2)存在函数关系,那么X1改变一个单位时,X2也会相应地改变,此时你无法做到固定其他条件,单独考查X1对因变量Y的作用,你所观察到的X1的效应总是混杂了X2的作用,这就造成了分析误差,使得对自变量效应的分析不准确,所以做回归分析时需要排除多重共线性的影响,就是自变量间存在很严重的相关关系。

在利用Scikit-Learn对数据进行逻辑回归之前。首先进行特征筛选。特征筛选的方法很多,主要包含在Scikit-Learn的feature-selection库中,比较简单的有通过 F 检验(f_regression)来给出各个特征的 F 值和 p 值,从而可以筛选变量(选择 F 值大的或者 p 值较小的特征)。

多重共线性的检验;

1、相关性分析,相关系数高于0.8,表明存在多重共线性;但相关系数低,并不能表示不存在多重共线性;

2、容忍度(tolerance)与方差扩大因子(VIF)。某个自变量的容忍度等于1减去该自变量为因变量而其他自变量为预测变量时所得到的线性回归模型的判定系数。容忍度越小,多重共线性越严重。通常认为容忍度小于0.1时,存在严重的多重共线性。方差扩大因子等于容忍度的倒数。显然,VIF越大,多重共线性越严重。一般认为VIF大于10时,存在严重的多重共线性。

3、回归系数的正负号与预期的相反。

多重共线性的处理方法

(一)删除不重要的自变量
自变量之间存在共线性,说明自变量所提供的信息是重叠的,可以删除不重要的自变量减少重复信息。但从模型中删去自变量时应该注意:从实际经济分析确定为相对不重要并从偏相关系数检验证实为共线性原因的那些变量中删除。如果删除不当,会产生模型设定误差,造成参数估计严重有偏的后果。

(二)追加样本信息(不过实际操作中,这个方法实现率不高)
多重共线性问题的实质是样本信息的不充分而导致模型参数的不能精确估计,因此追加样本信息是解决该问题的一条有效途径。但是,由于资料收集及调查的困难,要追加样本信息在实践中有时并不容易。

(三)利用非样本先验信息
非样本先验信息主要来自经济理论分析和经验认识。充分利用这些先验的信息,往往有助于解决多重共线性问题。

(四)改变解释变量的形式
改变解释变量的形式是解决多重共线性的一种简易方法,例如对于横截面数据采用相对数变量,对于时间序列数据采用增量型变量。

(五)逐步回归法(此法最常用的,也最有效)
逐步回归(Stepwise
Regression)是一种常用的消除多重共线性、选取“最优”回归方程的方法。其做法是将逐个引入自变量,引入的条件是该自变量经F检验是显著的,每引入一个自变量后,对已选入的变量进行逐个检验,如果原来引入的变量由于后面变量的引入而变得不再显著,那么就将其剔除。引入一个变量或从回归方程中剔除一个变量,为逐步回归的一步,每一步都要进行F

检验,以确保每次引入新变量之前回归方程中只包含显著的变量。这个过程反复进行,直到既没有不显著的自变量选入回归方程,也没有显著自变量从回归方程中剔除为止。

(六)可以做主成分回归
主成分分析法作为多元统计分析的一种常用方法在处理多变量问题时具有其一定的优越性,其降维的优势是明显的,主成分回归方法对于一般的多重共线性问题还是适用的,尤其是对共线性较强的变量之间。当采取主成分提取了新的变量后,往往这些变量间的组内差异小而组间差异大,起到了消除共线性的问题。

逻辑回归和线性回归的联系、异同?     经验风险、期望风险、经验损失、结构风险之间的区别与联系?


案例实战:Python实现逻辑回归与梯度下降策略

The data

我们将建立一个逻辑回归模型来预测一个学生是否被大学录取。假设你是一个大学系的管理员,你想根据两次考试的结果来决定每个申请人的录取机会。你有以前的申请人的历史数据,你可以用它作为逻辑回归的训练集。对于每一个培训例子,你有两个考试的申请人的分数和录取决定。为了做到这一点,我们将建立一个分类模型,根据考试成绩估计入学概率。

#三大件
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

data文件夹下 LogiReg_data.txt内容:

34.62365962451697,78.0246928153624,0
30.28671076822607,43.89499752400101,0
35.84740876993872,72.90219802708364,0
60.18259938620976,86.30855209546826,1
79.0327360507101,75.3443764369103,1
45.08327747668339,56.3163717815305,0
61.10666453684766,96.51142588489624,1
75.02474556738889,46.55401354116538,1
76.09878670226257,87.42056971926803,1
84.43281996120035,43.53339331072109,1
95.86155507093572,38.22527805795094,0
75.01365838958247,30.60326323428011,0
82.30705337399482,76.48196330235604,1
69.36458875970939,97.71869196188608,1
39.53833914367223,76.03681085115882,0
53.9710521485623,89.20735013750205,1
69.07014406283025,52.74046973016765,1
67.94685547711617,46.67857410673128,0
70.66150955499435,92.92713789364831,1
76.97878372747498,47.57596364975532,1
67.37202754570876,42.83843832029179,0
89.67677575072079,65.79936592745237,1
50.534788289883,48.85581152764205,0
34.21206097786789,44.20952859866288,0
77.9240914545704,68.9723599933059,1
62.27101367004632,69.95445795447587,1
80.1901807509566,44.82162893218353,1
93.114388797442,38.80067033713209,0
61.83020602312595,50.25610789244621,0
38.78580379679423,64.99568095539578,0
61.379289447425,72.80788731317097,1
85.40451939411645,57.05198397627122,1
52.10797973193984,63.12762376881715,0
52.04540476831827,69.43286012045222,1
40.23689373545111,71.16774802184875,0
54.63510555424817,52.21388588061123,0
33.91550010906887,98.86943574220611,0
64.17698887494485,80.90806058670817,1
74.78925295941542,41.57341522824434,0
34.1836400264419,75.2377203360134,0
83.90239366249155,56.30804621605327,1
51.54772026906181,46.85629026349976,0
94.44336776917852,65.56892160559052,1
82.36875375713919,40.61825515970618,0
51.04775177128865,45.82270145776001,0
62.22267576120188,52.06099194836679,0
77.19303492601364,70.45820000180959,1
97.77159928000232,86.7278223300282,1
62.07306379667647,96.76882412413983,1
91.56497449807442,88.69629254546599,1
79.94481794066932,74.16311935043758,1
99.2725269292572,60.99903099844988,1
90.54671411399852,43.39060180650027,1
34.52451385320009,60.39634245837173,0
50.2864961189907,49.80453881323059,0
49.58667721632031,59.80895099453265,0
97.64563396007767,68.86157272420604,1
32.57720016809309,95.59854761387875,0
74.24869136721598,69.82457122657193,1
71.79646205863379,78.45356224515052,1
75.3956114656803,85.75993667331619,1
35.28611281526193,47.02051394723416,0
56.25381749711624,39.26147251058019,0
30.05882244669796,49.59297386723685,0
44.66826172480893,66.45008614558913,0
66.56089447242954,41.09209807936973,0
40.45755098375164,97.53518548909936,1
49.07256321908844,51.88321182073966,0
80.27957401466998,92.11606081344084,1
66.74671856944039,60.99139402740988,1
32.72283304060323,43.30717306430063,0
64.0393204150601,78.03168802018232,1
72.34649422579923,96.22759296761404,1
60.45788573918959,73.09499809758037,1
58.84095621726802,75.85844831279042,1
99.82785779692128,72.36925193383885,1
47.26426910848174,88.47586499559782,1
50.45815980285988,75.80985952982456,1
60.45555629271532,42.50840943572217,0
82.22666157785568,42.71987853716458,0
88.9138964166533,69.80378889835472,1
94.83450672430196,45.69430680250754,1
67.31925746917527,66.58935317747915,1
57.23870631569862,59.51428198012956,1
80.36675600171273,90.96014789746954,1
68.46852178591112,85.59430710452014,1
42.0754545384731,78.84478600148043,0
75.47770200533905,90.42453899753964,1
78.63542434898018,96.64742716885644,1
52.34800398794107,60.76950525602592,0
94.09433112516793,77.15910509073893,1
90.44855097096364,87.50879176484702,1
55.48216114069585,35.57070347228866,0
74.49269241843041,84.84513684930135,1
89.84580670720979,45.35828361091658,1
83.48916274498238,48.38028579728175,1
42.2617008099817,87.10385094025457,1
99.31500880510394,68.77540947206617,1
55.34001756003703,64.9319380069486,1
74.77589300092767,89.52981289513276,1
import os
path = 'data' + os.sep + 'LogiReg_data.txt'
print(path)#打印出路径 data\LogiReg_data.txt
pdData = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])#header=None不从数据中读取列名,自己指定
pdData.head()

结果:

  Exam 1 Exam 2 Admitted
0 34.623660 78.024693 0
1 30.286711 43.894998 0
2 35.847409 72.902198 0
3 60.182599 86.308552 1
4 79.032736 75.344376 1
pdData.shape#查看数据维度   (100, 3)
positive = pdData[pdData['Admitted'] == 1] # returns the subset of rows such Admitted = 1, i.e. the set of *positive* examples
negative = pdData[pdData['Admitted'] == 0] # returns the subset of rows such Admitted = 0, i.e. the set of *negative* examples
print(positive.head())
print(negative.head())
fig, ax = plt.subplots(figsize=(10,5))#设置图的大小
ax.scatter(positive['Exam 1'], positive['Exam 2'], s=30, c='b', marker='o', label='Admitted')#c指得是颜色,s指的是点大小
ax.scatter(negative['Exam 1'], negative['Exam 2'], s=30, c='r', marker='x', label='Not Admitted')
ax.legend()
ax.set_xlabel('Exam 1 Score')
ax.set_ylabel('Exam 2 Score')

结果:

      Exam 1     Exam 2  Admitted
3 60.182599 86.308552 1
4 79.032736 75.344376 1
6 61.106665 96.511426 1
7 75.024746 46.554014 1
8 76.098787 87.420570 1
Exam 1 Exam 2 Admitted
0 34.623660 78.024693 0
1 30.286711 43.894998 0
2 35.847409 72.902198 0
5 45.083277 56.316372 0
10 95.861555 38.225278 0
Text(0,0.5,'Exam 2 Score')
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" alt="" />

The logistic regression

目标:建立分类器(求解出三个参数 θ0θ1θ2θ0θ1θ2

设定阈值,根据阈值判断录取结果

要完成的模块

  • sigmoid : 映射到概率的函数

  • model : 返回预测结果值

  • cost : 根据参数计算损失

  • gradient : 计算每个参数的梯度方向

  • descent : 进行参数更新

  • accuracy: 计算精度

sigmoid 函数

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

def sigmoid(z):
return 1 / (1 + np.exp(-z))
nums = np.arange(-10, 10, step=1) #creates a vector containing 20 equally spaced values from -10 to 10
fig, ax = plt.subplots(figsize=(12,4))
ax.plot(nums, sigmoid(nums), 'r')

结果:

[<matplotlib.lines.Line2D at 0xa937a90>]
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" alt="" />
机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测
def model(X, theta):

    return sigmoid(np.dot(X, theta.T))

(θ0θ1θ2)×1x1x2=θ0+θ1x1+θ2x

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

pdData.insert(0, 'Ones', 1) # in a try / except structure so as not to return an error if the block si executed several times
#增加一个全1的列
print(pdData.head())
# set X (training data) and y (target variable)
orig_data = pdData.as_matrix() # convert the Pandas representation of the data to an array useful for further computations
print(orig_data)
cols = orig_data.shape[1]
print(cols)#4
X = orig_data[:,0:cols-1]
print(X)
y = orig_data[:,cols-1:cols]
print(y)
# convert to numpy arrays and initalize the parameter array theta
#X = np.matrix(X.values)
#y = np.matrix(data.iloc[:,3:4].values) #np.array(y.values)
theta = np.zeros([1, 3])
print(theta)

结果:

   Ones     Exam 1     Exam 2  Admitted
0 1 34.623660 78.024693 0
1 1 30.286711 43.894998 0
2 1 35.847409 72.902198 0
3 1 60.182599 86.308552 1
4 1 79.032736 75.344376 1
[[ 1. 34.62365962 78.02469282 0. ]
[ 1. 30.28671077 43.89499752 0. ]
[ 1. 35.84740877 72.90219803 0. ]
[ 1. 60.18259939 86.3085521 1. ]
[ 1. 79.03273605 75.34437644 1. ]
[ 1. 45.08327748 56.31637178 0. ]
[ 1. 61.10666454 96.51142588 1. ]
[ 1. 75.02474557 46.55401354 1. ]
[ 1. 76.0987867 87.42056972 1. ]
[ 1. 84.43281996 43.53339331 1. ]
[ 1. 95.86155507 38.22527806 0. ]
[ 1. 75.01365839 30.60326323 0. ]
[ 1. 82.30705337 76.4819633 1. ]
[ 1. 69.36458876 97.71869196 1. ]
[ 1. 39.53833914 76.03681085 0. ]
[ 1. 53.97105215 89.20735014 1. ]
[ 1. 69.07014406 52.74046973 1. ]
[ 1. 67.94685548 46.67857411 0. ]
[ 1. 70.66150955 92.92713789 1. ]
[ 1. 76.97878373 47.57596365 1. ]
[ 1. 67.37202755 42.83843832 0. ]
[ 1. 89.67677575 65.79936593 1. ]
[ 1. 50.53478829 48.85581153 0. ]
[ 1. 34.21206098 44.2095286 0. ]
[ 1. 77.92409145 68.97235999 1. ]
[ 1. 62.27101367 69.95445795 1. ]
[ 1. 80.19018075 44.82162893 1. ]
[ 1. 93.1143888 38.80067034 0. ]
[ 1. 61.83020602 50.25610789 0. ]
[ 1. 38.7858038 64.99568096 0. ]
[ 1. 61.37928945 72.80788731 1. ]
[ 1. 85.40451939 57.05198398 1. ]
[ 1. 52.10797973 63.12762377 0. ]
[ 1. 52.04540477 69.43286012 1. ]
[ 1. 40.23689374 71.16774802 0. ]
[ 1. 54.63510555 52.21388588 0. ]
[ 1. 33.91550011 98.86943574 0. ]
[ 1. 64.17698887 80.90806059 1. ]
[ 1. 74.78925296 41.57341523 0. ]
[ 1. 34.18364003 75.23772034 0. ]
[ 1. 83.90239366 56.30804622 1. ]
[ 1. 51.54772027 46.85629026 0. ]
[ 1. 94.44336777 65.56892161 1. ]
[ 1. 82.36875376 40.61825516 0. ]
[ 1. 51.04775177 45.82270146 0. ]
[ 1. 62.22267576 52.06099195 0. ]
[ 1. 77.19303493 70.4582 1. ]
[ 1. 97.77159928 86.72782233 1. ]
[ 1. 62.0730638 96.76882412 1. ]
[ 1. 91.5649745 88.69629255 1. ]
[ 1. 79.94481794 74.16311935 1. ]
[ 1. 99.27252693 60.999031 1. ]
[ 1. 90.54671411 43.39060181 1. ]
[ 1. 34.52451385 60.39634246 0. ]
[ 1. 50.28649612 49.80453881 0. ]
[ 1. 49.58667722 59.80895099 0. ]
[ 1. 97.64563396 68.86157272 1. ]
[ 1. 32.57720017 95.59854761 0. ]
[ 1. 74.24869137 69.82457123 1. ]
[ 1. 71.79646206 78.45356225 1. ]
[ 1. 75.39561147 85.75993667 1. ]
[ 1. 35.28611282 47.02051395 0. ]
[ 1. 56.2538175 39.26147251 0. ]
[ 1. 30.05882245 49.59297387 0. ]
[ 1. 44.66826172 66.45008615 0. ]
[ 1. 66.56089447 41.09209808 0. ]
[ 1. 40.45755098 97.53518549 1. ]
[ 1. 49.07256322 51.88321182 0. ]
[ 1. 80.27957401 92.11606081 1. ]
[ 1. 66.74671857 60.99139403 1. ]
[ 1. 32.72283304 43.30717306 0. ]
[ 1. 64.03932042 78.03168802 1. ]
[ 1. 72.34649423 96.22759297 1. ]
[ 1. 60.45788574 73.0949981 1. ]
[ 1. 58.84095622 75.85844831 1. ]
[ 1. 99.8278578 72.36925193 1. ]
[ 1. 47.26426911 88.475865 1. ]
[ 1. 50.4581598 75.80985953 1. ]
[ 1. 60.45555629 42.50840944 0. ]
[ 1. 82.22666158 42.71987854 0. ]
[ 1. 88.91389642 69.8037889 1. ]
[ 1. 94.83450672 45.6943068 1. ]
[ 1. 67.31925747 66.58935318 1. ]
[ 1. 57.23870632 59.51428198 1. ]
[ 1. 80.366756 90.9601479 1. ]
[ 1. 68.46852179 85.5943071 1. ]
[ 1. 42.07545454 78.844786 0. ]
[ 1. 75.47770201 90.424539 1. ]
[ 1. 78.63542435 96.64742717 1. ]
[ 1. 52.34800399 60.76950526 0. ]
[ 1. 94.09433113 77.15910509 1. ]
[ 1. 90.44855097 87.50879176 1. ]
[ 1. 55.48216114 35.57070347 0. ]
[ 1. 74.49269242 84.84513685 1. ]
[ 1. 89.84580671 45.35828361 1. ]
[ 1. 83.48916274 48.3802858 1. ]
[ 1. 42.26170081 87.10385094 1. ]
[ 1. 99.31500881 68.77540947 1. ]
[ 1. 55.34001756 64.93193801 1. ]
[ 1. 74.775893 89.5298129 1. ]]
4
[[ 1. 34.62365962 78.02469282]
[ 1. 30.28671077 43.89499752]
[ 1. 35.84740877 72.90219803]
[ 1. 60.18259939 86.3085521 ]
[ 1. 79.03273605 75.34437644]
[ 1. 45.08327748 56.31637178]
[ 1. 61.10666454 96.51142588]
[ 1. 75.02474557 46.55401354]
[ 1. 76.0987867 87.42056972]
[ 1. 84.43281996 43.53339331]
[ 1. 95.86155507 38.22527806]
[ 1. 75.01365839 30.60326323]
[ 1. 82.30705337 76.4819633 ]
[ 1. 69.36458876 97.71869196]
[ 1. 39.53833914 76.03681085]
[ 1. 53.97105215 89.20735014]
[ 1. 69.07014406 52.74046973]
[ 1. 67.94685548 46.67857411]
[ 1. 70.66150955 92.92713789]
[ 1. 76.97878373 47.57596365]
[ 1. 67.37202755 42.83843832]
[ 1. 89.67677575 65.79936593]
[ 1. 50.53478829 48.85581153]
[ 1. 34.21206098 44.2095286 ]
[ 1. 77.92409145 68.97235999]
[ 1. 62.27101367 69.95445795]
[ 1. 80.19018075 44.82162893]
[ 1. 93.1143888 38.80067034]
[ 1. 61.83020602 50.25610789]
[ 1. 38.7858038 64.99568096]
[ 1. 61.37928945 72.80788731]
[ 1. 85.40451939 57.05198398]
[ 1. 52.10797973 63.12762377]
[ 1. 52.04540477 69.43286012]
[ 1. 40.23689374 71.16774802]
[ 1. 54.63510555 52.21388588]
[ 1. 33.91550011 98.86943574]
[ 1. 64.17698887 80.90806059]
[ 1. 74.78925296 41.57341523]
[ 1. 34.18364003 75.23772034]
[ 1. 83.90239366 56.30804622]
[ 1. 51.54772027 46.85629026]
[ 1. 94.44336777 65.56892161]
[ 1. 82.36875376 40.61825516]
[ 1. 51.04775177 45.82270146]
[ 1. 62.22267576 52.06099195]
[ 1. 77.19303493 70.4582 ]
[ 1. 97.77159928 86.72782233]
[ 1. 62.0730638 96.76882412]
[ 1. 91.5649745 88.69629255]
[ 1. 79.94481794 74.16311935]
[ 1. 99.27252693 60.999031 ]
[ 1. 90.54671411 43.39060181]
[ 1. 34.52451385 60.39634246]
[ 1. 50.28649612 49.80453881]
[ 1. 49.58667722 59.80895099]
[ 1. 97.64563396 68.86157272]
[ 1. 32.57720017 95.59854761]
[ 1. 74.24869137 69.82457123]
[ 1. 71.79646206 78.45356225]
[ 1. 75.39561147 85.75993667]
[ 1. 35.28611282 47.02051395]
[ 1. 56.2538175 39.26147251]
[ 1. 30.05882245 49.59297387]
[ 1. 44.66826172 66.45008615]
[ 1. 66.56089447 41.09209808]
[ 1. 40.45755098 97.53518549]
[ 1. 49.07256322 51.88321182]
[ 1. 80.27957401 92.11606081]
[ 1. 66.74671857 60.99139403]
[ 1. 32.72283304 43.30717306]
[ 1. 64.03932042 78.03168802]
[ 1. 72.34649423 96.22759297]
[ 1. 60.45788574 73.0949981 ]
[ 1. 58.84095622 75.85844831]
[ 1. 99.8278578 72.36925193]
[ 1. 47.26426911 88.475865 ]
[ 1. 50.4581598 75.80985953]
[ 1. 60.45555629 42.50840944]
[ 1. 82.22666158 42.71987854]
[ 1. 88.91389642 69.8037889 ]
[ 1. 94.83450672 45.6943068 ]
[ 1. 67.31925747 66.58935318]
[ 1. 57.23870632 59.51428198]
[ 1. 80.366756 90.9601479 ]
[ 1. 68.46852179 85.5943071 ]
[ 1. 42.07545454 78.844786 ]
[ 1. 75.47770201 90.424539 ]
[ 1. 78.63542435 96.64742717]
[ 1. 52.34800399 60.76950526]
[ 1. 94.09433113 77.15910509]
[ 1. 90.44855097 87.50879176]
[ 1. 55.48216114 35.57070347]
[ 1. 74.49269242 84.84513685]
[ 1. 89.84580671 45.35828361]
[ 1. 83.48916274 48.3802858 ]
[ 1. 42.26170081 87.10385094]
[ 1. 99.31500881 68.77540947]
[ 1. 55.34001756 64.93193801]
[ 1. 74.775893 89.5298129 ]]
[[0.]
[0.]
[0.]
[1.]
[1.]
[0.]
[1.]
[1.]
[1.]
[1.]
[0.]
[0.]
[1.]
[1.]
[0.]
[1.]
[1.]
[0.]
[1.]
[1.]
[0.]
[1.]
[0.]
[0.]
[1.]
[1.]
[1.]
[0.]
[0.]
[0.]
[1.]
[1.]
[0.]
[1.]
[0.]
[0.]
[0.]
[1.]
[0.]
[0.]
[1.]
[0.]
[1.]
[0.]
[0.]
[0.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]
[0.]
[0.]
[0.]
[1.]
[0.]
[1.]
[1.]
[1.]
[0.]
[0.]
[0.]
[0.]
[0.]
[1.]
[0.]
[1.]
[1.]
[0.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]
[0.]
[0.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]
[0.]
[1.]
[1.]
[0.]
[1.]
[1.]
[0.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]
[1.]]
[[0. 0. 0.]]
X[:5]

结果:

array([[ 1.        , 34.62365962, 78.02469282],
[ 1. , 30.28671077, 43.89499752],
[ 1. , 35.84740877, 72.90219803],
[ 1. , 60.18259939, 86.3085521 ],
[ 1. , 79.03273605, 75.34437644]])
y[:5]

结果:

array([[0.],
[0.],
[0.],
[1.],
[1.]])
theta#array([[0., 0., 0.]])
X.shape, y.shape, theta.shape#((100, 3), (100, 1), (1, 3))

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测注:损失函数为目标函数

def cost(X, y, theta):
left = np.multiply(-y, np.log(model(X, theta)))
right = np.multiply(1 - y, np.log(1 - model(X, theta)))
return np.sum(left - right) / (len(X))
cost(X, y, theta)#0.69314718055994529

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

def gradient(X, y, theta):
grad = np.zeros(theta.shape)
error = (model(X, theta)- y).ravel()
for j in range(len(theta.ravel())): #for each parmeter
term = np.multiply(error, X[:,j])
grad[0, j] = np.sum(term) / len(X) return grad

注意:.ravel用法

>>> x = np.array([[1, 2], [3, 4]])
>>> x
array([[1, 2],
[3, 4]])
>>> x.ravel()#将多维数组降为一维,默认是行序优先
array([1, 2, 3, 4])

Gradient descent

比较3中不同梯度下降方法

STOP_ITER = 0#迭代次数标志
STOP_COST = 1#损失标志 即两次迭代目标函数之间的差异
STOP_GRAD = 2#梯度变化标志
#以上为三种停止策略,分别是按迭代次数、按损失函数的变化量、按梯度变化量
def stopCriterion(type, value, threshold):#thershold为指定阈值
#设定三种不同的停止策略
if type == STOP_ITER: return value > threshold#按迭代次数停止
elif type == STOP_COST: return abs(value[-1]-value[-2]) < threshold#按损失函数是否改变停止
elif type == STOP_GRAD: return np.linalg.norm(value) < threshold#按梯度大小停止
import numpy.random
#洗牌
def shuffleData(data):
np.random.shuffle(data)
cols = data.shape[1]
X = data[:, 0:cols-1]
y = data[:, cols-1:]
return X, y
import time

def descent(data, theta, batchSize, stopType, thresh, alpha):
#最主要函数:梯度下降求解 batchSize:为1代表随机梯度下降,为整体值表示批量梯度下降,为某一数值表示小批量梯度下降
#stopType:停止策略类型 thresh阈值 alpha学习率
init_time = time.time()
i = 0 # 迭代次数
k = 0 # batch 迭代数据的初始量
X, y = shuffleData(data)
grad = np.zeros(theta.shape) # 计算的梯度
costs = [cost(X, y, theta)] # 损失值 while True:
grad = gradient(X[k:k+batchSize], y[k:k+batchSize], theta)#batchSize为指定的梯度下降策略
k += batchSize #取batch数量个数据
if k >= n:
k = 0
X, y = shuffleData(data) #重新洗牌
theta = theta - alpha*grad # 参数更新
costs.append(cost(X, y, theta)) # 计算新的损失
i += 1 if stopType == STOP_ITER: value = i
elif stopType == STOP_COST: value = costs
elif stopType == STOP_GRAD: value = grad
if stopCriterion(stopType, value, thresh): break return theta, i-1, costs, grad, time.time() - init_time
def runExpe(data, theta, batchSize, stopType, thresh, alpha):#损失率与迭代次数的展示函数
#import pdb; pdb.set_trace();
theta, iter, costs, grad, dur = descent(data, theta, batchSize, stopType, thresh, alpha)
name = "Original" if (data[:,1]>2).sum() > 1 else "Scaled"
name += " data - learning rate: {} - ".format(alpha)
if batchSize==n: strDescType = "Gradient"
elif batchSize==1: strDescType = "Stochastic"
else: strDescType = "Mini-batch ({})".format(batchSize)
name += strDescType + " descent - Stop: "
if stopType == STOP_ITER: strStop = "{} iterations".format(thresh)
elif stopType == STOP_COST: strStop = "costs change < {}".format(thresh)
else: strStop = "gradient norm < {}".format(thresh)
name += strStop
print ("***{}\nTheta: {} - Iter: {} - Last cost: {:03.2f} - Duration: {:03.2f}s".format(
name, theta, iter, costs[-1], dur))
fig, ax = plt.subplots(figsize=(12,4))
ax.plot(np.arange(len(costs)), costs, 'r')
ax.set_xlabel('Iterations')
ax.set_ylabel('Cost')
ax.set_title(name.upper() + ' - Error vs. Iteration')
return theta

不同的停止策略

设定迭代次数

#选择的梯度下降方法是基于所有样本的
n=100#数据样本就100个
runExpe(orig_data, theta, n, STOP_ITER, thresh=5000, alpha=0.000001)

结果:

***Original data - learning rate: 1e-06 - Gradient descent - Stop: 5000 iterations
Theta: [[-0.00027127 0.00705232 0.00376711]] - Iter: 5000 - Last cost: 0.63 - Duration: 1.18s
array([[-0.00027127,  0.00705232,  0.00376711]])
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" alt="" />

根据损失值停止

设定阈值 1E-6, 差不多需要110 000次迭代

runExpe(orig_data, theta, n, STOP_COST, thresh=0.000001, alpha=0.001)

结果:

***Original data - learning rate: 0.001 - Gradient descent - Stop: costs change < 1e-06
Theta: [[-5.13364014 0.04771429 0.04072397]] - Iter: 109901 - Last cost: 0.38 - Duration: 24.47s
array([[-5.13364014,  0.04771429,  0.04072397]])
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" alt="" />

根据梯度变化停止

设定阈值 0.05,差不多需要40 000次迭代

runExpe(orig_data, theta, n, STOP_GRAD, thresh=0.05, alpha=0.001)

结果:

***Original data - learning rate: 0.001 - Gradient descent - Stop: gradient norm < 0.05
Theta: [[-2.37033409 0.02721692 0.01899456]] - Iter: 40045 - Last cost: 0.49 - Duration: 10.79s
array([[-2.37033409,  0.02721692,  0.01899456]])
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" alt="" />

对比不同的梯度下降方法

Stochastic descent

runExpe(orig_data, theta, 1, STOP_ITER, thresh=5000, alpha=0.001)#1指的是每次只迭代1个样本

结果:

***Original data - learning rate: 0.001 - Stochastic descent - Stop: 5000 iterations
Theta: [[-0.38504802 0.09357723 -0.01034717]] - Iter: 5000 - Last cost: 1.59 - Duration: 0.42s
array([[-0.38504802,  0.09357723, -0.01034717]])
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" alt="" />
有点爆炸。。。很不稳定,再来试试把学习率调小一些
runExpe(orig_data, theta, 1, STOP_ITER, thresh=15000, alpha=0.000002)

结果:

***Original data - learning rate: 2e-06 - Stochastic descent - Stop: 15000 iterations
Theta: [[-0.00202012 0.01009114 0.00103943]] - Iter: 15000 - Last cost: 0.63 - Duration: 1.10s
array([[-0.00202012,  0.01009114,  0.00103943]])
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" alt="" />

速度快,但稳定性差,需要很小的学习率

Mini-batch descent

runExpe(orig_data, theta, 16, STOP_ITER, thresh=15000, alpha=0.001)#16指的是每次只迭代16个样本

结果:

***Original data - learning rate: 0.001 - Mini-batch (16) descent - Stop: 15000 iterations
Theta: [[-1.0352224 0.01668297 0.0124234 ]] - Iter: 15000 - Last cost: 0.57 - Duration: 1.44s
array([[-1.0352224 ,  0.01668297,  0.0124234 ]])
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*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" alt="" />

浮动仍然比较大,我们来尝试下对数据进行标准化 将数据按其属性(按列进行)减去其均值,然后除以其方差。最后得到的结果是,对每个属性/每列来说所有数据都聚集在0附近,方差值为1

from sklearn import preprocessing as pp

scaled_data = orig_data.copy()
scaled_data[:, 1:3] = pp.scale(orig_data[:, 1:3]) runExpe(scaled_data, theta, n, STOP_ITER, thresh=5000, alpha=0.001)

结果:

***Scaled data - learning rate: 0.001 - Gradient descent - Stop: 5000 iterations
Theta: [[ 0.3080807 0.86494967 0.77367651]] - Iter: 5000 - Last cost: 0.38 - Duration: 1.13s
array([[ 0.3080807 ,  0.86494967,  0.77367651]])
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" alt="" />
它好多了!原始数据,只能达到达到0.61,而我们得到了0.38个在这里!
所以对数据做预处理是非常重要的   
记住先改数据再改模型是基本套路
runExpe(scaled_data, theta, n, STOP_GRAD, thresh=0.02, alpha=0.001)

结果:

***Scaled data - learning rate: 0.001 - Gradient descent - Stop: gradient norm < 0.02
Theta: [[ 1.071 2.63 2.411]] - Iter: 59422 - Last cost: 0.22 - Duration: 12.00s
array([[ 1.071,  2.63 ,  2.411]])
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" alt="" />

更多的迭代次数会使得损失下降的更多!

theta = runExpe(scaled_data, theta, 1, STOP_GRAD, thresh=0.002/5, alpha=0.001)

结果:

***Scaled data - learning rate: 0.001 - Stochastic descent - Stop: gradient norm < 0.0004
Theta: [[ 1.14848169 2.79268789 2.5667383 ]] - Iter: 72637 - Last cost: 0.22 - Duration: 7.05s
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MqbnuSr1/npJRmkdd9n32yeKB6CNhhKG4sWtil+B3oMncspXQJuaRY43EQwNJlx1HdMPcVw+0TTdqAqLMz+S3GXwcQ3sJNjuNFSoa9kLytPh9tHnLmo/uAzSMnwYbCG8jn9HPKHsQLp5G3yS5N+tcbX/zWigivTT4nfrHVSMUN76bkt5vNqtcNRNNrBPnYexS4hFxN6WG6u0b8jHzft20Hw47k/a7T+e1CfmAvPccWCeqzgZXIJQGaiogVySU/mt2z3EauOjClrtvu5HPsL1pNu818FyoeiH5Prl74eeBGckKqnTeSS5g0ug5YNiL6JaDq5rsoueRSs/HXq1v3bySv58br+9/J1Vkar+9/Tf2LcV9Hvub0aZchIrYBdiMncIZbs/vfxeqGScXf78glGj9DPt/U+i1GrhJ4dxHzecVyfJScCHmG/LLrJ+TniitKpl86jRK/IZcuKnspsxcwPaV0f/H/88jXt++RqyidTK6m1a89nS78nHlVgz5EfkG7L3lZiYivFfO9hfzy9WTyvczlJcv+WvI98J/JVd5ryfYPAP8mlxY6BPgr8PWIqH9Z90XgDnKib2oRx+capv+KiNiVvB0XL8Y9gXyvdXXDPU1tm/+2+P1MEeMHi393rIqkwDfJC3hzRFwdEf8vIraP/m9KJxS/ndbDp3gIXpf8sFbLyD/I4B5gJpAvdvV//yqWoyMppQfJbRA0ewvb6XReJtcH7DOdYVpuyDvs39O8OlRnAhOjSaNg88lGlG+Pr9YPFDkb/jryWwuYVzyu2TpZrDi5Lh8Rm1CsS3KRu2a+Qt6XD2sxTEsppUvJJ5XPlRwDNWuTj9XbGntExLINF4dO2wmpPYS9NnJjRoeTi79dUDLscO0H36R8W65bN0ztZNfOSsXvwyX9Hqb9hWUg46/UYjg6mNeQSyn9h3zBeDPwQET8NiI+G20auGuj1tDlLS2GuYX8cFM7X9e2Xcfn7WL86ZTvC29oMs5U4NK6t9lnkts3WKJhuP9HbldhVuTGBo+IiMkDiK0TA75Wdek2YPWIaKxPejYl664uUXoZOTH2CeD+yI3OfjAaGi+MiJXI9WsHuhy7l82ffJNU5ijyW7v3DXA+w+Ub5BJ4t0XElZEbAtxmEA+PteOmse52vdvJN+wTGrpH3bl8fEQcRb4J/HNKqf6c08l5cR3ysdXNdaM+jjUj4gvkuufTS0pnQn54+EVRKiaRr5tTSoZr56+0LrFWb6Tvd53Mr5N9pXb+bdxX6u9ZJpNffNTWfTNnAHvWJQf3Bi7sphRTRLw+Ir5Fvtc8k3zdOwxYJaW0R5OSD/XjB7AC3V9LVyDvK83GXxCoveUequt71A9brMcTgB8NMJHarTdRvs8f1TBcAFellN6bUvpBSulHdf2WAk5JKX04pfR/KaWziwffr5Lb3tk2pXRySumz5OqF65LbHaHVNMqCLUqhXURDUiBy47YbU9xnRy4ZtCHwxZTSV1JKp6aUvpZS2io1b8OhY0Xpkdox9suU0hnF30uRSzl9BjgkpfS+Yn0dRa56tQ79zyerkKu0H1Ys+++L7u9MKe2bUjo+pfT9lNIe5GTEIXVxXESu3v1USmlaEUP9PXfjtb3WpsXmxXSPAt5O3vcbk8IBXJlSmlrM//3kJG2z82Gp+Z4UKN54bEbOYmxIzkhdBDwYfVufrb3t6lfNoIWp5LcpV9R1Owt4b8mNVKdmAduRL8y1v+3JjcEMxLN01ghcN9MZ8uWOiIXJRbOm1XW+iJxVrbK0wJ2Ub49TGoabCtyfigZ3iuKPrW5UDiKfYB8hP6BsDnw1pdS0CFxK6U7yej44Btei/FHkoqHNDt7asfBsSb8H6XuB6KQ0SgBXFcM/QN7Gj5PbE+hTEmGY94Na1rNxW86qDZBS+k5KaYGU0q/aTGsx8g1RWWNJs8kZ9lbnu1o2uNn4izUM22w4Goadb1JKh5GLq/6F3I7GscAtkYuedZOQrJ1nWp2Da/2WbvgdyHk7kW+cG/eFt5KToH0UNxBvoW+R17PIJRb6FL1LKZ1MrlZyFbnY3pHANZFbgR9USao63SxzN54lH7uNVWk+S/lx9AK8cu7bilyk+Vnyg8B3ycmjn9QlD7pdjisoPyeXFqVNKY2o0gIpN974FnJCdBJ5fV4K3BclX6DpwFLkfbrpeiwenJ9j3jqvWYF55/K7yDd+l1FXXSuldFtxTjyE1lpdNx4hP0zU5tX4Zr4+jr+RE+CXkkvo9BG58ej/pu81YhqwarRpsb1ELdZO7pWuYATvdx3Obylgdipp3LfOMxQlghq6f5x59yzXkNuJOjql1Ni4Yb1p5Lev20cuibU9A6w6EBHviIjp5ATO/uSk5CYppQ1TSt8eQGnGRcjL1e21tN01u36Y4bq+H0wuFTSYqpsDcTvl+3xj8f1E/6oS9Rr7bUHev04qXj7mieSH/QeYV2qw1TSaOQv474jYuK7beyna7Cr+/wy5pON2ETEUz0kDsSc5Qfub6FvS7j7ysm/TMPyTKaUzGydSvJgBXvmayHLkql/LRMTrGodvJ3K1xPHkNlaeq5vPteRqVo3bJNF/P/gT+Tzc8bP+fP/6ALxS9+ndRXb6DeSM76HAORGxUVE/6Oli8I52kGKh30NuxGGNumfh68j1MLcjZ00G6rnUvLX/gViSfPIeium8crMxjMu9C/mt0Q11DxRBbpRpb/LNdVPRv7juk/UHzSA80257FPvVnsB5DQ9D15KL+7+5KE1R7xxyy+oLk4tcfo78kNHOV8jr/9MUdYsGKqX0h8ifkTw8In5UMkhte5fVq387ubjlxuSHwI5mSa6ucB/5DdmB5Faxy1o9HdR+0MYd7d4mDMAL5LjKio4uCrxcPBy1Gp8W47/QMGzZZw4Xres/aJGrjdTvg7NTm9brU0qnAadFrkKwGbkhpz2BX0VujbnVOmhU2++WIt98lmlMHNSft5uNU2Z6SqksAVD2YDWVfEPx14Z98paiX5+iuCl/DeL84m3IxsUwHwB+FxHrppSeZnC6XeaBWpJ87NY/5CVyffiWx1FRjP0o4KiiRMA25GvufuT6swcxwGtunUe6uEYeRW7/5n1A2Tmva8V2rn+AmptSarldiuTxbpHrX76RnAj9OPDriFgv9f1KQDu1h7im67FI1i9B/8TB4+TjNcgPIfeklP45gHk3xgHl143tyS+FNiVfwxrV4qi1ZfA58lvXsnPbPuQi64/UHY+PkZMOU8k3pp2qxdpJYmpE7Xddzu8ZYNGIWKBFYqBZcvbMYpoLk19ifLb4d1MppQci4mrytXtN8vb8XfvF6GM/8nl0Jrmh6lYlyVr5D/n81eyaC62vpe2u2fXD1A/bWKVnUXKx7/rptp1mkVT5MrmB527aHlmW3J5BzXOp7msJTTw9gH1+VpPuT5eUDFmdvC36XYPJL+IaXyqUTaOZ35LX+XuY9xWPvYCra6WOUkpPR8SR5MT1OyN/gvR3wGkppeH+ssJ48nZ4oKRfKul+f8lwRMRG5NIWb6HvOTeRv5I0ULWqM2XbZCb53N2oMbYnyOfwsTSvVtRHJUmBmiIjNQOYERF/I7dcuyf5InUH+cK4Aa2LVtVsSy728176vw1O5ItTNw/Hg1a82RpLw+f+upjOguSi5PXFO4drufdmXh2VxmkSEZOLjFVZnIuQi1ol8jZMRWylRYyGwdvJDY/tR85k16utk8akwP11N9a/j4ingW9GxOV1xYP6SSndEfm7yAdHRMdVSkocRa6HeEBJvzuLuPs13JRS+iPken30L3rUyrUppduLcc8ll46YFhHrpL516breD+azWnG/lUr6rUSuW95u/CiGbbzJaRz/YfoX5ayfd7t5der/6NvY0nnkt95tFQ+6FwEXFYnDd5ETsAMpijez+N2Q3HBUmTeQ94Xbi//XGnzaoMU4g7U3ORF2Y0P3BMyJiNeklP7VOFLK7WFcCVxZHN+fJCdNf9047ADNj2WG/IWCe4u3zF1LuRj6GRHxK/INx97kpMA/ySWABlPlpNMYLozc6NLnI2KoP3N7APmzUzXP0v8ta7O4XiIn1K+LiPvJn6N7F7mV8k7VHzfNTCDff93e0P3FIXoJAfM+nVd23bgCXkmglOkTR0RcRo71JOoaTK5LwC9D/0/1JfLLn4/Wv31so7bvDepeqZlh3u+6md9M8jloA/LXHco0nmNr7mu4Z3kW+H/FPUure74zyFVmXk9uRHagn2c7knyu2Bu4qSg1cCpw1kASrCmlFBGP0PyaDa2vpY+Q10uz8V8mJ6ag7/1BY2J9Jfp+BvnhFtNMdTF9nvyw+7uY1/ZBrYHM5Ypu/2iR7LmIee1EJHKjhx9vMmw3miVUhuKlRcfTSCk9GxEXkM8Th0Vuu2UjcimL+uGOjYhzyO0zvI1c9e/wiNiyKJU7XMaQt+POlN9DN+4v/ZY9IpZnXlsqnyV/zeY/5OqcRzL/SuU329c6fjaook2BZmqNhdQOxgvJC9hpi/37kE8S7y75OxPYPcoboJkf9iMf9E0fLju0J7noUv10hny5Y17L3j8rmeae5LcIrYqOv8i8Yk2136G60enEPuTsXtk6+SW5Tl27hNhJxTSO6WB+R5O3y2DaFriY/GB+OA3Z/uLt8NXAW4vsdNPJdDnvl8mtjq8OfLjWfQj2g/npbvKblDeV9NuY5jdcNbeQ11+f8Yui1es1jH8zsHzk70vX27SYRrt5derL9C0m+IUup9N4bu3U+cXvfi2G2Zd8Qa3dhNYaHOr6SyutRG4odENyYz6N++RU8sWvky9j3MC8JNBgDesyAxTF2Fdk8NeQVxQPA7cBS0XE4kWy4QJgw+iwQdZBqtW5bkzcDtav6XvcdNKYX5lu95FbyA1/vrvFtXd/8rmiWQNdg1a8YZtObmhzMNXbKEpKnEKukli/b9QS8J+m//H4cXKyoOUXFhrsQ36Yu3Qw8bYxXPtdN/M7j7yPlZ5ji+p7e5EfNsoa0a33bXJ1wnb3LOeQ33pPpIuvDqSUbk8pfYxct752/v8u8HDk9ko6aSSy5mbKr9mbAk+0KqFTnL/ubDL+ZOD2ugfym8nrufH6vha51F/j9X39Yt03xjSXeS8pVyWfk+8kv5WfRT4/J/I2uIeSL3XU+Qh9qwD0+8rafFRrjHadkn5rF/0H4yxglYjYjFxi4GVKGrdMKf0tpXRcSml7cuJgLHV18gep2f3x3eSSITNTSpeV/LU77iAnMZYif/r6uymlC4uEXVmJp07v02vrvGybrEt5yYbBS/P/+5FbN+n+GfIB9/G6bqeQEwMfLRk+yG96ap/iegr4QZNpb1ZMe8+6bnOBE9vE2tH3JGnxrW/ym/znyPXyFm4zna1o8l1ccrb4EXLx1NcU3Qa83HX9Jhf99i7p9z/Nlqfo/1NypnjMEO0TixSxfKPNcNcA17UZZslifZduW3Kx2bnAO9rNm9wwV+O3Tj9UdHt9w7BnkIvf3tUYI/mCfna75SWfWOaS34D2mQf5bcIccrKs7HvaOxbj7tRm/ZTGX/S7mZzhXGCw+wH5zcHTTcZr+k32kmHHkk+Kpd/Gbhj2NHIRqXF13d5ZzGtKw7DrAK9t6HYl+Q3VInXdDinWwWZ13caTL2rH1nUbQ36IuLNFfEcW01p2KI6bhmkvXbadyOfJy4v5rlnSv+m5q26/nkP+pFljv8OKdfv1ku0wB3hfyThjyMmN/yr+f3Ax7NpN5t/n28zktwcvNluH5OTZtXX/7/ft74YYtyvp1/Q8XBbTQJd5oMdEsb/NovhEal33ft9ibjLtdYGVSrovT76e3F/X7fXkNyE3AMuUjDOBvt9MH8j34ufQcA0kv6G7m5xgHLLvxQ/w2NmmSfeji5gPKOm3ehHTJ5uM+8Gif79rM/nt0QvANQ3dzwEe6iDehcjnr9d0MOwORRznAYuW9H9H0f9t7eIg32v9h1ykt9btzGIfiCbzf4D8BrntMpJLiM6l4fv0TY63EbnfdTM/8jlrdtl+SH5QnNNwzC1RxHVsyfCHFcNvW9et3zmWXH3qi9Rduztdp02Wew1y9cUHi9hmAQd1MN4B9L/Hei1Lv1vKAAAgAElEQVT5XPf9hmFXA9Zq6HY0+ZPBE+q6vbGY5uF13YJ8b3NVw/jHk68nq9V125aGc3Gxzu8HLqrrNolccq/+76PFuN8hH1sD+oZ9m3XV7zgYyD5Y9Gt2bC9GLiX2Z2DBuu570nCeazaNNjEtVmzTE8hJlT809F8cWKih20JFTD+q67YSRQOqbebX79pIrk49B1ijYdj1iu7fLZlOUHcdbLYNyC8i5gBvbFjmO2i4vyJXi7i/ZBq1e4B31XW7k5xcWryu2yY0PL822+bMO/Y7vuesovrAScXbt1+TV9jC5EYu9iIv/E/qhv0U+WRzQuRvN55HvulfjbyzrkNuOOWd5CxNYxHnmlrL1lPp2zLrmyK3qtvo8lQ0UAeMjYjSt6EppZ/X/TeAnSKiVixwBfLJpdZw2q6p/ydOmnlLUaxvAXIWfgvyCecJYPc0r2hst8vdzlTg4ZRSY/Hcmt+SM8RvYwjfXAGbNdkef0gp1Yp3Ldtke8xJufGPPcgHY7N6clcyr5G8dnXpfkj+tunnyJ9faeUr5H14POWfyGkrpXRxURSv9sa5vt+lEfFJcmukd0XEGeQExCLkm/69yXWD+xWbHoDjyPWxp5IfcoZ7P5gcEc+VdL8zpVRbh/uSi/C+G2jX2OBR5AvxlRFxMvnYOYzclkTtKxREbqF+Jv2L43+O3KjXFRHxY3I9ukPJ35+/pjZQSunvEfF94DMRsST5zeB7yJnt3eoDKkp2fKj471uK309F/r7tv1LrRqEGYhlyuw9XkffVf5CXfw9yAvD0lL93X6ZV0bKDyOvhpxHxTnKJgDHkt687kpNUja3gHkx+aPpRREwphnmK/DWQvcjn9JMHuoCFKeSHqWafWPst8LWIGJ/y56YuiYibydt6Fjl5siN5n70i5a9/DIWhWubaMTEGWJa87XYnP4y9p2QbBrlxpuVLpjUj5fZ5JgPfj4jzyA8gTxaxvq+YxysNnKaUbo+I/ckJvzsi4jTysbIYsCW5KP0JDfNZvck5+cmU23No5SgGXqd5qP04Il4kN1B3FznZvhV5We+gbwN6HUkp/SAi3gR8ICI2JJ9/nibf0L2P/LDcSYmWMrUqhCfTprhxSumiiDiMXFy8/rqxGH2vG23bwkgpPVSMv3dEfJH8gPsO8qcXU5PRzgP2i4gl07z60ovW7S+LkY+Rd5ITTufT+ZvBV9N+12p+U8glI34fET8jv/xYgnyPuxnw49SiweMG3yefj2vXslKpb2v0g5ZSuodcReKL5AeyD5Cv2Y0NQDc6HfgYueri/5KPkY+RkyRfbRj2V+R7/vq2Or5NPp4ujvwlhDHk54ZZ1J1vU0op8jfjzyyKsv+SXGrgg8C30rzP4pFSuiwiLgS+HRGrkZMBB5KTqLvVDTeDhtIbdaVobkkpDcf+Na7JPv9SavIFgE6klF4o7r1PBC4rqsSuRt4WM8klQbpWTP935G21ZDGfem8kt3t0djG/RL6nWpJ5XwKDnCR7F7mxzHafWW28r5lRdDuuqDr3MvlLBLdFxLHk/Xcd8jnoOfK9/O7A18ntjbXyx2Kcs4p7z4WZ115PoxnkZ8VjyQmSJ1L+KkGZw8j7/TURcSq5VMvHyS/jOm1DbGAGku0Zij/yzdgPycUWnyJnzO8kZ+zGlQwf5Ba1ryDvBLPJGb9TgTcUw5xLrjfYLxNeN50fF+MuU/x/Tou/zxfDXN5quLpp79/Q7wVyxvT35JvFJTpcN1s1TGc2eeNfTq6nslzD8ANe7rruk4t57N3Q/bXkzGu/rFndMEsWy/izIdonFmmzPT5ZDHdNi2GeK4aptYy/UIv5nUE+gJesm/fXmwx7bNF/4+L/rd60196qXtvQ/SH6vi1pOk/ym5055BNW2Twmkh/Y7y22wVPkk8yx1GW7Wyx7q/gXKKb7F/JnV7reD8jH51NNxqtlZpv91WdAa5nOjt7WkEvUXELOSj9KrpffuO8vUUzz3JLxtyn2s+eK7XYcdSUH6oYbQ04Y3Uc+8d8E7NZkWec2Wc62pZAGcAwtTL7BOZd8Q1TbN64lv70oLdVDm5ICddM+rNjPniHfuE0v5tfsDeECxb72J3IyczY56fsD+paA6aSkwNXFv7cshv1Ui1hfXwzz5eL/+5BvKv5WbNNnySVivkCT8ybzzsOtSgpc3e0yd3hM/Iec4PtTsZ+VvenfmdbHUe28uRK5WtIfydel/xTHxu+BHZvEsy65EbPavvQkOaH6Ifq+SXq0xfxvrRvuOPI5rezt1XXF8D/vZnsMwbGzC/l8NbPYt18o/v0NSkpLFOOsXsR0aJtp70E+Hz1OPk/MJD/sLF0y7DnAgx3EW9tXThjAMk4iP4Ddx7xzww3kYs6rdhpHMe+XyTf1+xZx7NFivjtRV4KmmHb9PvI0+dg8A9i50+NtpO533c6P/KB7NPm++Dny+eMyykt51q5fxzSJ4RvUndNpc46tG+9fzdZFl8dVR2/JycnrU8mN/T1DPi+t32Q/6HdPQa6a8SvyOerJYh9btcm89iSf/18gn9sOp+QaRk5WHU8u5fkcuQ2qN3ewLLVjs20pyC7W5/Ut9vmn64ZrtQ+2PMeQr5e19fMI+f5p+YFMo8W038m855plG/qtQC5dMbPYBx4jX/t2Lpn3y43jl8yrtBQd+eXdg8U0+rxBJychrirm/xT56xr/C6zesA36XfuLfm8h3289Sz7PHkl+6dRYUmBpcpL4cerOV3X7zrsapvt2cgmO54pxzqZ/aYfSbU4XJQWiGFGSJEmSJPWYEdPQYEQcHBGzIuKFiJgefb9p2TjsqRExNyLmFL+1v780G0eSJEmSJPU1IpICEfEecjGNI8l1S24hf0qrWUvrHye3+rlS8bsK84pVSJIkSZKkDoyI6gNF42rXppQOKf4f5IZ4TkwpfaOD8Xcjf97idSml4flMgyRJkiRJo0zlJQUiYiFyIzivtAKdcqbiEnLLq504ALjEhIAkSZIkSZ2rPClA/rTEAuSWLus9Qq4a0FJErET+xNRQfdpLkiRJkqSesGDVAQyB95E/33Juq4EiYjny597uJX8SQ5IkSZKk4bQo+ROaF6WUHqs4llIjISnwb/J3FFdo6L4C8M8Oxn8/cFpK6eU2w+0A/Hzg4UmSJEmSNChTgTOqDqJM5UmBlNJLETED2A74LbzS0OB2wImtxo2IrYE1gR91MKt7AX72s58xYcKEQUSskeLQQw/l+OOPrzoMDRG35+ji9hx93Kaji9tzdHF7ji5uz9Fl5syZ7LPPPlA8j45ElScFCt8CflIkB64DDgUWB34CEBFfA1ZOKe3fMN4HyF8tmNnBPGYDTJgwgYkTJw5V3KrQ2LFj3ZajiNtzdHF7jj5u09HF7Tm6uD1HF7fnqDViq7CPiKRASunsiBgHHE2uNnAzsENK6dFikBWBVevHiYilgd2Bj8/PWCVJkiRJGi1GRFIAIKV0CnBKk37vL+n2NLDkcMclSZIkSdJoNRI+SShJkiRJkipgUkCvWlOmTKk6BA0ht+fo4vYcfdymo4vbc3Rxe44ubk/Nb5FSqjqG+SIiJgIzZsyYYcMdkiRJkqRhd+ONNzJp0iSASSmlG6uOp4wlBSRJkiRJ6lG9lxR47rmqI5AkSZIkaUTovaTAQw9VHYEkSZIkSSNC7yUF7ruv6ggkSZIkSRoRei8pYEkBSZIkSZKAXkwKXHRR1RFIkiRJkjQi9F5S4D//qToCSZIkSZJGhN5LCsyaVXUEkiRJkiSNCL2XFABIqeoIJEmSJEmqXG8mBR5+uOoIJEmSJEmqXG8mBe6+u+oIJEmSJEmqnEkBSZIkSZJ6VO8lBcaNMykgSZIkSRK9mBRYdVWTApIkSZIk0YtJgVVWMSkgSZIkSRK9mBRYdVX4+9+rjkKSJEmSpMr1ZlLg8cfznyRJkiRJPaz3kgKrrZZ///a3auOQJEmSJKlivZcUWHXV/GsVAkmSJElSj+u9pMASS8AKK1hSQJIkSZLU83ovKQCw1lomBSRJkiRJPa93kwJWH5AkSZIk9bjeTAqMH29JAUmSJElSz+vNpMBaa8ETT8Bjj1UdiSRJkiRJlendpABYWkCSJEmS1NN6Mymw5pr513YFJEmSJEk9rDeTAkstBSuuaEkBSZIkSVJP682kAPhZQkmSJElSz+vdpMD48VYfkCRJkiT1tN5NCtRKCqRUdSSSJEmSJFWit5MCTz7pZwklSZIkST2rd5MC48fnX6sQSJIkSZJ6lEkBGxuUJEmSJPWo3k0KLLkkrLSSSQFJkiRJUs/q3aQA5HYFrD4gSZIkSepRvZ0UGD/ekgKSJEmSpJ7V20mBtdeGO+/0s4SSJEmSpJ7U20mBDTaAZ56B++6rOhJJkiRJkua73k4KrL9+/r3ttmrjkCRJkiSpAr2dFFh1VVhqKZMCkiRJkqSe1NtJgQhYbz3461+rjkSSJEmSpPmut5MCkKsQmBSQJEmSJPUgkwLrrQczZ8KcOVVHIkmSJEnSfGVSYP31YfZsuOeeqiORJEmSJGm+Mimw3nr518YGJUmSJEk9xqTAiivCssvaroAkSZIkqeeYFIiwsUFJkiRJUk8yKQC5CoHVByRJkiRJPWbEJAUi4uCImBURL0TE9IjYuM3wC0fEMRFxb0TMjoh7IuJ9Xc18/fXhjjvgxRe7Gl2SJEmSpFejEZEUiIj3AP8LHAm8EbgFuCgixrUY7RxgG+D9wNrAFODOrgJYbz14+WX429+6Gl2SJEmSpFejEZEUAA4Fvp9SOi2ldAfwYeB54ICygSPi7cCWwE4ppctTSvenlK5NKV3T1dz9AoEkSZIkqQdVnhSIiIWAScCltW4ppQRcAmzWZLR3ADcAn42If0TEnRFxXEQs2lUQ48blrxDY2KAkSZIkqYcsWHUAwDhgAeCRhu6PAOs0GWcNckmB2cBuxTS+CywLfKCrKGxsUJIkSZLUY0ZCUqAbY4C5wN4ppWcBIuKTwDkRcVBK6T/NRjz00EMZO3Zsn25Tpkxhyvrrw4UXDmfMkiRJkqRRatq0aUybNq1Pt6eeeqqiaDo3EpIC/wbmACs0dF8B+GeTcR4GHqwlBAozgQBWAe5uNrPjjz+eiRMn9u/x7LNw0kkwezYs2l0tBEmSJElSb5oyZQpTpkzp0+3GG29k0qRJFUXUmcrbFEgpvQTMALardYuIKP7/5yajXQ2sHBGL13Vbh1x64B9dBbL++jB3bv40oSRJkiRJPaDypEDhW8CBEbFfRKwLfA9YHPgJQER8LSJ+Wjf8GcBjwKkRMSEi3gJ8A/hRq6oDLb3+9fnXxgYlSZIkST1iJFQfIKV0dkSMA44mVxu4GdghpfRoMciKwKp1wz8XEdsDJwHXkxMEZwFf6jqIsWNh1VVtbFCSJEmS1DNGRFIAIKV0CnBKk37vL+l2F7DDkAbx+tfDVVcN6SQlSZIkSRqpRkr1gZFhnXVg1qyqo5AkSZIkab4wKVBv883hwQfhsceqjkSSJEmSpGFnUqDehhvm31tuqTYOSZIkSZLmA5MC9dZaCxZdFG69tepIJEmSJEkadiYF6i24IKy/vkkBSZIkSVJPMCnQaMIEuOOOqqOQJEmSJGnYmRRotO66OSmQUtWRSJIkSZI0rEwKNBo/Hp54Av7xj6ojkSRJkiRpWJkUaLTOOvn3yiurjUOSJEmSpGFmUqDRBhvk38suqzYOSZIkSZKGmUmBRmPGwPLLw6mnVh2JJEmSJEnDyqRAmS23zA0NPv981ZFIkiRJkjRsTAqU+chH8u+tt1YbhyRJkiRJw8ikQJnNN4cImDmz6kgkSZIkSRo2JgXKLL44rLGGJQUkSZIkSaOaSYFmNtkErrmm6igkSZIkSRo2JgWa2WwzuOkmePHFqiORJEmSJGlYmBRoZuONc0LAKgSSJEmSpFHKpEAzG20ECy4I119fdSSSJEmSJA0LkwLNLLoobLCBSQFJkiRJ0qhlUqCVTTaB666rOgpJkiRJkoaFSYFWNtkEZs6EZ5+tOhJJkiRJkoacSYFWNtkE5s6FGTOqjkSSJEmSpCFnUqCVCRNgySWtQiBJkiRJGpVMCrSywALwpjfBtddWHYkkSZIkSUPOpEA7kyfDNddASlVHIkmSJEnSkDIp0M4WW8BDD8F991UdiSRJkiRJQ8qkQDtbbJF/r7yy2jgkSZIkSRpiJgXaWXZZWG89uOqqqiORJEmSJGlImRToxOabw/TpVUchSZIkSdKQMinQicmT4bbb4Jlnqo5EkiRJkqQhY1KgE1tsAXPnwtVXVx2JJEmSJElDxqRAJ9ZZB1ZeGa64oupIJEmSJEkaMiYFOhGRqxBcc03VkUiSJEmSNGRMCnRq661zY4MvvFB1JJIkSZIkDQmTAp16y1vgxRfhhhuqjkSSJEmSpCFhUqBTG2wASy1lY4OSJEmSpFHDpECnFlgANt3UpIAkSZIkadQwKTAQW2yRkwJz51YdiSRJkiRJg2ZSYCC22gqeeAJuvbXqSCRJkiRJGjSTAgOx2Waw2GJwySVVRyJJkiRJ0qCZFBiIRRbJXyG4+OKqI5EkSZIkadBMCgzU294Gf/oTzJ5ddSSSJEmSJA2KSYGB2m67nBCYPr3qSCRJkiRJGhSTAgO1wQaw3HJw2WVVRyJJkiRJ0qCYFBioMWNgm21MCkiSJEmSXvVMCnRj223h2mvh2WerjkSSJEmSpK6ZFOjGttvCyy/DVVdVHYkkSZIkSV0zKdCNtdeGlVeGSy+tOhJJkiRJkrpmUqAbEbD99nD++VVHIkmSJElS10wKdGuPPWDmTLjjjqojkSRJkiSpKyMmKRARB0fErIh4ISKmR8TGLYbdKiLmNvzNiYjXzLeAt9sOFlkELrxwvs1SkiRJkqShNCKSAhHxHuB/gSOBNwK3ABdFxLgWoyVgLWDF4m+llNK/hjvWVyy+eE4M/O53822WkiRJkiQNpRGRFAAOBb6fUjotpXQH8GHgeeCANuM9mlL6V+1v2KNstOuucOWV8MQT833WkiRJkiQNVuVJgYhYCJgEvNKUf0opAZcAm7UaFbg5Ih6KiIsjYvPhjbTELrvAnDlWIZAkSZIkvSpVnhQAxgELAI80dH+EXC2gzMPAh4A9gHcBDwBXRMRGwxVkqde+Ft70Jvjtb+frbCVJkiRJGgoLVh1AN1JKdwF31XWaHhFrkqsh7D9fg9l1V/jmN+Gll2ChhebrrCVJkiRJGoyRkBT4NzAHWKGh+wrAPwcwneuALdoNdOihhzJ27Ng+3aZMmcKUKVMGMKs6O+0ERxwBV10F22zT3TQkSZIkSa9q06ZNY9q0aX26PfXUUxVF07nI1fcrDiJiOnBtSumQ4v8B3A+cmFI6rsNpXAw8nVJ6d5P+E4EZM2bMYOLEiUMUOTB3Lqy2GuyxB5xwwtBNV5IkSZL0qnbjjTcyadIkgEkppRurjqfMSGhTAOBbwIERsV9ErAt8D1gc+AlARHwtIn5aGzgiDomIXSNizYhYLyK+DWwDnDzfIx8zBnbbDX7zGxgBCRZJkiRJkjo1IpICKaWzgcOAo4GbgA2BHVJKjxaDrAisWjfKwsD/ArcCVwAbANullK6YTyH3tdtucP/9cNNNlcxekiRJkqRujIQ2BQBIKZ0CnNKk3/sb/n8c0FG1gvliq61gmWXg17+GoayaIEmSJEnSMBoRJQVe9RZaCHbZJScFJEmSJEl6lTApMFR23x1uuw3uuqv9sJIkSZIkjQAmBYbKDjvAEkvAL39ZdSSSJEmSJHXEpMBQWXxx2G47uPDCqiORJEmSJKkjJgWG0o47wp//DE8+WXUkkiRJkiS1ZVJgKO24I8yZA+efX3UkkiRJkiS1ZVJgKK2+OowfD/vsU3UkkiRJkiS1ZVJgqO2/f/69775q45AkSZIkqQ2TAkPtYx+DhRf2KwSSJEmSpBHPpMBQGzsW3vEOOP30qiORJEmSJKklkwLDYepUuPlmuOOOqiORJEmSJKkpkwLDYccdYeml4cwzq45EkiRJkqSmukoKRMQREbF4SffFIuKIwYf1KrfoorDbbnDUUZBS1dFIkiRJklSq25ICRwJLlnRfvOinXXbJv1dfXW0ckiRJkiQ10W1SIICyV+BvAB7vPpxRZI89YLnl4Gc/qzoSSZIkSZJKDSgpEBFPRMTj5ITAXRHxeN3fU8AfgLOHI9BXnTFj4EMfgrPOgtmzq45GkiRJkqR+Fhzg8J8glxL4MbmawFN1/V4E7k0pXTNEsb367bcfHHss/Pa3sNdeVUcjSZIkSVIfA0oKpJR+ChARs4CrU0ovD0tUo8U668Cmm8JPf2pSQJIkSZI04nTbpsAzwITafyLinRHxm4g4NiIWHprQRol99oELLoD77qs6EkmSJEmS+ug2KfB9YG2AiFgDOAt4HtgT+MbQhDZK7LNP/j3mmGrjkCRJkiSpQbdJgbWBm4t/7wn8MaW0N/A+YI8hiGv0GDsWll0WfvhDeOmlqqORJEmSJOkVg/kkYW3ctwIXFP9+ABg32KBGnd/9Lv+ef361cUiSJEmSVKfbpMANwBcjYl9gK6D2tPs64JGhCGxU2XxzmDwZvv71qiORJEmSJOkV3SYFPgFMBE4Gjkkp/b3o/m7gz0MR2Khz4IEwfTr82dUjSZIkSRoZukoKpJRuTSltkFIam1I6qq7Xp4H9hya0UWbfffPvCSdUG4ckSZIkSYUFBzNyRExi3qcJb08p3Tj4kEaphReGI46Ab30Lnn4all666ogkSZIkST2uq5ICEfGaiLgcuB44sfi7ISIujYjlhzLAUeXAA2H2bDj11KojkSRJkiSp6zYFTgKWBNZLKS2bUloWWB9YmpwgUJlVVoF3vxtOOgnmzKk6GkmSJElSj+s2KfB24KCU0sxah5TS7cDBwI5DEdio9YlPwN13wwUXtB9WkiRJkqRh1G1SYAzwUkn3lwYxzd4weTKstBLsumvVkUiSJEmSely3D/CXASdExMq1DhHxWuB44NKhCGxUO+SQ/DtjRrVxSJIkSZJ6WrdJgY+S2w+4NyLujoi7gVlFt48NVXCj1qc+Ba99LfzgB1VHIkmSJEnqYV0lBVJKDwATgZ2Bbxd/O6WUJqaU/jGE8Y1OCy6Yv0Twgx/AvfdWHY0kSZIkqUcNKCkQEdtGxO0RsXTK/pBSOimldBJwfUTcFhE7DFOso8snPpF/Dzus2jgkSZIkST1roCUFPgH8MKX0dGOPlNJTwPex+kBnxo6Fz34WfvMbePDBqqORJEmSJPWggSYF3gD8vkX/i4ENuw+nx3z+8zBnDuyzT9WRSJIkSZJ60ECTAitQ/inCmpeB5bsPp8csvXSuPnDFFXD//VVHI0mSJEnqMQNNCjwIrN+i/4bAw92H04OOOALGjYOvfrXqSCRJkiRJPWagSYELgK9ExKKNPSJiMeAo4LyhCKxnLLVUblvg1FPhnnuqjkaSJEmS1EMGmhT4KrAscFdEfCYi3ln8fRa4s+h3zFAHOeoddFAuLXD00VVHIkmSJEnqIQNKCqSUHgE2B/4KfA34dfF3bNHtzcUwGojFF4fDD4fTT4c776w6GkmSJElSjxhoSQFSSvellHYCxgGTgU2BcSmlnVJKs4Y6wJ7xwQ/CyivDl79cdSSSJEmSpB4x4KRATUrpiZTS9Sml61JKTwxlUD1p0UXhi1+EM8+EG26oOhpJkiRJUg/oOimgYXDAAfkzhYcfXnUkkiRJkqQeYFJgJFloITjtNLjkErj44qqjkSRJkiSNciYFRppdd4U3vxk+/WmYM6fqaCRJkiRJo5hJgZEmAr75Tbj1VvjJT6qORpIkSZI0ipkUGIkmT4a9985tCzxhG46SJEmSpOFhUmCkOu44mD0bPv/5qiORJEmSJI1SJgVGqpVXhq98Bb73Pbj66qqjkSRJkiSNQiYFRrKDDsq/22wDKVUbiyRJkiRp1BkxSYGIODgiZkXECxExPSI27nC8LSLipYi4cbhjnO8WWgjOPRdeegl+/OOqo5EkSZIkjTIjIikQEe8B/hc4EngjcAtwUUSMazPeWOCnwCXDHmRVdt0V9tsPPvMZePzxqqORJEmSJI0iIyIpABwKfD+ldFpK6Q7gw8DzwAFtxvse8HNg+jDHV62vfz2XFjjssKojkSRJkiSNIpUnBSJiIWAScGmtW0opkd/+b9ZivPcDrwOOGu4YK7fiinD88XDqqXDeeVVHI0mSJEkaJSpPCgDjgAWARxq6PwKsWDZCRKwFHAtMTSnNHd7wRogDDoCddoL/+R/497+rjkaSJEmSNAqMhKTAgETEGHKVgSNTSnfXOlcY0vwRAf/3f7kawYc/7NcIJEmSJEmDtmDVAQD/BuYAKzR0XwH4Z8nwSwFvAjaKiO8U3cYAEREvAm9LKV3RbGaHHnooY8eO7dNtypQpTJkypbvo56eVVoLvfQ/22gvOOAOmTq06IkmSJEkSMG3aNKZNm9an21NPPVVRNJ2LNALeOEfEdODalNIhxf8DuB84MaV0XMOwAUxomMTBwDbAHsC9KaUXSuYxEZgxY8YMJk6cOAxLMR9NnQrnnw9//SusskrV0UiSJEmSStx4441MmjQJYFJK6caq4ykzUqoPfAs4MCL2i4h1yV8VWBz4CUBEfC0ifgq5EcKU0u31f8C/gNkppZllCYFR5+STYYklYLfdYG5vNKkgSZIkSRp6IyIpkFI6GzgMOBq4CdgQ2CGl9GgxyIrAqhWFN/Iss0z+EsGMGflzhZIkSZIkdWFEJAUAUkqnpJT+O6W0WEpps5TSDXX93p9S2rbFuEellF7ldQIG6G1vy20LfP7zcOWVVUcjSZIkSXoVGjFJAXXhtNNy44P77w/PPFN1NJIkSZKkVxmTAq9miywCl14Kjz0Gb30rzJlTdUSSJEmSpFcRkwKvdhMmwOmnw3XX2b6AJEmSJGlATAqMBu98Jxx2GBx5ZE4OSJIkSZLUAZMCo8Uxx8BGG8HkyfDPf1YdjSRJkiTpVXP16EMAACAASURBVMCkwGix8MLwi1/kf0+dCi+9VG08kiRJkqQRz6TAaLL66nD55XDZZfmThXPnVh2RJEmSJGkEMykw2my9NZx0ElxxRa5SIEmSJElSEwtWHYCGwUc/Ck88AUccAeuvD7vvXnVEkiRJkqQRyJICo9UXvwjvfjfstx/85S9VRyNJkiRJGoFMCoxWEXDqqTB+PLz1rTBrVtURSZIkSZJGGJMCo9mSS8LFF8PSS+fEwL/+VXVEkiRJkqQRxKTAaLf88nDJJfD887DDDvD441VHJEmSJEkaIUwK9ILVV88lBh54IH+q8Mknq45IkiRJkjQCmBToFRtskEsM3HMP7LgjPP101RFJkiRJkipmUqCXbLQR/OEPMHMm7LQTPPts1RFJkiRJkipkUqDXTJoEF10Et94Ku+4Ks2dXHZEkSZIkqSImBXrR5Mlw3nlwzTW5xMBzz1UdkSRJkiSpAiYFetVb3pIbH7z++tzGgFUJJEmSJKnnmBToZVtumRMDN9+cSww89ljVEUmSJEmS5iOTAr1us83g97/PjQ9uthn8/e9VRyRJkiRJmk9MCgg23xymT4cI2HRTuPrqqiOSJEmSJM0HJgWUrblmbnhwvfVgu+3grLOqjkiSJEmSNMxMCmieZZfNbQzsuSe8971w7LGQUtVRSZIkSZKGyYJVB6ARZpFF4LTTYPx4+MIX4J574LvfhYUWqjoySZIkSdIQMymg/iLgyCNhjTXgAx+A++6DX/wCxo6tOjJJkiRJ0hCy+oCa23ffXJ3ghhtgiy1yckCSJEmSNGqYFFBrW2+dGyB8/vn8ycILLqg6IkmSJEnSEDEpoPbWXTcnBtZfH3beGb78ZZg7t+qoJEmSJEmDZFJAnVlhBbjoIvjqV+Hoo2GXXeDRR6uOSpIkSZI0CCYF1LmI/EWCCy7I7QxstBH88Y9VRyVJkiRJ6pJJAQ3c298ON98Ma60F226bSw689FLVUUmSJEmSBsikgLqz8spw6aW55MCRR8LkyXD77VVHJUmSJEkaAJMC6t4CC+RSAjfcALNnw6RJcOKJNkIoSZIkSa8SJgU0eJMmwYwZ8MEPwiGHwA47wAMPVB2VJEmSJKkNkwIaGostBiecABdfDDNnwoQJcNJJlhqQJEmSpBHMpICG1vbbw223wX77wcc/Dm9+M/zlL1VHJUmSJEkqYVJAQ2/sWDjlFLjySnjySZg4MTdI+MILVUcmSZIkSapjUkDDZ8st4aab4Etfgm9+E9ZbD847r+qoJEmSJEkFkwIaXossAkcckasQjB8P73gH7Lwz3HVX1ZFJkiRJUs/7/+3deZxcVZ338c+vk84egiSEBIgQ9h2SYGQZoiwKMojDoiyK2+PCoAOio48+yqDoo7gMoyAyiAuIEGBURhEkGRZFDIgk7AREwhIISUgISchGljN/nCrrdqW76SZJV1fV5/16nVfVvffcqlN1Up2ub597jqGAesYuu8CUKfDLX8Kjj8Jee8HnPw9Ll9a6ZZIkSZLUtAwF1HMi4PjjcyjwpS/l1Qo22wwuuQTWrKl16yRJkiSp6RgKqOcNHJgvKXjsMfinf4IzzoB994UbboCUat06SZIkSWoahgKqne22g+uvh3vvhZEj4dhj4bDDYNq0WrdMkiRJkpqCoYBqb8IEuO22PFJg4UI4+OA8GeH999e6ZZIkSZLU0AwF1DtEwDHH5CDgmmvgiSdg3Dg4+WT4y19q3TpJkiRJakiGAupdWlrgpJPgkUfghz+Eu+6CiRPhqKPyfUmSJEnSRmMooN6ptRU++lF48km47jqYPRsOOiiHA3/8oxMSSpIkSdJGYCig3q1vX3j3u+Ghh/JlBc89B5MmwQEH5LBg7dpat1CSJEmS6pahgOpD+bKCBx+EG2+EIUPy9s47w4UXwtKltW6hJEmSJNUdQwHVl5YWOPpouPXWvJThgQfCZz4DY8bA5z6XLzOQJEmSJHVJrwkFIuITEfFURKyIiLsj4k2d1D04Iu6MiAURsTwiZkbEp3qyveoFJkyAq66CWbPg4x/PExOOHZtHENx5p/MOSJIkSdJr6BWhQEScBPw7cC4wDngAmBIRIzo4ZRlwEXAIsBvwVeBrEfGRHmiuepsxY+Cb38yjBC64AB54AA45BPbeGy69FJYsqXULJUmSJKlX6hWhAHA2cGlK6WcppceA04HlwIfbq5xSuj+ldG1KaWZK6dmU0tXAFHJIoGY1dCiceSY8+ihMnZrnGzjjDBg5Et77XkcPSJIkSVKVmocCEdEKTABuLe9LKSXgFuDALj7GuFLd32+CJqretLTA294G118PTz8N550H99yTRw+MGwcXXQQLF9a6lZIkSZJUczUPBYARQB9gXtX+ecCozk6MiNkRsRK4B7g4pfTTTdNE1a3yBISPPw433ZTnHPj0p2HrreGEE3JwsGpVrVspSZIkSTXRG0KBDfEP5FEGpwNnl+YmkNbX0gLveEcOAZ5/Hs4/P48iOP54GDUKPvYx+MMfYN26WrdUkiRJknpMpBpfY126fGA5cEJK6TeF/ZcDw1JKx3Xxcb4IvC+ltHsHx8cD0ydNmsSwYcPaHDvllFM45ZRTXucrUF2bOTOvYHDVVTkkGDMGTj0VPvAB2L3df0qSJEmStJ7JkyczefLkNvsWL17MHXfcATAhpTSjJg17DTUPBQAi4m7gzymls0rbATwLXJhS+nYXH+PfgA+mlHbo4Ph4YPr06dMZP378Rmq5GkZKMG0a/PzncN118NJLef6Bk0+Gd787X3YgSZIkSd0wY8YMJkyYAL04FOgtlw9cAHw0It4fEbsB/wkMAi4HiIhvRMQV5coRcUZEHBMRO5XK/wE+A1xZg7arEUTAwQfDJZfAnDnwy1/CDjvAl7+cbydOhO98B/72t1q3VJIkSZI2ml4RCqSUrgP+FTgPuA/YBzgypfRiqcooYEzhlBbgG6W6fwH+GfhsSuncHmu0Glf//nmugV/8AubPh2uugW22gXPOycscjh8P554L99/vEoeSJEmS6lqvuHygJ3j5gDbYsmXwu9/lUQQ33wwvv5xHEbzrXXDMMXnJw9bWWrdSkiRJUi/h5QNSIxk8GE48ESZPhnnzcjBwxBFw7bVw+OF5FYP3vS8fX7iw1q2VJEmSpNfUt9YNkOpSv35w5JG5pAT33ZeXO/ztb/NKBhHw5jfD0UfnMm5cXhZRkiRJknoRv6VIGyoizzPw1a/mcGD2bPjxj2HbbfPkhPvvD6NHw2mnweWX5+OSJEmS1As4UkDa2LbdFj70oVxWr4Y774QpU2Dq1DyKICXYaad8ycFhh8Ghh8KWW9a61ZIkSZKakKGAtCm1tuYv/YceCuefn+ca+P3v4bbb4NZb4dJLc7199skBweGHw6RJsNlmNW22JEmSpOZgKCD1pOHD4YQTcgF4/vkcENx2W17V4LvfhT598iUH5ZEEBx0EAwfWtt2SJEmSGpKhgFRL22yT5xo47bR8WcGTT1ZCgssug69/Hfr3h4kT4YADckBw4IGw1Va1brkkSZKkBmAoIPUWEXmugZ12go99DNatg0ceyQHBnXfC1VfDt7+d6+64Yw4IymXPPfMIA0mSJEnqBkMBqbdqaYG9987lrLPyvtmzYdq0Srn6ali7FoYOrYwkOOigvBzisGG1bb8kSZKkXs9QQKonY8bASSflArB8Odx7byUk+P734StfyaMO9tyzcrnBxImw666OJpAkSZLUhqGAVM8GDcqrFUyalLdTgieeqIQEf/oT/PCH+djAgbDffjBuXJ7I8IADYJddDAokSZKkJmYoIDWSiPxFf5dd4IMfzPsWL4bp02HGDLj/frj9drjkkhwgDB6cQ4IJE3JgMH487LEH9PVHgyRJktQM/M1fanTDhuWlDQ87rLJv8eJ82cH06bnceCN873v5WP/+eR6D/farjCzYZx8YMqQ27ZckSZK0yRgKSM1o2DA4/PBcyl55JY8muO++PKLg3nvhiitg9ep8fOxY2Hdf2GuvPF/BPvvkEQmOKpAkSZLqlr/NS8qGDGk7PwHAq6/Co4/mkOChh+DBB+HHP4YXXsjH+/eH3XbLIwv22itferDHHjlAaGmpzeuQJEmS1GWGApI61q9f5TKCooULc0jwwAPw8MO5/PrXsHRpPj5kSF7tYLfd2t7uvHOe8FCSJElSr2AoIKn7hg+Ht741l7KUYM6cHBA8+CA89hg8/jjcfHMOESBPhLjddm2DgvL90aPzcUmSJEk9xlBA0sYRAdtsk8uRR7Y9tmBBDgjK5bHHclhw8cWwZk2uM3RonqPA0QWSJElSjzEUkLTpjRiRy8EHt92/ejXMmtU2LHj8cZgyJQcJ0HZ0wa675uBg++3zvAXbbw+DBvX0q5EkSZIahqGApNppba182a+2cOH6YcHUqXDJJZUVESBfdrDDDuuXsWPzMSc8lCRJkjpkKCCpdxo+HA46KJeidevy6gezZsFTT+XbcrnllsrKCJBXRxg7tuPQYMiQnn1NkiRJUi9jKCCpvrS0VOYuOOSQ9Y8vXw5PP902LJg1C37/e/jJT/LxspEj86UJY8bAG9+Y7xfLFls4+aEkSZIamqGApMYyaBDssUcu1VKC+fMrQcGTT8Izz8Ds2XDTTfDss7ByZaX+4MGVgGDMGNh22xxGlG+32QaGDTM4kCRJUt0yFJDUPCJgq61yOfDA9Y+XQ4NnnskBwTPPVMo998D118OLL7Y9Z/DgtkFBMTAo3x85Evr06ZnXKEmSJHWDoYAklRVDg4kT26+zalWet+C55+D55yu3zz+fRx7ccUe+X15qEaBv3zzpYXuBQfl2661hwICeeZ2SJElSiaGAJHVH//55KcTtt++4zrp1eURBMTQo3j78cL595ZW2540YUQkNRo/OpXh/9OgcWPTrtylfoSRJkpqIoYAkbWwtLZURB+PHd1xvyZL1Rxs89xzMmQMPPQQ33wxz58LatW3Pe8Mb8iUJo0blEQajR+ftctlyy8r9QYM27WuVJElSXTMUkKRa2WyzXHbfveM6a9fCggX5koVyefHFPPfBCy/kAGHGjLy9aNH65w8e3DYw6KyMGJEvdZAkSVLT8Lc/SerN+vSpjDrYb7/O6776ag4Q5s9vW8ohwvz5eQTC/Pkwbx6sWNH2/Ii2owy23LJSqrdHjMgjFgwRJEmS6pq/zUlSo+jXL19OsPXWXau/bNn6AcILL7QNEh59NN9/8cX1L2OAHAyMGJHL8OG5lIOD8naxbLEFtLZu3NctSZKk181QQJKa1eDBMHZsLq9l3Tp4+eVKQLBgASxcmG8XLMj7Fi6Ev/4V7rwz33/55fYfa+jQtiFBdXDwhjfA5puvX4YMyaMZJEmStNEYCkiSXltLS/4Cv8UWsOuuXTtnzZo8z8HChbm89FLlfrHMnZtHJJS3V65s//H69Gk/LOisFAOGQYMMFSRJkqoYCkiSNo2+fSuXEnTHypV5lMHixfl20aJ821F57rlKvUWLYPXqjtvTlfCgozJwoKGCJElqOIYCkqTeZcCAvNziqFHdPzelSqjQWSkGDc8803b/mjXtP3Zra9cDhM03zytLDBmSb4cNy7dOzChJknoZfzuRJDWOiPwX/YEDYfTo7p+fUl6VoaMAobq89BLMmtW2bnsTMpYNHpzDgWJoMHRoDg3KwcHQoZUgYciQSinvHzo0P05Ly+t/nyRJkkoMBSRJKovIcw8MGtT1VRyKUoJXXsmXPixZku8vWZK3i+Xll/P+5cvz7RNP5P1Ll+btJUvy5I6dtXPw4BwQFEt1iFAsxfrl48X6rgohSVJTMhSQJGljiah88d4QKeUlI5cty8HC0qVtA4OlS9vuL5dXXoF58+DJJyvHy/VT6vw5W1vbhgRDhuQgoaPbYmlvX7k4waMkSb2aoYAkSb1NROWL+VZbbfjjledaqA4SyqFDsVTvW7YsLzn59NNtjy1bli+16MprGTSoEh6UR2KUL/MYOLDz7e7U7dfPAEKSpG4yFJAkqdEV51ro7moQnVm3Ll8CUR7VUA4NitvF/a+8kuuvWFEpy5fnuRnK96uPrVrV9fa0tGyasKGjY336bLz3UpKkGjEUkCRJr09LS2VEw6aybl0e5dBeYNDe/dfaXrQI5szp+HE6myiyWmvrhoUN3Tl3wABHQUiSNglDAUmS1Hu1tFQuOegJq1d3P3jo7NjcuZ3X7Y7OwoUBA9qW9vb1718pxX3Vx9ur66UZktSwDAUkSZLKWltz2WyzTf9c5bkeNjR4WLmyUpYsabtdLitW5EsxVq7sfGWLzlQHBtXhQUf7+/Vrv17xeLFO+X57+6qPG1RI0gYzFJAkSaqF4lwPPWnNmkpA0NltsVSHDO3VW7kSXn0131+6tO3x8v7qsmbNhr2W1tb1g4Ly/fIIh9bW9o+X73cUOJTPK94v3w4YUAmQqusWA4/WVueekNTrGQpIkiQ1k759cxk8uNYtyaMlyoHBq6+uHx4Uj1WHC+3dLz9GObxYvTqX8vHly/O8EqtWVfa39zjlY92ZY6IjLS3thwfFUg4YikFD377r1+nonOJ2375tj22sbUdlSA3LUECSJEm1EVH5q3pvtHZt2/CgfH/lyjzKYc2ayrHqQKNct/q2+rGKpfh4a9bky0Gq65TPLZbiORs6+qIjffps2tChFtt9+xp2SBgKSJIkSe3r0yeXAQNq3ZKuSykHA6tXV27LpdbbK1a8/vM3xqiN9pTDjo5Cg85KV+ps6Dnt1e/Tp+1t9f6ubPfpk0exSBgKSJIkSY0jovKltpGsW1cZudFTIcbatZXRF52V1avbjh55vaXchp7S0rJ+wHDoofCrX/VcG9QrGApIkiRJ6t1aWirzMzSylHIA0llwUH28vfCis33lwKNYp3x/zJhavwOqAUMBSZIkSeoNIiqXrfTWuTbUcLyQRJIkSZKkJmUoIEmSJElSk+o1oUBEfCIinoqIFRFxd0S8qZO6x0XE1IiYHxGLI2JaRLy9J9ur2ps8eXKtm6CNyP5sLPZn47FPG4v92Vjsz8Zif6qn9YpQICJOAv4dOBcYBzwATImIER2cMgmYCrwDGA/cDtwQEfv2QHPVS/gDs7HYn43F/mw89mljsT8bi/3ZWOxP9bReEQoAZwOXppR+llJ6DDgdWA58uL3KKaWzU0rfSSlNTyk9mVL6IvAE8M6ea7IkSZIkSfWt5qFARLQCE4Bby/tSSgm4BTiwi48RwFDgpU3RRkmSJEmSGlHNQwFgBNAHmFe1fx4wqouP8VlgMHDdRmyXJEmSJEkNrW+tG7ChIuJU4Bzg2JTSgk6qDgCYOXNmj7RLm97ixYuZMWNGrZuhjcT+bCz2Z+OxTxuL/dlY7M/GYn82lsL3zwG1bEdnIo/Ur2ED8uUDy4ETUkq/Key/HBiWUjquk3NPBn4EnJhSuvk1nudU4KqN0mhJkiRJkrruvSmlq2vdiPbUfKRASml1REwHDgd+A3+fI+Bw4MKOzouIU8iBwEmvFQiUTAHeCzwNrNzAZkuSJEmS9FoGANuTv4/2SjUfKQAQEe8BLievOnAPeTWCE4HdUkovRsQ3gK1TSh8o1T+1VP9M4PrCQ61IKS3pwaZLkiRJklS3aj5SACCldF1EjADOA7YC7geOTCm9WKoyChhTOOWj5MkJLy6VsivoYBlDSZIkSZLUVq8YKSBJkiRJknpeb1iSUJIkSZIk1YChgCRJkiRJTaopQoGI+EREPBURKyLi7oh4U63b1Gwi4pCI+E1EPB8R6yLi2HbqnBcRcyJieUT8T0TsVHW8f0RcHBELImJpRPwiIkZW1XlDRFwVEYsjYlFE/CgiBlfVGRMRN0bEsoiYGxHfioim+CxsLBHxhYi4JyKWRMS8iLg+InZpp559Wgci4vSIeKD0Hi+OiGkRcVRVHfuyTkXE50s/dy+o2m+f1omIOLfUh8XyaFUd+7OORMTWEXFlqT+Wl34Gj6+qY5/WgcjfMao/n+si4qJCHfuyTkRES0R8NSJmlfrrbxHxpXbqNVafppQaugAnkZcgfD+wG3Ap8BIwotZta6YCHEWeSPJdwFrg2Krj/7fUL8cAewH/DTwJ9CvUuYS8pORbgHHANOCPVY/zO2AGsD9wEPBX4OeF4y3AQ+QlQfYGjgTmA1+r9XtUTwW4CTgN2L30Pv621DcD7dP6K8A/lj6jOwI7AV8DVgG725f1XYA3AbOA+4ALCvvt0zoqwLnAg8CWwMhS2cL+rM8CbA48RV5aewKwHXAEMNY+rb8CDC98LkeSl1VfCxxiX9ZfAf5f6X07CngjcDywBPhkoU7D9WnN3/ge6Ni7ge8VtgN4DvhcrdvWrAVYx/qhwBzg7ML2ZsAK4D2F7VXAcYU6u5Yea2Jpe/fS9rhCnSOBNcCo0vY7gNUUQiHg48AioG+t35t6LcCI0nv/D/ZpYxRgIfAh+7J+CzAEeBw4DLidtqGAfVpHhRwKzOjkuP1ZRwU4H/jDa9SxT+u0AN8F/mpf1mcBbgAuq9r3C+BnjdynDT2cJCJayQnsreV9Kb+btwAH1qpdaisixpKXnSz20xLgz1T6aX/yEprFOo8DzxbqHAAsSindV3j4W4AEvLlQ56GU0oJCnSnAMGDPjfSSmtHm5Pf5JbBP61lp2NzJwCBgmn1Z1y4Gbkgp3VbcaZ/WrZ0jX4L3ZET8PCLGgP1Zp94J3BsR10W+BG9GRHykfNA+rV+l7x7vBX5c2rYv68804PCI2BkgIvYFDiaPkm3YPm3oUID818s+wLyq/fPInaneYRT5A9BZP20FvFr60HVUZxR5SM3fpZTWkr+oFuu09zzgv4nXJSKCnIrfmVIqX+Nqn9aZiNgrIpaSk+0fkNPtx7Ev61Ip2NkP+EI7h+3T+nM38EHyX5FOB8YCd5SuPbU/688OwD+TR/K8nTzM+MKIOK103D6tX8eRv7BdUdq2L+vP+cC1wGMR8SowHfhuSuma0vGG7NO+G/PBJDWlHwB7kFNU1a/HgH3Jv8ycCPwsIibVtkl6PSJiW3JQd0RKaXWt26MNl1KaUth8OCLuAZ4B3kP+7Kq+tAD3pJTOKW0/EBF7kQOfK2vXLG0EHwZ+l1KaW+uG6HU7CTgVOBl4lBywfy8i5qSUGvbz2egjBRaQJ/rYqmr/VoAf1t5jLnmuh876aS7QLyI2e4061bN69gG2qKrT3vOA/ya6LSK+DxwNvDWl9ELhkH1aZ1JKa1JKs1JK96WUvgg8AJyFfVmPJpAnpJsREasjYjV5oqOzSn/1mId9WtdSSovJE1LthJ/RevQCMLNq30zypGZgn9aliHgjecLIywq77cv68y3g/JTSf6WUHkkpXQX8B5WRdw3Zpw0dCpT+QjKdPAso8PehzoeTrxdRL5BSeor8D7vYT5uRr6cp99N08sQbxTq7kv8Dvau06y5g84gYV3j4w8kf3D8X6uwdESMKdd4OLCangeqiUiDwLuDQlNKzxWP2aUNoAfrbl3XpFvIsxfuRR3/sC9wL/BzYN6U0C/u0rkXEEHIgMMfPaF36E3nSsaJdyaM//D+0fn2YHLreVN5hX9alQeQ/Kheto/S9uWH7dGPOWtgbC3lo3XLaLkm4ENiy1m1rpgIMJv9iuh/5g/Wp0vaY0vHPlfrlneRfZv8beIK2S3v8gLyEz1vJfwn7E+sv7XET+ZffN5GHsz8OXFk43kL+C+jvgH3I12fOA75a6/eonkqpLxYBh5ATy3IZUKhjn9ZJAb5e6svtyEvrfIP8n9lh9mVjFNZffcA+raMCfBuYVPqMHgT8T+l9HG5/1l8hT0K2ivyXxx3JQ5WXAicX6tindVTIX+SeBv5/O8fsyzoqwE/JEwIeXfqZexz52v+vN3Kf1vyN76HOPaP0QV1BTlz2r3Wbmq2Qh66uIydvxfKTQp0vk5f4WE6eWXOnqsfoD1xEvixkKfBfwMiqOpuT/xq2mPyl9TJgUFWdMcBvgVdKH6xvAi21fo/qqXTQl2uB91fVs0/roJDXyp5V+hk5F5hKKRCwLxujALdRCAXs0/oqwGTycsoryL+sXk1hTXv7s/4K+QvHg6X+egT4cDt17NM6KcDbyL8H7dTBcfuyTgr5D5kXkL/QLyN/2f8KVUsANlqfRunJJEmSJElSk2noOQUkSZIkSVLHDAUkSZIkSWpShgKSJEmSJDUpQwFJkiRJkpqUoYAkSZIkSU3KUECSJEmSpCZlKCBJkiRJUpMyFJAkSZIkqUkZCkiSpNclIp6KiDNr3Q5JkvT6GQpIklQHIuKnEfGr0v3bI+KCHnzuD0TEonYO7Q/8sKfaIUmSNr6+tW6AJEmqjYhoTSmt7kpVIFXvTCkt3PitkiRJPcmRApIk1ZGI+CnwFuCsiFgXEWsj4o2lY3tFxE0RsTQi5kbEzyJieOHc2yPiooj4j4h4Ebi5tP/siHgwIl6JiGcj4uKIGFQ69hbgJ8CwwvP9W+lYm8sHImJMRPy69PyLI+LaiBhZOH5uRNwXEe8rnftyREyOiMGFOieW2rI8IhZExNSIGLhJ31RJkpqYoYAkSfXlTOAu4DJgK2A0MDsihgG3AtOB8cCRwEjguqrz3w+sAg4CTi/tWwv8C7BH6fihwLdKx6YBnwKWFJ7vO9WNiogAfgNsDhwCHAHsAFxTVXVH4F3A0cA/kgOOz5ceYxRwNfAjYLfSsV+RRypIkqRNwMsHJEmqIymlpRHxKrA8pfRieX9EfBKYkVI6p7DvI8CzEbFTSulvpd1PpJQ+X/WYFxY2n42Ic4BLgE+mlFZHxOJcrfJ87TgC2BPYPqU0p/T87wceiYgJKaXp5WYBH0gpLS/VuRI4HDiHHDj0Aa5PKc0u1X+kq++NJEnqPkcKSJLUGPYFDisN3V8aEUuBmeS5AHYs1JtefWJEHBERt0TEcxGxBLgSGB4RA7rx/LsBs8uBAEBKaSbwMrB7od7T5UCg5AXyiAaAB8ijHR6OiOsi4iMRsXk32iBJkrrJUECSJD6WjwAAAeFJREFUpMYwhDx8fx9yQFAuOwN3FOotK54UEdsBNwD3A8eTLz34ROlwv03QzuqJDROl30dSSutSSm8HjiKPEPgX4LFSGyVJ0iZgKCBJUv15lTzMvmgGefj+MymlWVVlRSePNQGIlNK/ppTuKV1msE0Xnq/aTGBMRPz93IjYgzzHQLcuAUgp3ZVS+gowjhwiHNed8yVJUtcZCkiSVH+eBt4cEdsVVhe4GNgCuCYi9o+IHSLiyIj4SWkSwI78DWiNiDMjYmxEnAZ8vJ3nGxIRh0XE8PZWA0gp3QI8DFwVEeMiYiJwBXB7Sum+rryoiJgYEV+IiAkRMQY4ARgBPNqV8yVJUvcZCkiSVH++Q14x4FFgfkS8MaX0AnAw+f/2KcCDwAXAopRSKp2Xqh8opfQg8Gngc8BDwCmUVgMo1LkL+E/gWmA+8NkOHu9YYBHwB2AqOXA4uRuvawkwCbgReBw4D/h0SmlqNx5DkiR1Q1R+T5AkSZIkSc3EkQKSJEmSJDUpQwFJkiRJkpqUoYAkSZIkSU3KUECSJEmSpCZlKCBJkiRJUpMyFJAkSZIkqUkZCkiSJEmS1KQMBSRJkiRJalKGApIkSZIkNSlDAUmSJEmSmpShgCRJkiRJTcpQQJIkSZKkJvW/hiZfaxVu5AsAAAAASUVORK5CYII=" alt="" />

随机梯度下降更快,但是我们需要迭代的次数也需要更多,所以还是用batch的比较合适!!!

runExpe(scaled_data, theta, 16, STOP_GRAD, thresh=0.002*2, alpha=0.001)

结果:

***Scaled data - learning rate: 0.001 - Mini-batch (16) descent - Stop: gradient norm < 0.004
Theta: [[ 1.17096801 2.83171736 2.61095087]] - Iter: 3940 - Last cost: 0.21 - Duration: 0.50s
array([[ 1.17096801,  2.83171736,  2.61095087]])
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" alt="" />

精度

#设定阈值
def predict(X, theta):
return [1 if x >= 0.5 else 0 for x in model(X, theta)]
scaled_X = scaled_data[:, :3]
y = scaled_data[:, 3]
predictions = predict(scaled_X, theta)
correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]
accuracy = (sum(map(int, correct)) % len(correct))
print ('accuracy = {0}%'.format(accuracy))

结果:accuracy = 89%

g(+∞)=1
g(+∞)=1

g(+∞)=1

项目实战:使用逻辑回归判断信用卡欺诈检测

故事背景:

原始数据为个人交易记录,但是考虑数据本身的隐私性,已经对原始数据进行了类似PCA的处理,现在已经把特征数据提取好了,接下来的目的就是如何建立模型使得检测的效果达到最好,这里我们虽然不需要对数据做特征提取的操作,但是面对的挑战还是蛮大的。

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np %matplotlib inline
data = pd.read_csv("creditcard.csv")
data.head()

结果:

  Time V1 V2 V3 V4 V5 V6 V7 V8 V9 ... V21 V22 V23 V24 V25 V26 V27 V28 Amount Class
0 0.0 -1.359807 -0.072781 2.536347 1.378155 -0.338321 0.462388 0.239599 0.098698 0.363787 ... -0.018307 0.277838 -0.110474 0.066928 0.128539 -0.189115 0.133558 -0.021053 149.62 0
1 0.0 1.191857 0.266151 0.166480 0.448154 0.060018 -0.082361 -0.078803 0.085102 -0.255425 ... -0.225775 -0.638672 0.101288 -0.339846 0.167170 0.125895 -0.008983 0.014724 2.69 0
2 1.0 -1.358354 -1.340163 1.773209 0.379780 -0.503198 1.800499 0.791461 0.247676 -1.514654 ... 0.247998 0.771679 0.909412 -0.689281 -0.327642 -0.139097 -0.055353 -0.059752 378.66 0
3 1.0 -0.966272 -0.185226 1.792993 -0.863291 -0.010309 1.247203 0.237609 0.377436 -1.387024 ... -0.108300 0.005274 -0.190321 -1.175575 0.647376 -0.221929 0.062723 0.061458 123.50 0
4 2.0 -1.158233 0.877737 1.548718 0.403034 -0.407193 0.095921 0.592941 -0.270533 0.817739 ... -0.009431 0.798278 -0.137458 0.141267 -0.206010 0.502292 0.219422 0.215153 69.99 0

5 rows × 31 columns

首先我们用pandas将数据读进来并显示最开始的5行,看见木有!用pandas读取数据就是这么简单!这里的数据为了考虑用户隐私等,已经通过PCA处理过了,现在大家只需要把数据当成是处理好的特征就好啦!

接下来我们核心的目的就是去检测在数据样本中哪些是具有欺诈行为的!

count_classes = pd.value_counts(data['Class'], sort = True).sort_index()#查看该列不同属性值的个数
count_classes.plot(kind = 'bar')
plt.title("Fraud class histogram")
plt.xlabel("Class")
plt.ylabel("Frequency")

结果:<matplotlib.text.Text at 0x216366d8860>

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" 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千万不要着急去用机器学习算法建模做这个分类问题。首先我们来观察一下数据的分布情况,在数据样本中有明确的label列指定了class为0代表正常情况,class为1代表发生了欺诈行为的样本。从上图中可以看出来。。。等等,你不是说有两种情况吗,为啥图上只有class为0的样本啊?再仔细看看,纳尼。。。class为1的并不是木有,而是太少了,少到基本看不出来了,那么此时我们面对一个新的挑战,样本极度不均衡,接下来我们首先要解决这个问题,这个很常见也是很头疼的问题。 这里我们提出两种解决方案 也是数据分析中最常用的两种方法,下采样和过采样! 先挑个软柿子捏,下采样比较简单实现,咱们就先搞定第一种方案!下采样的意思就是说,不是两类数据不均衡吗,那我让你们同样少(也就是1有多少个 0就消减成多少个),这样不就均衡了吗?

补充:

Scikit-Learn-机器学习库 非常实用的机器学习算法库,这里面包含了基本你觉得你能用上所有机器学习算法啦。但还远不止如此,还有很多预处理和评估的模块等你来挖掘的!
from sklearn.preprocessing import StandardScaler
#预处理模块中的标准化
data['normAmount'] = StandardScaler().fit_transform(data['Amount'].reshape(-1, 1))#fit_transform指的是对数据做变换
data = data.drop(['Time','Amount'],axis=1)
data.head()

结果:

  V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 ... V21 V22 V23 V24 V25 V26 V27 V28 Class normAmount
0 -1.359807 -0.072781 2.536347 1.378155 -0.338321 0.462388 0.239599 0.098698 0.363787 0.090794 ... -0.018307 0.277838 -0.110474 0.066928 0.128539 -0.189115 0.133558 -0.021053 0 0.244964
1 1.191857 0.266151 0.166480 0.448154 0.060018 -0.082361 -0.078803 0.085102 -0.255425 -0.166974 ... -0.225775 -0.638672 0.101288 -0.339846 0.167170 0.125895 -0.008983 0.014724 0 -0.342475
2 -1.358354 -1.340163 1.773209 0.379780 -0.503198 1.800499 0.791461 0.247676 -1.514654 0.207643 ... 0.247998 0.771679 0.909412 -0.689281 -0.327642 -0.139097 -0.055353 -0.059752 0 1.160686
3 -0.966272 -0.185226 1.792993 -0.863291 -0.010309 1.247203 0.237609 0.377436 -1.387024 -0.054952 ... -0.108300 0.005274 -0.190321 -1.175575 0.647376 -0.221929 0.062723 0.061458 0 0.140534
4 -1.158233 0.877737 1.548718 0.403034 -0.407193 0.095921 0.592941 -0.270533 0.817739 0.753074 ... -0.009431 0.798278 -0.137458 0.141267 -0.206010 0.502292 0.219422 0.215153 0 -0.073403

5 rows × 30 columns

下采样:

X = data.ix[:, data.columns != 'Class']
y = data.ix[:, data.columns == 'Class'] # Number of data points in the minority class
number_records_fraud = len(data[data.Class == 1])
fraud_indices = np.array(data[data.Class == 1].index) # Picking the indices of the normal classes
normal_indices = data[data.Class == 0].index # Out of the indices we picked, randomly select "x" number (number_records_fraud)
random_normal_indices = np.random.choice(normal_indices, number_records_fraud, replace = False)#随机选择
random_normal_indices = np.array(random_normal_indices) # Appending the 2 indices
under_sample_indices = np.concatenate([fraud_indices,random_normal_indices]) # Under sample dataset下采样
under_sample_data = data.iloc[under_sample_indices,:] X_undersample = under_sample_data.ix[:, under_sample_data.columns != 'Class']
y_undersample = under_sample_data.ix[:, under_sample_data.columns == 'Class'] # Showing ratio
print("Percentage of normal transactions: ", len(under_sample_data[under_sample_data.Class == 0])/len(under_sample_data))
print("Percentage of fraud transactions: ", len(under_sample_data[under_sample_data.Class == 1])/len(under_sample_data))
print("Total number of transactions in resampled data: ", len(under_sample_data))

结果:

Percentage of normal transactions:  0.5
Percentage of fraud transactions: 0.5
Total number of transactions in resampled data: 984

很简单的实现方法,在属于0的数据中,进行随机的选择,就选跟class为1的那类样本一样多就好了,那么现在我们已经得到了两组都是非常少的数据,接下来就可以建模啦!不过在建立任何一个机器学习模型之前不要忘了一个常 规的操作,就是要把数据集切分成训练集和测试集,这样会使得后续验证的结果更为靠谱。

交叉验证:

from sklearn.cross_validation import train_test_split

# Whole dataset
X_train, X_test, y_train, y_test = train_test_split(X,y,test_size = 0.3, random_state = 0)#设置随机种子,可以去掉 print("Number transactions train dataset: ", len(X_train))
print("Number transactions test dataset: ", len(X_test))
print("Total number of transactions: ", len(X_train)+len(X_test)) # Undersampled dataset
X_train_undersample, X_test_undersample, y_train_undersample, y_test_undersample = train_test_split(X_undersample
,y_undersample
,test_size = 0.3
,random_state = 0)
print("")
print("Number transactions train dataset: ", len(X_train_undersample))
print("Number transactions test dataset: ", len(X_test_undersample))
print("Total number of transactions: ", len(X_train_undersample)+len(X_test_undersample))

结果:

Number transactions train dataset:  199364
Number transactions test dataset: 85443
Total number of transactions: 284807 Number transactions train dataset: 688
Number transactions test dataset: 296
Total number of transactions: 984

建模操作:

from sklearn.linear_model import LogisticRegression#逻辑回归
from sklearn.cross_validation import KFold, cross_val_score#K折交叉验证和交叉验证评估结果两个模块
def printing_Kfold_scores(x_train_data,y_train_data):
fold = KFold(len(y_train_data),5,shuffle=False) # Different C parameters
c_param_range = [0.01,0.1,1,10,100]#不同的惩罚力度λ,即正则化惩罚项的系数 results_table = pd.DataFrame(index = range(len(c_param_range),2), columns = ['C_parameter','Mean recall score'])
results_table['C_parameter'] = c_param_range # the k-fold will give 2 lists: train_indices = indices[0], test_indices = indices[1]
j = 0
for c_param in c_param_range:#用不同的正则化系数
print('-------------------------------------------')
print('C parameter: ', c_param)
print('-------------------------------------------')
print('') recall_accs = []
for iteration, indices in enumerate(fold,start=1):#各个验证集循环进行交叉验证 # Call the logistic regression model with a certain C parameter实例化逻辑回归模型
lr = LogisticRegression(C = c_param, penalty = 'l1')#这里选择的L1惩罚,也可以选择L2 # Use the training data to fit the model. In this case, we use the portion of the fold to train the model
# with indices[0]. We then predict on the portion assigned as the 'test cross validation' with indices[1]
lr.fit(x_train_data.iloc[indices[0],:],y_train_data.iloc[indices[0],:].values.ravel()) # Predict values using the test indices in the training data
y_pred_undersample = lr.predict(x_train_data.iloc[indices[1],:].values) # Calculate the recall score and append it to a list for recall scores representing the current c_parameter
recall_acc = recall_score(y_train_data.iloc[indices[1],:].values,y_pred_undersample)
recall_accs.append(recall_acc)
print('Iteration ', iteration,': recall score = ', recall_acc) # The mean value of those recall scores is the metric we want to save and get hold of.
results_table.ix[j,'Mean recall score'] = np.mean(recall_accs)
j += 1
print('')
print('Mean recall score ', np.mean(recall_accs))
print('') best_c = results_table.loc[results_table['Mean recall score'].idxmax()]['C_parameter'] # Finally, we can check which C parameter is the best amongst the chosen.
print('*********************************************************************************')
print('Best model to choose from cross validation is with C parameter = ', best_c)
print('*********************************************************************************') return best_c
best_c = printing_Kfold_scores(X_train_undersample,y_train_undersample)

上述代码中做了一件非常常规的事情,就是对于一个模型,咱们再选择一个算法的时候伴随着很多的参数要调节,那么如何找到最合适的参数可不是一件简单的事,依靠经验值并不是十分靠谱,通常情况下我们需要大量的实验也就是不断去尝试最终得出这些合适的参数。 不同C参数对应的最终模型效果:

-------------------------------------------
C parameter: 0.01
------------------------------------------- Iteration 1 : recall score = 0.958904109589
Iteration 2 : recall score = 0.917808219178
Iteration 3 : recall score = 1.0
Iteration 4 : recall score = 0.972972972973
Iteration 5 : recall score = 0.954545454545 Mean recall score 0.960846151257 -------------------------------------------
C parameter: 0.1
------------------------------------------- Iteration 1 : recall score = 0.835616438356
Iteration 2 : recall score = 0.86301369863
Iteration 3 : recall score = 0.915254237288
Iteration 4 : recall score = 0.932432432432
Iteration 5 : recall score = 0.878787878788 Mean recall score 0.885020937099 -------------------------------------------
C parameter: 1
------------------------------------------- Iteration 1 : recall score = 0.835616438356
Iteration 2 : recall score = 0.86301369863
Iteration 3 : recall score = 0.966101694915
Iteration 4 : recall score = 0.945945945946
Iteration 5 : recall score = 0.893939393939 Mean recall score 0.900923434357 -------------------------------------------
C parameter: 10
------------------------------------------- Iteration 1 : recall score = 0.849315068493
Iteration 2 : recall score = 0.86301369863
Iteration 3 : recall score = 0.966101694915
Iteration 4 : recall score = 0.959459459459
Iteration 5 : recall score = 0.893939393939 Mean recall score 0.906365863087 -------------------------------------------
C parameter: 100
------------------------------------------- Iteration 1 : recall score = 0.86301369863
Iteration 2 : recall score = 0.86301369863
Iteration 3 : recall score = 0.966101694915
Iteration 4 : recall score = 0.959459459459
Iteration 5 : recall score = 0.893939393939 Mean recall score 0.909105589115 *********************************************************************************
Best model to choose from cross validation is with C parameter = 0.01
*********************************************************************************

在使用机器学习算法的时候,很重要的一部就是参数的调节,在这里我们选择使用最经典的分类算法,逻辑回归!千万别把逻辑回归当成是回归算法,它就是最实用的二分类算法!这里我们需要考虑的c参数就是正则化惩罚项的力度,那么如何选择到最好的参数呢?这里我们就需要交叉验证啦,然后用不同的C参数去跑相同的数据,目的就是去看看啥样的C参数能够使得最终模型的效果最好!可以到不同的参数对最终的结果产生的影响还是蛮大的,这里最好的方法就是用验证集去寻找了!

模型评估

模型已经造出来了,那么怎么评判哪个模型好,哪个模型不好呢?我们这里需要好好想一想! 一般都是用精度来衡量,也就是常说的准确率,但是我们来想一想,我们的目的是什么呢?是不是要检测出来那些异常的样本呀!换个例子来说,假如现在医院给了我们一个任务要检测出来1000个病人中,有癌症的那些人。那么假设数据集中1000个人中有990个无癌症,只有10个有癌症,我们需要把这10个人检测出来。假设我们用精度来衡量,那么即便这10个人没检测出来,也是有 990/1000 也就是99%的精度,但是这个模型却没任何价值!这点是非常重要的,因为不同的评估方法会得出不同的答案,一定要根据问题的本质,去选择最合适的评估方法。

所以用召回率,不用精度
#Recall = TP/(TP+FN) 召回率

TP和FN的解释:

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

这里我们采用recall来计算模型的好坏,也就是说那些异常的样本我们的检测到了多少,这也是咱们最初的目的!这里通常用混淆矩阵来展示。

from sklearn.metrics import confusion_matrix,recall_score,classification_report #confusion_matrix指的是混淆矩阵
def plot_confusion_matrix(cm, classes,
title='Confusion matrix',
cmap=plt.cm.Blues):
"""
This function prints and plots the confusion matrix.
"""
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(classes))
plt.xticks(tick_marks, classes, rotation=0)
plt.yticks(tick_marks, classes) thresh = cm.max() / 2.
for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):
plt.text(j, i, cm[i, j],
horizontalalignment="center",
color="white" if cm[i, j] > thresh else "black") plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
import itertools
lr = LogisticRegression(C = best_c, penalty = 'l1')
lr.fit(X_train_undersample,y_train_undersample.values.ravel())
y_pred_undersample = lr.predict(X_test_undersample.values) # Compute confusion matrix
cnf_matrix = confusion_matrix(y_test_undersample,y_pred_undersample)
np.set_printoptions(precision=2) print("Recall metric in the testing dataset: ", cnf_matrix[1,1]/(cnf_matrix[1,0]+cnf_matrix[1,1])) # Plot non-normalized confusion matrix
class_names = [0,1]
plt.figure()
plot_confusion_matrix(cnf_matrix
, classes=class_names
, title='Confusion matrix')
plt.show()

此为下采样数据集得出的结果:

Recall metric in the testing dataset:  0.931972789116
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*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" alt="" />
这个图就非常漂亮了!(并不是说画的好而是展示的很直接)从图中可以清晰的看到原始数据中样本的分布以及我们的模型的预测结果。
从混淆矩阵中可以得到:
  精度=(129+137)/(129+137+20+10);Recall = TP/(TP+FN)=137/(137+10)=0.931972789116
利用混淆矩阵我们可以很直观的考察模型的精度以及recall,也是非常推荐大家在评估模型的时候不妨把这个图亮出来可以帮助咱们很直观的看清楚现在模型的效果以及存在的问题。
lr = LogisticRegression(C = best_c, penalty = 'l1')
lr.fit(X_train_undersample,y_train_undersample.values.ravel())
y_pred = lr.predict(X_test.values) # Compute confusion matrix
cnf_matrix = confusion_matrix(y_test,y_pred)
np.set_printoptions(precision=2) print("Recall metric in the testing dataset: ", cnf_matrix[1,1]/(cnf_matrix[1,0]+cnf_matrix[1,1])) # Plot non-normalized confusion matrix
class_names = [0,1]
plt.figure()
plot_confusion_matrix(cnf_matrix
, classes=class_names
, title='Confusion matrix')
plt.show()

此为原始数据集得出的结果:Recall = TP/(TP+FN)=135/(135+12)=0.918367346939

Recall metric in the testing dataset:  0.918367346939
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" alt="" />

这可还木有完事,我们刚才只是在下采样的数据集中去进行测试的,那么这份测试还不能完全可信,因为它并不是原始的测试集,我们需要在原始的,大量的测试集中再次去衡量当前模型的效果。可以看到效果其实还不错,但是哪块有些问题呢,是不是我们误杀了很多呀,有8581个样本由0误杀成1,有些样本并不是异常的,但是并我们错误的当成了异常的,所以造成精度偏低了,这个现象其实就是下采样策略本身的一个缺陷。另外一个缺陷就是实际中工作量增加,本来只要找135个,缺误杀了8000多个,不能直接去通知8000多个客户吧,这工作量太大了,误杀已经超出了容忍范围。

 
补充:
上边一些列采用了下采样的方法,如果不采用下采样,直接对原始数据进行建模:
best_c = printing_Kfold_scores(X_train,y_train)

结果很差:

-------------------------------------------
C parameter: 0.01
------------------------------------------- Iteration 1 : recall score = 0.492537313433
Iteration 2 : recall score = 0.602739726027
Iteration 3 : recall score = 0.683333333333
Iteration 4 : recall score = 0.569230769231
Iteration 5 : recall score = 0.45 Mean recall score 0.559568228405 -------------------------------------------
C parameter: 0.1
------------------------------------------- Iteration 1 : recall score = 0.567164179104
Iteration 2 : recall score = 0.616438356164
Iteration 3 : recall score = 0.683333333333
Iteration 4 : recall score = 0.584615384615
Iteration 5 : recall score = 0.525 Mean recall score 0.595310250644 -------------------------------------------
C parameter: 1
------------------------------------------- Iteration 1 : recall score = 0.55223880597
Iteration 2 : recall score = 0.616438356164
Iteration 3 : recall score = 0.716666666667
Iteration 4 : recall score = 0.615384615385
Iteration 5 : recall score = 0.5625 Mean recall score 0.612645688837 -------------------------------------------
C parameter: 10
------------------------------------------- Iteration 1 : recall score = 0.55223880597
Iteration 2 : recall score = 0.616438356164
Iteration 3 : recall score = 0.733333333333
Iteration 4 : recall score = 0.615384615385
Iteration 5 : recall score = 0.575 Mean recall score 0.61847902217 -------------------------------------------
C parameter: 100
------------------------------------------- Iteration 1 : recall score = 0.55223880597
Iteration 2 : recall score = 0.616438356164
Iteration 3 : recall score = 0.733333333333
Iteration 4 : recall score = 0.615384615385
Iteration 5 : recall score = 0.575 Mean recall score 0.61847902217 *********************************************************************************
Best model to choose from cross validation is with C parameter = 10.0
*********************************************************************************

逻辑回顾阈值对结果的影响:

对于逻辑回归算法来说,我们还可以指定这样一个阈值,也就是说最终结果的概率是大于多少我们把它当成是正或者负样本。不同的阈值会对结果产生很大的影响。

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

lr = LogisticRegression(C = best_c, penalty = 'l1')
lr.fit(X_train,y_train.values.ravel())
y_pred_undersample = lr.predict(X_test.values) # Compute confusion matrix
cnf_matrix = confusion_matrix(y_test,y_pred_undersample)
np.set_printoptions(precision=2) print("Recall metric in the testing dataset: ", cnf_matrix[1,1]/(cnf_matrix[1,0]+cnf_matrix[1,1])) # Plot non-normalized confusion matrix
class_names = [0,1]
plt.figure()
plot_confusion_matrix(cnf_matrix
, classes=class_names
, title='Confusion matrix')
plt.show()
Recall metric in the testing dataset:  0.619047619048
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" alt="" />
lr = LogisticRegression(C = 0.01, penalty = 'l1')
lr.fit(X_train_undersample,y_train_undersample.values.ravel())
y_pred_undersample_proba = lr.predict_proba(X_test_undersample.values)#由lr.predict变成lr.predict_proba thresholds = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9] plt.figure(figsize=(10,10)) j = 1
for i in thresholds:
y_test_predictions_high_recall = y_pred_undersample_proba[:,1] > i plt.subplot(3,3,j)
j += 1 # Compute confusion matrix
cnf_matrix = confusion_matrix(y_test_undersample,y_test_predictions_high_recall)
np.set_printoptions(precision=2) print("Recall metric in the testing dataset: ", cnf_matrix[1,1]/(cnf_matrix[1,0]+cnf_matrix[1,1])) # Plot non-normalized confusion matrix
class_names = [0,1]
plot_confusion_matrix(cnf_matrix
, classes=class_names
, title='Threshold >= %s'%i)
Recall metric in the testing dataset:  1.0
Recall metric in the testing dataset: 1.0
Recall metric in the testing dataset: 1.0
Recall metric in the testing dataset: 0.986394557823
Recall metric in the testing dataset: 0.931972789116
Recall metric in the testing dataset: 0.884353741497
Recall metric in the testing dataset: 0.836734693878
Recall metric in the testing dataset: 0.748299319728
Recall metric in the testing dataset: 0.571428571429
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*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" alt="" />

上图中我们可以看到不用的阈值产生的影响还是蛮大的,阈值较小,意味着我们的模型非常严格宁肯错杀也不肯放过,这样会使得绝大多数样本都被当成了异常的样本,recall很高,精度稍低 当阈值较大的时候我们的模型就稍微宽松些啦,这个时候会导致recall很低,精度稍高,综上当我们使用逻辑回归算法的时候,还需要根据实际的应用场景来选择一个最恰当的阈值!

过采样:

说完了下采样策略,我们继续唠一下过采样策略,跟下采样相反,现在咱们的策略是要让class为0和1的样本一样多,也就是我们需要去进行数据的生成啦!

机器学习_线性回归和逻辑回归_案例实战:Python实现逻辑回归与梯度下降策略_项目实战:使用逻辑回归判断信用卡欺诈检测

SMOTE算法是用的非常广泛的数据生成策略,流程可以参考上图,还是非常简单的,下面我们使用现成的库来帮助我们完成过采样数据生成策略。

import pandas as pd
from imblearn.over_sampling import SMOTE
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import confusion_matrix
from sklearn.model_selection import train_test_split
credit_cards=pd.read_csv('creditcard.csv')

columns=credit_cards.columns
# The labels are in the last column ('Class'). Simply remove it to obtain features columns
features_columns=columns.delete(len(columns)-1) features=credit_cards[features_columns]
labels=credit_cards['Class']
features_train, features_test, labels_train, labels_test = train_test_split(features,
labels,
test_size=0.2,
random_state=0)
oversampler=SMOTE(random_state=0)
os_features,os_labels=oversampler.fit_sample(features_train,labels_train)#只需要训练集进行过采样,测试集不要动
len(os_labels[os_labels==1])#227454
os_features = pd.DataFrame(os_features)
os_labels = pd.DataFrame(os_labels)
best_c = printing_Kfold_scores(os_features,os_labels)

结果:

-------------------------------------------
C parameter: 0.01
------------------------------------------- Iteration 1 : recall score = 0.890322580645
Iteration 2 : recall score = 0.894736842105
Iteration 3 : recall score = 0.968861347792
Iteration 4 : recall score = 0.957595541926
Iteration 5 : recall score = 0.958430881173 Mean recall score 0.933989438728 -------------------------------------------
C parameter: 0.1
------------------------------------------- Iteration 1 : recall score = 0.890322580645
Iteration 2 : recall score = 0.894736842105
Iteration 3 : recall score = 0.970410534469
Iteration 4 : recall score = 0.959980655302
Iteration 5 : recall score = 0.960178498807 Mean recall score 0.935125822266 -------------------------------------------
C parameter: 1
------------------------------------------- Iteration 1 : recall score = 0.890322580645
Iteration 2 : recall score = 0.894736842105
Iteration 3 : recall score = 0.970454796946
Iteration 4 : recall score = 0.96014552489
Iteration 5 : recall score = 0.960596168431 Mean recall score 0.935251182603 -------------------------------------------
C parameter: 10
------------------------------------------- Iteration 1 : recall score = 0.890322580645
Iteration 2 : recall score = 0.894736842105
Iteration 3 : recall score = 0.97065397809
Iteration 4 : recall score = 0.960343368396
Iteration 5 : recall score = 0.960530220596 Mean recall score 0.935317397966 -------------------------------------------
C parameter: 100
------------------------------------------- Iteration 1 : recall score = 0.890322580645
Iteration 2 : recall score = 0.894736842105
Iteration 3 : recall score = 0.970543321899
Iteration 4 : recall score = 0.960211472725
Iteration 5 : recall score = 0.960903924995 Mean recall score 0.935343628474 *********************************************************************************
Best model to choose from cross validation is with C parameter = 100.0
*********************************************************************************
lr = LogisticRegression(C = best_c, penalty = 'l1')
lr.fit(os_features,os_labels.values.ravel())
y_pred = lr.predict(features_test.values) # Compute confusion matrix
cnf_matrix = confusion_matrix(labels_test,y_pred)
np.set_printoptions(precision=2) print("Recall metric in the testing dataset: ", cnf_matrix[1,1]/(cnf_matrix[1,0]+cnf_matrix[1,1])) # Plot non-normalized confusion matrix
class_names = [0,1]
plt.figure()
plot_confusion_matrix(cnf_matrix
, classes=class_names
, title='Confusion matrix')
plt.show()

结果:

Recall metric in the testing dataset:  0.90099009901
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" alt="" />

过采样,即采用数据生成,recall召回率会相对于下采样低点,但是精度提高,误杀率降低。

我们对比一下下采样和过采样的效果,可以说recall的效果都不错,都可以检测到异常样本,但是下采样是不是误杀的比较少呀,所以如果我们可以进行数据生成,那么在处理样本数据不均衡的情况下,过采样是一个可以尝试的方案!首选也是数据生成策略,因为机器学习就是需要大量数据,数据尽量多,减少过拟合。

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