【udacity】机器学习-2模型验证

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1、模型的评估与验证简介

机器学习通常是大量传入数据,然后会有一些关于数据的决策、想法和摘要。

2、模型评估

评估模型使用的是各种数据分析的方法,至少需要使用python编程和一些统计学的知识

9、用一个数据描述数据

通常情况下可以使用一个数字来对整个数据集进行描述

10、选择哪个数字

一般情况下,我们使用众数来对整个数据集的大多数来描述

12、众数-负偏斜分布

14、众数的更多信息!

  • 众数是否可用于描述任何数据类型,数值型和类别型都可以?
  • 数据集中的所有分支都会影响众数,是对还是错?
  • 如果有一个总体,我们从中取出了很多样本,找到的每个样本的众数将会相同
  • 众数有公式

17、找出均值

与众数不同,平均值将会在全部数值考虑在内,因为我们将其累加起来,然后除以数值的个数

18、找出均值的步骤

求和->找到个数相除

19、迭代过程

20、有用的符号

μ=x=nx

21、均值的特性

  • 分布中的所有得分都将影响平均值
  • 平均值可以用公式来描述,
  • 同一个总体中有很多样本会有相似的平均值
  • 一个样本的平均值可以用来推论其所在的总体,
  • 向数据集中添加一个极值,则平均值会发生改变

22、含异常值的均值

含有异常值的均值将会影响到数据的表达,异常值的数据使得均值不能准确的判断出来

25、中位数的要求

中位数的出现需要将数据进行排序,然后取其中间值

26、含有异常值的中位数

对于含有异常值的数据集, 中位数即使偏离了数据基准也不会受很大的影响
中位数往往更能后反应数据的集中趋势

 

36、小结-中心测量值

数据类型 是否具有简单的等式 是否随数据值的变化而改变 是否不受组距改变的影响 受异常值影响是否巨大 在直方图中是否容易体现
Mean yes yes yes yes no
Median no no yes yes no
Mode no no no yes yes

41、量化数据的分布形态

range=max(x)min(x)

方差(Variance):

σ2=n11i=1n(xix)2

标准差(StandardDeviation):

σ=(n11i=1n(xix)2)

平均绝对偏差(MeanAbsoluteDeviation):

MAD=n1i=1n(xix)

42、值域是否改变

值域有时候会改变,当我们将数值在中间加入大量数据的时候不会发生改变,但是在高于最大值或其他地方的时候,值域就会发生改变。值域在有异常值是增大了差异性。值域不可能准确的代表数据的差异性。

44、砍掉尾巴

一般的处理值域的方式就是砍掉头和尾,然后只考虑中间的数据值
一般习惯上会忽略较低的25%和较高的25%

47、IQR(interquartile range)

四分位差(Q3-Q1)

  • 约50%的数据属于IQR
  • IQR要受到数据集中每个值的影响
  • QR不受异常值的影响

49、什么是异常值

50、定义异常值

异常值定义:小于第一个四分位数-1.5倍的IQR
异常值定义:小于第二个四分位数+1.5倍的IQR
IQR=Q3-Q1

51、箱型图认识

【udacity】机器学习-2模型验证_第1张图片

 

51、均值不一定在IQR中

因为均值受到异常值的影响,但是IQR却不受异常值的影响

52、IQR的不足

IQR和值域无法将所有的数据全部考虑进去

53、衡量差异性的最好的方法

找到数据集的每两个数值的距离和数据集的平均值

55、离均差

Deviation from Mean

xix

x=10x=52793.60

sample Deviation from Mean Absolute Feviations
33219 -19574.6 19574.6
36259 -16534.6 16534.6
38801 -13992.6 13992.6
46335 -6458.6 6458.6
46840 -5953.6 5953.6
47594 -5199.6 5199.6
55130 2336.4 2336.4
56863 4069.4 4069.4
78070 25276.4 25276.4
88830 36036.4 36036.4

Average deviation = 0

61、平均绝对偏差的公式

n(xxi)

62、平方偏差

sample Deviation from Mean Squared Deviations
33219 -19574.6 383337241
36259 -16534.6 273564984
38801 -13992.6 195776064
46335 -6458.6 41705764
46840 -5953.6 35438209
47594 -5199.6 27029601
55130 2336.4 5456896
56863 4069.4 16556761
78070 25276.4 638876176
88830 36036.4 1298593296

70、标准偏差的求法

  • 求平均值
  • 求离均差
  • 求每个偏差的平方值
  • 取平均值后再去平方根值

71、用语言来描述标准偏差

σ=nΣ(xix)2

  • Square root of average
  • (Average squared deviation)Squared
  • Sum of squared deviations
  • Sum of (absolute deviations squared)
  • Square root of ((sum of squared deviations)divided by n)

74、标准差的重要性

标准差可以在统计分析时提供大量的帮助,事实证明,在正态分布中,即数据分布均匀,平均值等于中位数也等于众数,同时这些统计量位于分布的中心
标准差具有重要意义,大约68%的数据与平均值的偏差不超过一个标准差,而95%的数据与平均值的偏差不超过2个标准差

以正态分布举例
65%的数据

xσ,x+σ

95%的数据

x2σ,x+2σ

【udacity】机器学习-2模型验证_第2张图片

 

77、贝塞尔校正

通常,抽样会低估了总体中差异性的数量,因为抽样往往是总体居于中间的值,特别是正态分布,多数值居于中间位置,因此我们从正态分布的总体中抽样时,多数值也在此处附近
为了纠正这种现象,我们使用内塞尔校正系数,我们把除以n用除以n-1代替

78、样本标准差

sample standard deviation

s=n1Σ(xix)2σ=nΣ(xix)2

81、Numpy

Numpy内置了进行数据分析时所要执行的大量的基础任务所需的函数

  • 数组的平均差
  • 数组的中位数差
  • 数组的标准差

82、Pandas


import numpy as np
import pandas as pd
"""
 d = {'name':pd.Series(['Braund','Cummings','Heikkinen','Allen'],index=['a','b','c','d']),     'age':pd.Series([22,38,26,35],index=['a','b','c','d']),      'fare':pd.Series([7.25,71.83,8.05],index=['a','b','d']),      'survived':pd.Series([False,True,True,False],index=['a','b','c','d'])}
 df = pd.DataFrame(d)
 print(df)
 """
 d= {   
 'counties':pd.Series(['Russian Fed.', 'Norway', 'Canada', 'United States',                 'Netherlands', 'Germany', 'Switzerland', 'Belarus',                 'Austria', 'France', 'Poland', 'China', 'Korea',                 'Sweden', 'Czech Republic', 'Slovenia', 'Japan',                 'Finland', 'Great Britain', 'Ukraine', 'Slovakia',                 'Italy', 'Latvia', 'Australia', 'Croatia', 'Kazakhstan']),    
 'gold':pd.Series([13, 11, 10, 9, 8, 8, 6, 5, 4, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 
0]),    
'silver':pd.Series([11, 5, 10, 7, 7, 6, 3, 0, 8, 4, 1, 4, 3, 7, 4, 2, 4, 3, 1, 0, 0, 2, 2, 2, 1, 
0]),   
'bronze':pd.Series([9, 10, 5, 12, 9, 5, 2, 1, 5, 7, 1, 2, 2, 6, 2, 4, 3, 1, 2, 1, 0, 6, 2, 1, 0, 
1]),}
df = pd.DataFrame(d)
print(df)

100、选择合适的指标

在构建机器学习模型时,我们首先要选择性能指标,然后测试模型的表现如何。相关的指标有多个,具体取决于我们要尝试解决的问题。

在可以选择性能指标之前,首先务必要认识到,机器学习研究的是如何学习根据数据进行预测。对于本课程和后续的“监督式机器学习”课程,我们将重点关注那些创建分类或创建预测回归类型的已标记数据。

此外,在测试模型时,也务必要将数据集分解为训练数据和测试数据。如果不区分训练数据集和测试数据集,则在评估模型时会遇到问题,因为它已经看到了所有数据。我们需要的是独立的数据集,以确认模型可以很好地泛化,而不只是泛化到训练样本。在下一课中,我们将探讨模型误差的一些常见来源,并介绍如何正确分解本课程的“数据建模和验证”部分中的数据集。

102、分类指标和回归指标

在分类中,我们想了解模型隔多久正确或不正确地识别新样本一次。而在回归中,我们可能更关注模型的预测值与真正值之间差多少。

在本节课的余下部分,我们会探讨几个性能指标。对于分类,我们会探讨准确率、精确率、召回率和 F 分数。对于回归,我们会探讨平均绝对误差和均方误差。

103、分类指标

对于分类,我们处理的是根据离散数据进行预测的模型。这就是说,此类模型确定新实例是否属于给定的一组类别。在这里,我们测量预测是否准确地将所讨论的实例进行分类。

104、准确率

最基本和最常见的分类指标就是准确率。在这里,准确率被描述为在特定类的所有项中正确分类或标记的项的数量。

举例而言,如果教室里有 15 个男孩和 16 个女孩,人脸识别软件能否正确识别所有男孩和所有女孩?如果此软件能识别 10 个男孩和 8 个女孩,则它识别男孩和女孩的准确率分别为 66% 和 50%:

准确率 = 正确识别的实例的数量/所有实例数量

有关准确率和如何在 sklearn 中使用它的更多信息,请查看此链接 此处。分类指标
对于分类,我们处理的是根据离散数据进行预测的模型。这就是说,此类模型确定新实例是否属于给定的一组类别。在这里,我们测量预测是否准确地将所讨论的实例进行分类。

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