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1、Artificial Intelligence30 10.1.Classification 10.2.Regression 10.3.Clustering 10.4.Ranking 10.5.Dimensionality ReductionContents:10.Tasks in Machine LearningRegressionArtificial Intelligence:Learning:Tasks32 A longer description 较长描述Regression analysis is a statistical process for estimating the rel
2、ationships among variables.It includes many techniques for modeling and analyzing several variables,when the focus is on the relationship between a dependent variable and one or more independent variables.回归分析是估计变量间关系的统计过程。它包含对多变量进行建模与分析的许多技术，其焦点是某个自变量与一个或多个因变量之间的关系。A shorter description 较短描述To reso
3、lve such problems where the output is a real continuous value.要解决输出是真实连续值的问题。A very short description 极简描述Predict a real value for each item.预测每个项的真实值。What is Regression 什么是回归10.2.RegressionArtificial Intelligence:Learning:Tasks33 Similarity 相似性Need training processing需要训练过程 Difference 差异性As shown i
4、n the following table 如下表所示Regression vs.Classification 回归与分类10.2.RegressionRegression回归Classification分类Difference差异性Output is a real continuous value.输出是一个真实连续值。Output is a discrete categories.输出是一个离散的类别。Example举例 Used-car price二手车价格 Tomorrows stock price明天的股票价格 sunny,cloudy,rainy 0,1,2,.,9Artifici
5、al Intelligence34 10.2.1.How Regression Works 10.2.2.Linear and Nonlinear 10.2.3.Applications and AlgorithmsContents:10.2.RegressionArtificial Intelligence:Learning:Tasks35Regression:Training 回归：训练10.2.1.How Regression Worksx1y1x2y2Known Output Value已知输出值Labeled Data标注数据(x,y)f(X)h(X)Hypothesis(Regre
6、ssion function)假设（回归函数）Training训练with small generalization and empirical errors具有小的泛化和经验错误Learning Algorithm学习算法Labeling function标注函数Artificial Intelligence:Learning:Tasks36Regression:Testing 回归：实测10.2.1.How Regression Worksx1y1x2y2Labeled Data标注数据f(X)h(X)Regression回归XYUnknown Output Value未知输出值Unsee
7、n Data未知数据x1?x2?Regressed Data回归后的数据x1y1x2y2(x,y)Training训练Learning Algorithm学习算法with small generalization and empirical errors具有小的泛化和经验错误Known Output Value已知输出值Artificial Intelligence:Learning:Tasks37Let n(n1)denote a set of n-dimensional real-valued vectors,+is a set of non-negative real numbers,i
8、nput space X is a subset of n,output space Y is a set of real numbers+,is an unknown distribution over X Y,then:设n(n1)为n维实值向量集，+是非负实数集，输入空间X是n的子集，输出空间Y是实数集+，D是X Y的未知分布，则：Let target labeling function:设目标标注函数 Training set(Labeled training sample set):训练集（标注的训练样本集）Regression algorithm:回归算法Given hypothe
9、sis set,to determine a hypothesis(regressive function)给定假设集H，来决定一个假设（回归函数）：With small generalization error R(h):具有小的泛化错误A Formal Description of Regression 一种回归的形式化描述10.2.1.How Regression Worksf X YS=(x(i),y(i)|(x,y)X Y,i 1,mh X Y and h HR(h)=ExL(h(x),f(x)Artificial Intelligence:Learning:Tasks38 Regr
10、ession 回归Given a testing data set of unknown output:给定一个未知输出的实测数据集：Using the regressive hypothesis h(X)=Y determined at above to predicate regressive results:使用前面训练好的回归函数h(X)=Y来预测回归结果：Note,in which:注意，其中Y is a set of real continues numbers.Y是一个真实连续数值的集合。A Formal Description of Regression 一种回归的形式化描述1
11、0.2.1.How Regression WorksX=x(i)|x X,i 1,mR=h(X)=y(i)|y Y,i 1,n,h(x)=yArtificial Intelligence:Learning:Tasks39 To have a system that can predict the price of a used car.构建一个预测二手车价格的系统。Inputs are the car attributes:brand,year,engine capacity,mileage,and other information.输入是车的属性：品牌、年式、引擎功率、里程、以及其它信息。
12、The output is the price of the car.输出是车的价格。Example:Used Car Prices 二手车价格10.2.1.How Regression WorksUsed car prices二手车价格Artificial Intelligence40 10.2.1.How Regression Works 10.2.2.Linear and Nonlinear 10.2.3.Applications and AlgorithmsContents:10.2.RegressionArtificial Intelligence:Learning:Tasks41
13、In linear regression,the observational data are modeled by a function with the following features:线性回归中，采用具有如下特征的函数对观测数据进行建模：The function is a linear combination of the model parameters;该函数是模型参数的线性组合；The function depends on one or more independent variables.该函数取决于一个或多个独立变量。Linear Regression 线性回归10.2
14、.2.Linear and Nonlineary(x)=wx+b Artificial Intelligence:Learning:Tasks42 In nonlinear regression,observational data are modeled by a function with the following features:非线性回归中，采用具有如下特征的函数对观测数据进行建模：The function is a nonlinearcombination of the model parameters;该函数是模型参数的非线性组合；The function depends on
15、 one or more independent variables.该函数取决于一个或多个独立变量。Nonlinear Regression 非线性回归10.2.2.Linear and Nonlineary(x)=w2x2+w1x+b Artificial Intelligence43 10.2.1.How Regression Works 10.2.2.Linear and Nonlinear 10.2.3.Applications and AlgorithmsContents:10.2.RegressionArtificial Intelligence:Learning:Tasks44
16、Be widely used for prediction and forecasting.被广泛地用于预测和预报。Trend estimation 趋势估计 Epidemiology 传染病学 Finance 金融analyzing and quantifying the systematic risk of an investment.分析与量化投资的系统性风险。Economics 经济predicting consumption spending,fixed investment spending,the demand to hold liquid assets,and etc.预测消费
17、支出、固定资产投资支出、持有流动资产需求、等等。Environmental science 环境科学Typical Applications of Regression 回归的典型应用10.2.3.Applications and AlgorithmsArtificial Intelligence:Learning:Tasks45 Bayesian linear regression Percentage regression Kernel ridge regression,Support-vector regression,Quantile regression,Regression Trees,Cascade Correlation,Group Method Data Handling(GMDH),Multivariate Adaptive Regression Splines(MARS),Multilinear InterpolationTypical Algorithms of Regression 回归的典型算法10.2.3.Applications and Algorithms贝叶斯线性回归百分比回归核岭回归支撑向量回归分位数回归回归树级联相关分组方法数据处理多元自适应回归样条多线性插值