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  • ") print('=' * 70) # 检测异常值 outlier = data[(data[column] ) | (data[column] >= upper)] return outlier, upper, lower 调用函数 outlier, upper, lower = outlier_test(data=df, column='price', method='z'...

    1、、数据清洗

    1.1、数据缺失,即存在某些数据等于0

    在这里插入图片描述
        解决办法:选中缺失数据的列,然后采用选择菜单:点击数据——筛选,选中数据是0的,点击确定在这里插入图片描述
    然后点击删除行即可以删除数据
    在这里插入图片描述
    同样的操作删除后一列bathroom的缺失值。

    1.2、存在重复数据

        解决办法:excel打开数据集,选中需要处理的数据,然后选择数据——数据工具——删除重复值,在弹出的窗口里利用唯一标识house_id,删除重复值在这里插入图片描述

    1.3、存在非数值性属性

        原始数据中的neighborhood和style为非数值型数据,需要转换成数值型数据才能够进行回归分析。
        解决办法:选中开始——查找和替换——替换
    在这里插入图片描述
    全部替换完成所有A的转换,同理进行B和C以及style的替换
        完成清理之后的数据在这里插入图片描述
    对数据进行保存

    2、多元线性回归代码实现

    2.1、基础包、数据导入

        

    import pandas as pd
    import numpy as np
    import seaborn as sns
    from sklearn import datasets
    from sklearn.linear_model import LinearRegression
    df = pd.read_csv('house_prices.csv')
    df.info()#显示列名和数据类型类型
    df.head(6)#显示前n行,n默认为5
    
    

    导入包并读取导入包读取文件house_prices.csv’数据
    在这里插入图片描述

    2.2、数据处理、探索

        进行数据处理

    # 异常值处理
    # ================ 异常值检验函数:iqr & z分数 两种方法 =========================
    def outlier_test(data, column, method=None, z=2):
        """ 以某列为依据,使用 上下截断点法 检测异常值(索引) """
        """ 
        full_data: 完整数据
        column: full_data 中的指定行,格式 'x' 带引号
        return 可选; outlier: 异常值数据框 
        upper: 上截断点;  lower: 下截断点
        method:检验异常值的方法(可选, 默认的 None 为上下截断点法),
                选 Z 方法时,Z 默认为 2
        """
        # ================== 上下截断点法检验异常值 ==============================
        if method == None:
            print(f'以 {column} 列为依据,使用 上下截断点法(iqr) 检测异常值...')
            print('=' * 70)
            # 四分位点;这里调用函数会存在异常
            column_iqr = np.quantile(data[column], 0.75) - np.quantile(data[column], 0.25)
            # 1,3 分位数
            (q1, q3) = np.quantile(data[column], 0.25), np.quantile(data[column], 0.75)
            # 计算上下截断点
            upper, lower = (q3 + 1.5 * column_iqr), (q1 - 1.5 * column_iqr)
            # 检测异常值
            outlier = data[(data[column] <= lower) | (data[column] >= upper)]
            print(f'第一分位数: {q1}, 第三分位数:{q3}, 四分位极差:{column_iqr}')
            print(f"上截断点:{upper}, 下截断点:{lower}")
            return outlier, upper, lower
        # ===================== Z 分数检验异常值 ==========================
        if method == 'z':
            """ 以某列为依据,传入数据与希望分段的 z 分数点,返回异常值索引与所在数据框 """
            """ 
            params
            data: 完整数据
            column: 指定的检测列
            z: Z分位数, 默认为2,根据 z分数-正态曲线表,可知取左右两端的 2%,
               根据您 z 分数的正负设置。也可以任意更改,知道任意顶端百分比的数据集合
            """
            print(f'以 {column} 列为依据,使用 Z 分数法,z 分位数取 {z} 来检测异常值...')
            print('=' * 70)
            # 计算两个 Z 分数的数值点
            mean, std = np.mean(data[column]), np.std(data[column])
            upper, lower = (mean + z * std), (mean - z * std)
            print(f"取 {z} 个 Z分数:大于 {upper} 或小于 {lower} 的即可被视为异常值。")
            print('=' * 70)
            # 检测异常值
            outlier = data[(data[column] <= lower) | (data[column] >= upper)]
            return outlier, upper, lower
    
    

        调用函数

    outlier, upper, lower = outlier_test(data=df, column='price', method='z')
    outlier.info(); outlier.sample(5)
    

        删除错误数据

    # 这里简单的丢弃即可
    df.drop(index=outlier.index, inplace=True)
    
    

        定义变量进行数据分析

    # 类别变量,又称为名义变量,nominal variables
    nominal_vars = ['neighborhood', 'style']
    
    for each in nominal_vars:
        print(each, ':')
        print(df[each].agg(['value_counts']).T)
        # 直接 .value_counts().T 无法实现下面的效果
         ## 必须得 agg,而且里面的中括号 [] 也不能少
        print('='*35)
        # 发现各类别的数量也都还可以,为下面的方差分析做准备
    
    

    在这里插入图片描述
        调用热力图查看各变量之间的关联性

    # 热力图 
    def heatmap(data, method='pearson', camp='RdYlGn', figsize=(10 ,8)):
        """
        data: 整份数据
        method:默认为 pearson 系数
        camp:默认为:RdYlGn-红黄蓝;YlGnBu-黄绿蓝;Blues/Greens 也是不错的选择
        figsize: 默认为 10,8
        """
        ## 消除斜对角颜色重复的色块
        #     mask = np.zeros_like(df2.corr())
        #     mask[np.tril_indices_from(mask)] = True
        plt.figure(figsize=figsize, dpi= 80)
        sns.heatmap(data.corr(method=method), \
                    xticklabels=data.corr(method=method).columns, \
                    yticklabels=data.corr(method=method).columns, cmap=camp, \
                    center=0, annot=True)
        # 要想实现只是留下对角线一半的效果,括号内的参数可以加上 mask=mask
    
    

        然后调用函数输出结果

    heatmap(data=df, figsize=(6,5))
    
    

        查看其热力图, 通过热力图可以看出 area,bedrooms,bathrooms 等变量与房屋价格 price 的关系都还比较强
    所以值得放入模型,但分类变量 style 与 neighborhood 两者与 price 的关系未知
    在这里插入图片描述

    2.3、模型拟合

        利用回归模型中的方差分析,从线性回归结果中提取方差分析结果
    代码:

        
    import statsmodels.api as sm
    from statsmodels.formula.api import ols # ols 为建立线性回归模型的统计学库
    from statsmodels.stats.anova import anova_lm
    
    

        随机抽取600条数据样本

    df = df.copy().sample(600)
    
    # C 表示告诉 Python 这是分类变量,否则 Python 会当成连续变量使用
    ## 这里直接使用方差分析对所有分类变量进行检验
    ## 下面几行代码便是使用统计学库进行方差分析的标准姿势
    lm = ols('price ~ C(neighborhood) + C(style)', data=df).fit()
    anova_lm(lm)
    
    # Residual 行表示模型不能解释的组内的,其他的是能解释的组间的
    # df: 自由度(n-1)- 分类变量中的类别个数减1
    # sum_sq: 总平方和(SSM),residual行的 sum_eq: SSE
    # mean_sq: msm, residual行的 mean_sq: mse
    # F:F 统计量,查看卡方分布表即可
    # PR(>F): P 值
    
    # 反复刷新几次,发现都很显著,所以这两个变量也挺值得放入模型中
    
    

    得到
    在这里插入图片描述

        建立多元线性回归模型

    from statsmodels.formula.api import ols
    
    lm = ols('price ~ area + bedrooms + bathrooms', data=df).fit()
    lm.summary()
    
    

    在这里插入图片描述

    二、Excel实现多元线性回归,求解回归方程

    在这里插入图片描述

        1、在上图的回归统计子表中,字段Multiple R代表复相关系数R,也就是R2的平方根,又称相关系数,用来衡量自变量x与y之间的相关程度的大小。本次数据集回归分析得到的R=0.818661,这表明x和y之间的关系为高度正相关。R Square是复测定系数,也就是相关系数R的平方。Adjusted R Square是调整后的复测定系数R2,该值为0.670205,说明自变量能说明因变量y的67.02%,因变量y的32.98%要由其他因素来解释。标准误差用来衡量拟合程度的大小,也用于计算与回归相关的其它统计量,此值为306690.576138747,此值越小,而306690.576138747偏大,说明拟合程度不太理想。观察值是用于估计回归方程的数据的观察值个数,本次数据集抽取了前100条数据,所以观察值为100。

        2、设因变量房屋售价为y,自变量房屋编号为x1,自变量街区为x2,自变量卧室面积为x3,自变量总面积为x4,自变量浴室面积为x5,自变量房屋风格为x6,在上图的表中,Coefficients为常数项和X Variable的值,据此便可以估算得出回归方程为:y= 37.1024* x1+ 239.1956* x2+391.3354* x3-19165.5x4+66373.13x5-2231.02*x6-331017。但根据Coefficients估算出的回归方程可能存在较大的误差,在第三张子表中更为重要的一列是P-value列,P-value为回归系数t统计量的P值。由表中P-value的值可以发现,自变量房屋总面积的P值小于显著性水平0.05,因此这个自变量与y相关。浴室面积和卧室面积的P值大于显著性水平0.05,说这两个自变量与y相关性较弱,甚至不存在线性相关关系。

    三、Sklearn库实现多元线性回归,对结果进行对比分析

    3.1、初次线性回归

        导入相关包和没有处理过的数据数据

    import pandas as pd
    import numpy as np
    import seaborn as sns
    from sklearn import datasets
    from sklearn.linear_model import LinearRegression
    df = pd.read_csv('house_prices.csv')
    df.info()#显示列名和数据类型类型
    df.head(7)#显示前7行,默认5行
    
    

    在这里插入图片描述

        实现多元线性回归

    # 读取数据
    data_x=df[['area','bedrooms','bathrooms']]
    data_y=df['price']
    # 进行多元线性回归
    model=LinearRegression()
    l_model=model.fit(data_x,data_y)
    print('回归系数')
    print(model.coef_)
    print('截距')
    print(model.intercept_)
    print('回归方程: Y=(',model.coef_[0],')*x1 +(',model.coef_[1],')*x2 +(',model.coef_[2],')*x3 +(',model.intercept_,')')
    

    在这里插入图片描述

    3.2、数据处理并再次模拟

        进行异常数据处理

    # 异常值处理
    # ================ 异常值检验函数:iqr & z分数 两种方法 =========================
    def outlier_test(data, column, method=None, z=2):
        """ 以某列为依据,使用 上下截断点法 检测异常值(索引) """
        """ 
        full_data: 完整数据
        column: full_data 中的指定行,格式 'x' 带引号
        return 可选; outlier: 异常值数据框 
        upper: 上截断点;  lower: 下截断点
        method:检验异常值的方法(可选, 默认的 None 为上下截断点法),
                选 Z 方法时,Z 默认为 2
        """
        # ================== 上下截断点法检验异常值 ==============================
        if method == None:
            print(f'以 {column} 列为依据,使用 上下截断点法(iqr) 检测异常值...')
            print('=' * 70)
            # 四分位点;这里调用函数会存在异常
            column_iqr = np.quantile(data[column], 0.75) - np.quantile(data[column], 0.25)
            # 1,3 分位数
            (q1, q3) = np.quantile(data[column], 0.25), np.quantile(data[column], 0.75)
            # 计算上下截断点
            upper, lower = (q3 + 1.5 * column_iqr), (q1 - 1.5 * column_iqr)
            # 检测异常值
            outlier = data[(data[column] <= lower) | (data[column] >= upper)]
            print(f'第一分位数: {q1}, 第三分位数:{q3}, 四分位极差:{column_iqr}')
            print(f"上截断点:{upper}, 下截断点:{lower}")
            return outlier, upper, lower
        # ===================== Z 分数检验异常值 ==========================
        if method == 'z':
            """ 以某列为依据,传入数据与希望分段的 z 分数点,返回异常值索引与所在数据框 """
            """ 
            params
            data: 完整数据
            column: 指定的检测列
            z: Z分位数, 默认为2,根据 z分数-正态曲线表,可知取左右两端的 2%,
               根据您 z 分数的正负设置。也可以任意更改,知道任意顶端百分比的数据集合
            """
            print(f'以 {column} 列为依据,使用 Z 分数法,z 分位数取 {z} 来检测异常值...')
            print('=' * 70)
            # 计算两个 Z 分数的数值点
            mean, std = np.mean(data[column]), np.std(data[column])
            upper, lower = (mean + z * std), (mean - z * std)
            print(f"取 {z} 个 Z分数:大于 {upper} 或小于 {lower} 的即可被视为异常值。")
            print('=' * 70)
            # 检测异常值
            outlier = data[(data[column] <= lower) | (data[column] >= upper)]
            return outlier, upper, lower
    outlier, upper, lower = outlier_test(data=df, column='price', method='z')
    outlier.info(); outlier.sample(5)
    # 这里简单的丢弃即可
    df.drop(index=outlier.index, inplace=True)
    
    

    在这里插入图片描述

        再次进行回归模型模拟

    # 读取数据
    data_x=df[['area','bedrooms','bathrooms']]
    data_y=df['price']
    # 进行多元线性回归
    model=LinearRegression()
    l_model=model.fit(data_x,data_y)
    print('回归系数')
    print(model.coef_)
    print('截距')
    print(model.intercept_)
    print('回归方程: Y=(',model.coef_[0],')*x1 +(',model.coef_[1],')*x2 +(',model.coef_[2],')*x3 +(',model.intercept_,')')
    

    在这里插入图片描述

        
        

    参考:回归模型

    展开全文
  • house price

    2020-10-13 17:47:19
    train_data = pd.read_csv('F:/跨媒体计算实验组/NLP/数据集/house price/house-prices-advanced-regression-techniques/train.csv') test_data = pd.read_csv('F:/跨媒体计算实验组/NLP/数据集/house price/house-...

    Kaggle房价预测

    链接:link

    供个人学习复习用

    import pandas as pd
    import numpy as np
    import matplotlib.pyplot as plt
    import seaborn as sns
    from sklearn import ensemble, tree, linear_model
    from sklearn.model_selection import train_test_split, cross_val_score
    from sklearn.metrics import r2_score, mean_squared_error
    from sklearn.utils import shuffle
    
    %matplotlib inline
    import warnings
    warnings.filterwarnings('ignore')
    
    train_data = pd.read_csv('F:/跨媒体计算实验组/NLP/数据集/house price/house-prices-advanced-regression-techniques/train.csv')
    test_data = pd.read_csv('F:/跨媒体计算实验组/NLP/数据集/house price/house-prices-advanced-regression-techniques/test.csv')
    train = train_data.copy()
    test = test_data.copy()
    

    在这里插入图片描述

    train.shape,test.shape
    

    在这里插入图片描述

    #check for dupes for Id
    idsUnique = len(set(train.Id))#set是集合
    idsTotal = train.shape[0]
    #这里是集合过滤重复id,只余下唯一值,然后总数减去唯一值查看不重复的数量
    idsdupe = idsTotal - idsUnique
    print(idsdupe)  #输出是0
    #drop id col
    train.drop(['Id'],axis=1,inplace=True)
    

    进行可视化

    #correlation matrix相关矩阵
    corrmat = train.corr()
    f,ax = plt.subplots(figsize=(20,9))
    sns.heatmap(corrmat,vmax=.8,annot=True)
    

    在这里插入图片描述

    # most correlated features
    corrmat = train.corr()
    top_corr_features = corrmat.index[abs(corrmat['SalePrice'])>0.5]#corrmat.index取出所有特征名,然后取出与特征SalePrice相关性大于0.5的其他特征
    plt.figure(figsize=(10,10))
    g = sns.heatmap(train[top_corr_features].corr(),annot=True,cmap='RdYlGn')#再查看这些特征与特征之间的相关性
    

    在这里插入图片描述

    #我们将在下图中看到OverallQual如何影响销售价格。(因为它与销售价格高度相关)
    sns.barplot(train.OverallQual,train.SalePrice)
    

    在这里插入图片描述

    #下面可以看到每一个特征与销售价格之间的关联
    sns.set()
    cols = ['SalePrice', 'OverallQual', 'GrLivArea', 'GarageCars', 'TotalBsmtSF', 'FullBath', 'YearBuilt']
    sns.pairplot(train[cols],size=2.5)
    plt.show()
    

    在这里插入图片描述
    在这里插入图片描述

    因为最终目的是要预测销售价格,所以下面可以进行对改变量进行分析

    from scipy import stats
    from scipy.stats import norm, skew #for some statistics,norm实现正态分布,skew表示概率分布密度曲线相对于平均值不对称程度的特征数,也即偏度
    #skew直观来看就是密度函数曲线尾部的相对长度
    sns.distplot(train['SalePrice'] , fit=norm);#正态分布曲线拟合图
    #通过函数获取拟合参数(Get the fitted parameters used by the function)
    #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    (mu, sigma) = norm.fit(train['SalePrice'])#返回mu均值,sigma是方差
    print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma))    #{:,2f}是保留两位小数
    plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],
                loc='best')
    plt.ylabel('Frequency')
    plt.title('SalePrice distribution')
    
    fig = plt.figure()
    res = stats.probplot(train['SalePrice'], plot=plt)  #检验样本数据概率分布图(如正态分布(默认))的方法
    plt.show()
    

    在这里插入图片描述

    train.SalePrice = np.log1p(train.SalePrice)#对销售价格进行平滑处理(即将数据压缩到一个区间,逆运算是expm1)
    y = train.SalePrice
    

    在这里插入图片描述

    #进行加工预处理,查看两个特征之间的散点图
    plt.scatter(y=train.SalePrice,x=train.GrLivArea,c='black')
    plt.show()
    

    在这里插入图片描述
    在这里插入图片描述

    train_nas = train.isnull().sum()#计算每个特征的空值总数
    train_nas = train_nas[train_nas>0]#筛选出有空值的特征
    train_nas.sort_values(ascending = False)#按空值数量进行排序
    

    在这里插入图片描述

    #同理对训练集进行相同的操作
    test_nas = test.isnull().sum()
    test_nas = test_nas[test_nas>0]
    test_nas.sort_values(ascending = False)
    

    在这里插入图片描述

    print("Find most important features relative to target")
    corr = train.corr()#得到特征之间的相关性矩阵
    corr.sort_values(['SalePrice'],ascending=False,inplace=True)#按照列(特征)SalePrice进行排序
    print(corr.SalePrice)
    

    在这里插入图片描述

    #区分数字特征(减去目标)和分类特征,Differentiate numerical features (minus the target) and categorical features
    categorical_features = train.select_dtypes(include=['object']).columns#只获取分类特征
    categorical_features
    

    在这里插入图片描述

    numerical_features = train.select_dtypes(exclude = ["object"]).columns#获取非分类特征
    numerical_features
    
    categorical_features = train.select_dtypes(include = ["object"]).columns
    numerical_features = train.select_dtypes(exclude = ["object"]).columns
    numerical_features = numerical_features.drop("SalePrice")#非分类特征中删去目标值(销售价格)
    print("Numerical features : " + str(len(numerical_features)))
    print("Categorical features : " + str(len(categorical_features)))
    train_num = train[numerical_features]
    train_cat = train[categorical_features]
    

    在这里插入图片描述

    #使用mean()来填充na值,实际上在进行特征工程时有很多需要探索的地方。
    #NOTE: i simply used median() to fill na values, actually there is lot to explore when you do feature engineering. But this notebook aim is to simplify things(no heavy code)

    ## Handle remaining missing values for numerical features by using median as replacement
    #使用中位数来填充处理数值特征缺失的部分
    print('NAs for numerical features in train:' + str(train_num.isnull().values.sum()))
    train_num = train_num.fillna(train_num.median())
    print('Remaining NAs for numerical features in train:'+str(train_num.isnull().values.sum()))
    
    

    在这里插入图片描述

    from scipy.stats import skew
    skewness = train_num.apply(lambda x:skew(x))#遍历每一列,将每一列都调用匿名函数
    skewness.sort_values(ascending=False)
    

    在这里插入图片描述

    skewness = skewness[abs(skewness)>0.5]
    skewness.index#取dataframe的特征名,---没有复制过来图片
    
    skew_features = train[skewness.index]#从训练集中选出已经挑选出的特征,(它们是非分类型特征且这些特征之间的不对称度大于0.5)
    skew_features.columns
    

    在这里插入图片描述

    #we can treat skewness of a feature with the help fof log transformation.so we'll apply the same here.
    #借助对数转换来处理特征的偏斜度,因此我们将在此处应用相同的偏度。
    skew_features = np.log1p(skew_features)  #将目标矩阵skew_features中的值全部取对数
    train_cat.head()
    

    在这里插入图片描述

    str(train_cat.isnull().values.sum())#查看非分类特征中有无空值---0
    

    下面开始进行模型

    import pandas as pd
    import numpy as np
    from sklearn.model_selection import cross_val_score, train_test_split
    from sklearn.preprocessing import StandardScaler
    from sklearn.linear_model import LinearRegression, RidgeCV, LassoCV, ElasticNetCV
    from sklearn.metrics import mean_squared_error, make_scorer #metrics 是指标,make_scorer从性能指标或损失函数中创建一个计分标准
    import matplotlib.pyplot as plt
    import seaborn as sns
    
    train = pd.concat([train_cat,train_num],axis=1)#将预处理的训练集合并(原本分为了分类集和非分类集,用来预处理)
    X_train,X_test,y_train,y_test = train_test_split(train,y,test_size = 0.3,random_state= 0)
    
    
    #用交叉验证集分布检测训练集和测试集
    n_folds = 5
    from sklearn.metrics import make_scorer
    from sklearn.model_selection import KFold#K折交叉验证
    scorer = make_scorer(mean_squared_error,greater_is_better = False)
    def rmse_CV_train(model):
        kf = KFold(n_folds,shuffle=True,random_state=42).get_n_splits(train.values)#在K折交叉验证中将训练集再次划分
        rmse = np.sqrt(-cross_val_score(model,X_train,y_train,scoring ="neg_mean_squared_error",cv=kf))
        return (rmse)
    def rmse_CV_test(model):
        kf = KFold(n_folds,shuffle=True,random_state=42).get_n_splits(train.values)
        rmse = np.sqrt(-cross_val_score(model,X_test,y_test,scoring ="neg_mean_squared_error",cv=kf))
        return (rmse)
    
    #Linear model without Regularization
    lr = LinearRegression()
    lr.fit(X_train,y_train)
    test_pre = lr.predict(X_test)
    train_pre = lr.predict(X_train)
    print('rmse on train',rmse_CV_train(lr).mean())
    print('rmse on train',rmse_CV_test(lr).mean())
    

    在这里插入图片描述

    #plot between predicted values and residuals
    plt.scatter(train_pre, train_pre - y_train, c = "blue",  label = "Training data")#残差即预测值与真实值之间的差异
    plt.scatter(test_pre,test_pre - y_test, c = "black",  label = "Validation data")
    plt.title("Linear regression")
    plt.xlabel("Predicted values")
    plt.ylabel("Residuals")
    plt.legend(loc = "upper left")
    plt.hlines(y = 0, xmin = 10.5, xmax = 13.5, color = "red")
    plt.show()
    

    在这里插入图片描述

    # Plot predictions - Real values绘画真实值和预测值散点图
    plt.scatter(train_pre, y_train, c = "blue",  label = "Training data")
    plt.scatter(test_pre, y_test, c = "black",  label = "Validation data")
    plt.title("Linear regression")
    plt.xlabel("Predicted values")
    plt.ylabel("Real values")
    plt.legend(loc = "upper left")
    plt.plot([10.5, 13.5], [10.5, 13.5], c = "red")
    plt.show()
    

    在这里插入图片描述

    正则化是处理共线性,从数据中滤除噪声并最终防止过度拟合的非常有用的方法。
    正则化背后的概念是引入附加信息(偏差)以惩罚极端参数权重。

    Regularization is a very useful method to handle collinearity, filter out noise from data, and eventually prevent overfitting.
    The concept behind regularization is to introduce additional information (bias) to penalize extreme parameter weights.
    在这里插入图片描述

    #RidgeCV内置交叉验证的岭回归,默认情况下,它执行通用的交叉验证,这是一种有效的留一交叉验证的形式。alpha是正则化的力度
    #Ridge:固定阿尔法,求出最佳w,阿尔法与w的范数成反比,
    #RidgeCV:多个阿尔法,得出多个对应最佳的w,然后得到最佳的w及对应的阿尔法
    ridge = RidgeCV(alphas = [0.01, 0.03, 0.06, 0.1, 0.3, 0.6, 1, 3, 6, 10, 30, 60])
    
    ridge.fit(X_train,y_train)
    alpha = ridge.alpha_#一轮下来得到最好的alpha
    print('best alpha',alpha)
    
    print("Try again for more precision with alphas centered around " + str(alpha))
    ridge = RidgeCV(alphas = [alpha * .6, alpha * .65, alpha * .7, alpha * .75, alpha * .8, alpha * .85, 
                              alpha * .9, alpha * .95, alpha, alpha * 1.05, alpha * 1.1, alpha * 1.15,
                              alpha * 1.25, alpha * 1.3, alpha * 1.35, alpha * 1.4],cv = 5)
    ridge.fit(X_train, y_train)
    alpha = ridge.alpha_
    print("Best alpha :", alpha)
    print("Ridge RMSE on Training set :", rmse_CV_train(ridge).mean())#K折交叉验证结果的均值
    print("Ridge RMSE on Test set :", rmse_CV_test(ridge).mean())
    y_train_rdg = ridge.predict(X_train)#岭回归的返回分数
    y_test_rdg = ridge.predict(X_test)
    

    在这里插入图片描述

    print("Kcv RMSE on Training set :", y_train_rdg.mean())#K折交叉验证结果的均值
    print("Kcv RMSE on Test set :", y_test_rdg.mean())
    

    在这里插入图片描述

    coef = pd.Series(ridge.coef_, index = X_train.columns)
    
    print("Ridge picked " + str(sum(coef != 0)) + " variables and eliminated the other " +  str(sum(coef == 0)) + " variables")
    

    在这里插入图片描述

    # Plot residuals
    plt.scatter(y_train_rdg, y_train_rdg - y_train, c = "blue",  label = "Training data")
    plt.scatter(y_test_rdg, y_test_rdg - y_test, c = "black", marker = "v", label = "Validation data")
    plt.title("Linear regression with Ridge regularization")
    plt.xlabel("Predicted values")
    plt.ylabel("Residuals")
    plt.legend(loc = "upper left")
    plt.hlines(y = 0, xmin = 10.5, xmax = 13.5, color = "red")
    plt.show()
    

    在这里插入图片描述

    # Plot predictions - Real values
    plt.scatter(y_train_rdg, y_train, c = "blue",  label = "Training data")
    plt.scatter(y_test_rdg, y_test, c = "black",  label = "Validation data")
    plt.title("Linear regression with Ridge regularization")
    plt.xlabel("Predicted values")
    plt.ylabel("Real values")
    plt.legend(loc = "upper left")
    plt.plot([10.5, 13.5], [10.5, 13.5], c = "red")
    plt.show()
    

    在这里插入图片描述

    展开全文
  • In this exercise, you'll work on the "Happy House" problem, which we'll explain below. Let's load the required packages and solve the problem of the Happy House! 目录 1 - The Happy House 2 ...

    本文节选自吴恩达老师《深度学习专项课程》编程作业,在此表示感谢。

    课程链接:https://www.deeplearning.ai/deep-learning-specialization/

    Welcome to the first assignment of week 2. In this assignment, you will:

    1. Learn to use Keras, a high-level neural networks API (programming framework), written in Python and capable of running on top of several lower-level frameworks including TensorFlow and CNTK.
    2. See how you can in a couple of hours build a deep learning algorithm.

    Why are we using Keras? Keras was developed to enable deep learning engineers to build and experiment with different models very quickly. Just as TensorFlow is a higher-level framework than Python, Keras is an even higher-level framework and provides additional abstractions. Being able to go from idea to result with the least possible delay is key to finding good models. However, Keras is more restrictive than the lower-level frameworks, so there are some very complex models that you can implement in TensorFlow but not (without more difficulty) in Keras. That being said, Keras will work fine for many common models.

    In this exercise, you'll work on the "Happy House" problem, which we'll explain below. Let's load the required packages and solve the problem of the Happy House!

    目录

    1 - The Happy House

    2 - Building a model in Keras

    3 - Conclusion

    4 - Other useful functions in Keras


    import numpy as np
    #import tensorflow as tf
    from keras import layers
    from keras.layers import Input, Dense, Activation, ZeroPadding2D, BatchNormalization, Flatten, Conv2D
    from keras.layers import AveragePooling2D, MaxPooling2D, Dropout, GlobalMaxPooling2D, GlobalAveragePooling2D
    from keras.models import Model
    from keras.preprocessing import image
    from keras.utils import layer_utils
    from keras.utils.data_utils import get_file
    from keras.applications.imagenet_utils import preprocess_input
    import pydot
    from IPython.display import SVG
    from keras.utils.vis_utils import model_to_dot
    from keras.utils import plot_model
    from kt_utils import *
    
    import keras.backend as K
    K.set_image_data_format('channels_last')
    import matplotlib.pyplot as plt
    from matplotlib.pyplot import imshow
    
    %matplotlib inline

    Note: As you can see, we've imported a lot of functions from Keras. You can use them easily just by calling them directly in the notebook. Ex: X = Input(...) or X = ZeroPadding2D(...).


    1 - The Happy House

    For your next vacation, you decided to spend a week with five of your friends from school. It is a very convenient house with many things to do nearby. But the most important benefit is that everybody has commited to be happy when they are in the house. So anyone wanting to enter the house must prove their current state of happiness.

    As a deep learning expert, to make sure the "Happy" rule is strictly applied, you are going to build an algorithm which that uses pictures from the front door camera to check if the person is happy or not. The door should open only if the person is happy.

    You have gathered pictures of your friends and yourself, taken by the front-door camera. The dataset is labbeled.

    X_train_orig, Y_train_orig, X_test_orig, Y_test_orig, classes = load_dataset()
    
    # Normalize image vectors
    X_train = X_train_orig/255.
    X_test = X_test_orig/255.
    
    # Reshape
    Y_train = Y_train_orig.T
    Y_test = Y_test_orig.T
    
    print ("number of training examples = " + str(X_train.shape[0]))
    print ("number of test examples = " + str(X_test.shape[0]))
    print ("X_train shape: " + str(X_train.shape))
    print ("Y_train shape: " + str(Y_train.shape))
    print ("X_test shape: " + str(X_test.shape))
    print ("Y_test shape: " + str(Y_test.shape))

    2 - Building a model in Keras

    Keras is very good for rapid prototyping. In just a short time you will be able to build a model that achieves outstanding results.

    Here is an example of a model in Keras:

    def model(input_shape):
        # Define the input placeholder as a tensor with shape input_shape. Think of this as your input image!
        X_input = Input(input_shape)
    
        # Zero-Padding: pads the border of X_input with zeroes
        X = ZeroPadding2D((3, 3))(X_input)
    
        # CONV -> BN -> RELU Block applied to X
        X = Conv2D(32, (7, 7), strides = (1, 1), name = 'conv0')(X)
        X = BatchNormalization(axis = 3, name = 'bn0')(X)
        X = Activation('relu')(X)
    
        # MAXPOOL
        X = MaxPooling2D((2, 2), name='max_pool')(X)
    
        # FLATTEN X (means convert it to a vector) + FULLYCONNECTED
        X = Flatten()(X)
        X = Dense(1, activation='sigmoid', name='fc')(X)
    
        # Create model. This creates your Keras model instance, you'll use this instance to train/test the model.
        model = Model(inputs = X_input, outputs = X, name='HappyModel')
    
        return model

    Note that Keras uses a different convention with variable names than we've previously used with numpy and TensorFlow. In particular, rather than creating and assigning a new variable on each step of forward propagation such as X, Z1, A1, Z2, A2, etc. for the computations for the different layers, in Keras code each line above just reassigns X to a new value using X = .... In other words, during each step of forward propagation, we are just writing the latest value in the commputation into the same variable X. The only exception was X_input, which we kept separate and did not overwrite, since we needed it at the end to create the Keras model instance (model = Model(inputs = X_input, ...) above).

    Exercise: Implement a HappyModel(). This assignment is more open-ended than most. We suggest that you start by implementing a model using the architecture we suggest, and run through the rest of this assignment using that as your initial model. But after that, come back and take initiative to try out other model architectures. For example, you might take inspiration from the model above, but then vary the network architecture and hyperparameters however you wish. You can also use other functions such as AveragePooling2D(), GlobalMaxPooling2D(), Dropout().

    Note: You have to be careful with your data's shapes. Use what you've learned in the videos to make sure your convolutional, pooling and fully-connected layers are adapted to the volumes you're applying it to.

    def HappyModel(input_shape):
        """
        Implementation of the HappyModel.
        
        Arguments:
        input_shape -- shape of the images of the dataset
    
        Returns:
        model -- a Model() instance in Keras
        """
        
       
        # Feel free to use the suggested outline in the text above to get started, and run through the whole
        # exercise (including the later portions of this notebook) once. The come back also try out other
        # network architectures as well. 
       
        X_input = Input(input_shape)
    
        X = ZeroPadding2D((1,1))(X_input)
        x = Conv2D(8, (3,3), strides=(1,1))(X)
        X = BatchNormalization(axis=3)(X)
        X = Activation('relu')(X)
        X = MaxPooling2D(pool_size=(2,2), strides=(2,2), padding='valid')(X)
        
        X = ZeroPadding2D(padding=(1, 1))(X)
        X = Conv2D(16, kernel_size=(3,3), strides=(1,1))(X)
        X = BatchNormalization(axis=3)(X)
        X = Activation('relu')(X)
        X = MaxPooling2D(pool_size=(2,2), strides=(2,2), padding='valid')(X)
        
        X = ZeroPadding2D(padding=(1, 1))(X)
        X = Conv2D(32, kernel_size=(3,3), strides=(1,1))(X)
        X = BatchNormalization(axis=3)(X)
        X = Activation('relu')(X)
        X = MaxPooling2D(pool_size=(2,2), strides=(2,2), padding='valid')(X)
        
        # FC
        X = Flatten()(X)
        Y = Dense(1, activation='sigmoid')(X)
        
        model = Model(inputs = X_input, outputs = Y, name='HappyModel')
        
        return model

    You have now built a function to describe your model. To train and test this model, there are four steps in Keras:

    1. Create the model by calling the function above
    2. Compile the model by calling model.compile(optimizer = "...", loss = "...", metrics = ["accuracy"])
    3. Train the model on train data by calling model.fit(x = ..., y = ..., epochs = ..., batch_size = ...)
    4. Test the model on test data by calling model.evaluate(x = ..., y = ...)

    If you want to know more about model.compile(), model.fit(), model.evaluate() and their arguments, refer to the official Keras documentation.

    Exercise: Implement step 1, i.e. create the model.

    happyModel = HappyModel((64,64,3))
    

    Exercise: Implement step 2, i.e. compile the model to configure the learning process. Choose the 3 arguments of compile() wisely. Hint: the Happy Challenge is a binary classification problem.

    import keras
    
    happyModel.compile(optimizer=keras.optimizers.Adam(lr=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-08, decay=0.0), loss='binary_crossentropy', metrics=['accuracy'])
    

    Exercise: Implement step 3, i.e. train the model. Choose the number of epochs and the batch size.

    happyModel.fit(x=X_train, y=Y_train, batch_size=16, epochs=20)
    
    preds = happyModel.evaluate(x=X_test, y=Y_test)
    
    print()
    print ("Loss = " + str(preds[0]))
    print ("Test Accuracy = " + str(preds[1]))

    If your happyModel() function worked, you should have observed much better than random-guessing (50%) accuracy on the train and test sets. To pass this assignment, you have to get at least 75% accuracy.

    To give you a point of comparison, our model gets around 95% test accuracy in 40 epochs (and 99% train accuracy) with a mini batch size of 16 and "adam" optimizer. But our model gets decent accuracy after just 2-5 epochs, so if you're comparing different models you can also train a variety of models on just a few epochs and see how they compare.

    If you have not yet achieved 75% accuracy, here're some things you can play around with to try to achieve it:

    • Try using blocks of CONV->BATCHNORM->RELU such as:
      X = Conv2D(32, (3, 3), strides = (1, 1), name = 'conv0')(X)
      X = BatchNormalization(axis = 3, name = 'bn0')(X)
      X = Activation('relu')(X)
      until your height and width dimensions are quite low and your number of channels quite large (≈32 for example). You are encoding useful information in a volume with a lot of channels. You can then flatten the volume and use a fully-connected layer.
    • You can use MAXPOOL after such blocks. It will help you lower the dimension in height and width.
    • Change your optimizer. We find Adam works well.
    • If the model is struggling to run and you get memory issues, lower your batch_size (12 is usually a good compromise)
    • Run on more epochs, until you see the train accuracy plateauing.

    Even if you have achieved 75% accuracy, please feel free to keep playing with your model to try to get even better results.

    Note: If you perform hyperparameter tuning on your model, the test set actually becomes a dev set, and your model might end up overfitting to the test (dev) set. But just for the purpose of this assignment, we won't worry about that here.


    3 - Conclusion

    Congratulations, you have solved the Happy House challenge!

    Now, you just need to link this model to the front-door camera of your house. We unfortunately won't go into the details of how to do that here.

    **What we would like you to remember from this assignment:** - Keras is a tool we recommend for rapid prototyping. It allows you to quickly try out different model architectures. Are there any applications of deep learning to your daily life that you'd like to implement using Keras? - Remember how to code a model in Keras and the four steps leading to the evaluation of your model on the test set. Create->Compile->Fit/Train->Evaluate/Test.


    4 - Other useful functions in Keras

    wo other basic features of Keras that you'll find useful are:

    • model.summary(): prints the details of your layers in a table with the sizes of its inputs/outputs
    • plot_model(): plots your graph in a nice layout. You can even save it as ".png" using SVG() if you'd like to share it on social media ;). It is saved in "File" then "Open..." in the upper bar of the notebook.

    Run the following code.

    happyModel.summary()
    
    plot_model(happyModel, to_file='HappyModel.png')
    SVG(model_to_dot(happyModel).create(prog='dot', format='svg'))

     

    展开全文
  • 综述house of spirit是一种常用的堆溢出技术,而在如今的malloc实现中依然没有对这种方法进行保护,所以在目前还是一种有效的堆溢出技术。下面我们先从这种方法的来源之本讲起,即2005 Malloc Maleficarumcsdn原文 ...

    综述

    house of spirit是一种常用的堆溢出技术,而在如今的malloc实现中依然没有对这种方法进行保护,所以在目前还是一种有效的堆溢出技术。下面我们先从这种方法的来源之本讲起,即2005 Malloc Maleficarum

    原文

     The House of Spirit
    
    The House of Spirit is primarily interesting because of the nature
    of the circumstances leading to its application. It is the only
    House in the Malloc Maleficarum that can be used to leverage both a
    heap and stack overflow. This is because the first step is not to
    control the header information of a chunk, but to control a pointer
    that is passed to free(). Whether this pointer is on the heap or
    not is largely irrelevant.
    
    The general idea involves overwriting a pointer that was previously
    returned by a call to malloc(), and that is subsequently passed to
    free(). This can lead to the linking of an arbitrary address into a
    fastbin. A further call to malloc() can result in this arbitrary
    address being used as a chunk of memory by the application. If the
    designer can control the applications use of the fake chunk, then
    it is possible to overwrite execution control data.
    
    Assume that the designer has overflowed a pointer that is being
    passed to free(). The first problem that must be considered is
    exactly what the pointer should be overflowed with. Keep in mind
    that the ultimate goal of the House of Spirit is to allow the
    designer to overwrite some sort of execution control data by
    returning an arbitrary chunk to the application. Exactly what
    "execution control data" is doesn't particularly matter so long as
    overflowing it can result in execution being passed to a designer
    controlled memory location. The two most common examples that are
    suitable for use with the House of Spirit are function pointers and
    pending saved return addresses, which will herein be referred to as
    the "target".
    
    In order to successfully apply the House of Spirit it is necessary
    to have a designer controlled word value at a lower address than
    the target. This word will correspond to the size field of the
    chunk header for the fakechunk passed to free(). This means that
    the overflowed pointer must be set to the address of the designer
    controlled word plus 4. Furthermore, the size of the fakechunk must
    be must be located no more than 64 bytes away from the target. This
    is because the default maximum data size for a fastbin entry is 64,
    and at least the last 4 bytes of data are required to overwrite the
    target.
    
    There is one more requirement for the layout of the fakechunk data
    which will be described shortly. For the moment, assume that all of
    the above conditions have been met, and that a call to free() is
    made on the suitable fakechunk. A call to free() is handled by a
    wrapper function called public_fREe():
    
    void
    public_fREe(Void_t* mem)
    {
        mstate ar_ptr;
        mchunkptr p;          /* chunk corresponding to mem */
        ...
        p = mem2chunk(mem);
        if (chunk_is_mmapped(p))
        {
          munmap_chunk(p);
          return;
        }
        ...
        ar_ptr = arena_for_chunk(p);
        ...
        _int_free(ar_ptr, mem);
    
    In this situation mem is the value that was originally overflowed
    to point to a fakechunk. This is converted to the "corresponding
    chunk" of the fakechunk's data, and passed to arena_for_chunk() in
    order to find the corresponding arena. In order to avoid special
    treatment as an mmap() chunk, and also to get a sensible arena, the
    size field of the fakechunk header must have the IS_MMAPPED and
    NON_MAIN_ARENA bits cleared. To do this, the designer can simply
    ensure that the fake size is a multiple of 8. This would mean the
    internal function _int_free() is reached:
    
    void_int_free(mstate av, Void_t* mem){
        mchunkptr       p;           /* chunk corresponding to mem */
        INTERNAL_SIZE_T size;        /* its size */
        mfastbinptr*    fb;          /* associated fastbin */
        ...
        p = mem2chunk(mem);
        size = chunksize(p);
        ...
        if ((unsigned long)(size) <= (unsigned long)(av->max_fast))
        {
          if (chunk_at_offset (p, size)->size <= 2 * SIZE_SZ
              || __builtin_expect (chunksize (chunk_at_offset (p, size))
                                              >= av->system_mem, 0))
            {
              errstr = "free(): invalid next size (fast)";
              goto errout;
            }
          ...
          fb = &(av->fastbins[fastbin_index(size)]);
          ...
          p->fd = *fb;
          *fb = p;
        }
    
    This is all of the code in free() that concerns the House of
    Spirit. The designer controlled value of mem is again converted to
    a chunk and the fake size value is extracted. Since size is
    designer controlled, the fastbin code can be triggered simply by
    ensuring that it is less than av->max_fast, which has a default of
    64 + 8. The final point of consideration in the layout of the
    fakechunk is the nextsize integrity tests.
    
    Since the size of the fakechunk has to be large enough to encompass
    the target, the size of the nextchunk must be at an address higher
    than the target. The nextsize integrity tests must be handled for
    the fakechunk to be put in a fastbin, which means that there must
    be yet another designer controlled value at an address higher than
    the target.
    
    The exact location of the designer controlled values directly
    depend on the size of the allocation request that will subsequently
    be used by the designer to overwrite the target. That is, if an
    allocation request of N bytes is made (such that N <= 64), then the
    designer's lower value must be within N bytes of the target and
    must be equal to (N + 8). This is to ensure that the fakechunk is
    put in the right fastbin for the subsequent allocation request.
    Furthermore, the designer's upper value must be at (N + 8) bytes
    above the lower value to ensure that the nextsize integrity tests
    are passed.
    
    If such a memory layout can be achieved, then the address of this
    "structure" will be placed in a fastbin. The code for the
    subsequent malloc() request that uses this arbitrary fastbin entry
    is simple and need not be reproduced here. As far as _int_malloc()
    is concerned the fake chunk that it is preparing to return to the
    application is perfectly valid. Once this has occurred it is simply
    up to the designer to manipulate the application in to overwriting
    the target.

    翻译

    house of spirit因为其应用情况受到广泛关注,他是这篇文章中提到方法里,唯一一种同时可以利用堆和栈溢出的方法。这是因为他第一步不是去控制一个chunk的头信息,而是去控制一个传给free函数的指针,至于这个指针是不是在堆上并没有太大的关系。

    他的中心思想主要是重写一个之前由malloc分配然后被放进free里的一个指针,这就会导致一个任意地址被链接进fastbin。之后的某个malloc调用可以导致这个任意地址被分配作为一个chunk,如果攻击者可以控制这个fake chunk的应用,那么就有机会可以重写关于执行控制的数据。

    假设攻击者溢出了一个被放入free调用的指针,需要考虑的第一个问题是用什么来溢出后填充这个指针。需记住的是house of spirit的最终目的是允许攻击者通过返回给这个应用一个任意位置的chunk来重写某些执行控制数据,至于执行控制数据具体是什么并不是太重要只要溢出它能够导致攻击者想要的执行内容被传送到攻击者控制的内存地址。两个最为常见最为适合用house of spirit的例子的指针是函数指针和存储的返回地址,
    这里我们把他们称作“目标”。

    为了成功应用house of spirit,攻击者必须要求能够控制低于目标的地址的一个字值(word value),这个字(word)将会和被放进free的fake chunk的头的size域对应。这意味着被溢出的指针将会被设置为攻击者控制的字的地址再加上4,以及fake chunk必须离目标不到64字节。这是因为fastbin的默认块大小是64,而至少我们需要最后4个字节来重写目标。

    另外,对于fake chunk的数据分布还有一个要求,我们马上将会讲到。现在我们就先假设之前提到的所有要求都已经被满足了,然后一个对free的调用将会在合适的fake chunk上应用。一个对free的调用将会被一个包装函数,名为public_fREe处理:

    void 
    public_fRE(Void_t* mem)
    {
        mstate ar_ptr;
        mchunkptr p; // mem相应的chunk
        ...
        p = mem2chunk(mem);
        if (chunk_is_mmapped(p))
        {
            munmap_chunk(p);
            return;
        }
        ...
        ar_ptr = arena_for_chunk(p);
        ...
        _int_free(ar_ptr, mem);
    }

    在这种情况下,mem是之前已经被溢出并使得指向fake chunk的一个值,然后被转换为fake chunk相应的chunk指针,然后被传仅arena_for_chunk来找到相应的arena,为了避免对于mmap chunk的特殊处理,以及为了得到一个有用的arena,fake chunk头的size域的IS_MMAPPED和NON_MAIN_ARENA位必须为0. 为了做到这个,攻击者只需要确认fake 的size是8的倍数就可以了。这样的话,_int_free函数就会被调用了:

    void _int_free(mstate av, Void_t* mem)
    {
        mchunkptr p; // mem相应的chunk
        INTERNAL_SIZE_T size; //size,大小
        mfastbinptr* fb; //联系的fast bin
        ...
        p = mem2chunk(mem);
        size = chunksize(p);
        ...
        if ((unsigned long)(size) <= (unsigned long)(av->max_fast))
        {
            if (chunk_at_offset(p, size)->size <= 2 * SIZE_SZ
                || __builtin_expect(chunksize(chunk_at_offset(p, size))
                                                >= av->system_mem, 0))
            {
                errstr = "free(): invalid next size (fast)";
                goto errout;
            }
            ...
            fb = &(av->fastbins[fastbin_index(size)]);
            ...
            p->fd = *fb;
            *fb = p;
        }
    }

    这里是free对于使用house of spirit所需要了解的全部代码了。攻击者控制的mem值再次被转换为chunk指针,然后fake的size值被提取出来。因为size已经是攻击者控制的了,只需要保证这个值小于av->max_fast,fastbin的代码就会被执行了,这里,av->max_fast的默认值为64+8。最后fake chunk的布局需要考虑的是如何通过nextsize正确性的检测。

    因为fake chunk的大小必须要足够大才能包裹住目标,所以nextchunk的size的地址必须高于目标。为了能够使得fake chunk被放进fastbin,nextsize一正确性检验必须被处理一下,这就意味着必须有另外一个攻击者控制的值在高于目标的地址出现。

    攻击者控制的值的具体位置依赖于将被用来重写目标的分配请求的大小,这就是说,如果一个分配请求了N个字节(N <= 64),那么这个攻击者可以控制的低于这个目标地址的值必须在离目标的N 字节以内,并且必须等于N + 8。这是为了保证fake chunk被放在了之后分配请求所需要的正确的fastbin里。另外,攻击者能控制的另外一个,高于目标地址的值必须比低于的那个值的地址高出(N + 8)字节来保证nextsize的正确性检测可以通过。

    如果满足了这样一个内存布局,那么这个结构的地址将会被放进fastbin里。其后对于这个已经被控制的fastbin块的malloc请求的代码非常简单,这里就不再给出了。只要_int_malloc被调用,那么这个准备被返回的fake chunk就是有效的。只要这种情况发生了,那么操纵应用来重写目标就非常简单了。

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