前言

本文是多元线性回归的练习,这里练习的是最简单的二元线性回归,参考斯坦福大学的教学网http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=DeepLearning&doc=exercises/ex2/ex2.html。本题给出的是50个数据样本点,其中x为这50个小朋友到的年龄,年龄为2岁到8岁,年龄可有小数形式呈现。Y为这50个小朋友对应的身高,当然也是小数形式表示的。现在的问题是要根据这50个训练样本,估计出3.5岁和7岁时小孩子的身高。通过画出训练样本点的分布凭直觉可以发现这是一个典型的线性回归问题。

matlab函数介绍:

legend:

比如legend('Training data', 'Linear regression'),它表示的是标出图像中各曲线标志所代表的意义,这里图像的第一条曲线(其实是离散的点)表示的是训练样本数据,第二条曲线(其实是一条直线)表示的是回归曲线。

hold on, hold off:

hold on指在前一幅图的情况下打开画纸,允许在上面继续画曲线。hold off指关闭前一副画的画纸。

linspace:

比如linspace(-3, 3, 100)指的是给出-3到3之间的100个数,均匀的选取,即线性的选取。

logspace:

比如logspace(-2, 2, 15),指的是在10^(-2)到10^(2)之间选取15个数,这些数按照指数大小来选取,即指数部分是均匀选取的,但是由于都取了10为底的指数,所以最终是服从指数分布选取的。

实验结果:

训练样本散点和回归曲线预测图:

损失函数与参数之间的曲面图:

损失函数的等高线图:

程序代码及注释:

采用normal equations方法求解:

%%方法一
x = load('ex2x.dat');
y = load('ex2y.dat');
plot(x,y,'*')
xlabel('height')
ylabel('age')
x = [ones(size(x),1),x];
w=inv(x'*x)*x'*y
hold on
%plot(x,0.0639*x+0.7502)
plot(x(:,2),0.0639*x(:,2)+0.7502)%更正后的代码

采用gradient descend过程求解:

% Exercise 2 Linear Regression

% Data is roughly based on 2000 CDC growth figures
% for boys
%
% x refers to a boy's age
% y is a boy's height in meters
% clear all; close all; clc
x = load('ex2x.dat'); y = load('ex2y.dat'); m = length(y); % number of training examples % Plot the training data
figure; % open a new figure window
plot(x, y, 'o');
ylabel('Height in meters')
xlabel('Age in years') % Gradient descent
x = [ones(m, 1) x]; % Add a column of ones to x
theta = zeros(size(x(1,:)))'; % initialize fitting parameters
MAX_ITR = 1500;
alpha = 0.07; for num_iterations = 1:MAX_ITR
% This is a vectorized version of the
% gradient descent update formula
% It's also fine to use the summation formula from the videos % Here is the gradient
grad = (1/m).* x' * ((x * theta) - y); % Here is the actual update
theta = theta - alpha .* grad; % Sequential update: The wrong way to do gradient descent
% grad1 = (1/m).* x(:,1)' * ((x * theta) - y);
% theta(1) = theta(1) + alpha*grad1;
% grad2 = (1/m).* x(:,2)' * ((x * theta) - y);
% theta(2) = theta(2) + alpha*grad2;
end
% print theta to screen
theta % Plot the linear fit
hold on; % keep previous plot visible
plot(x(:,2), x*theta, '-')
legend('Training data', 'Linear regression')%标出图像中各曲线标志所代表的意义
hold off % don't overlay any more plots on this figure,指关掉前面的那幅图 % Closed form solution for reference
% You will learn about this method in future videos
exact_theta = (x' * x)\x' * y % Predict values for age 3.5 and 7
predict1 = [1, 3.5] *theta
predict2 = [1, 7] * theta % Calculate J matrix % Grid over which we will calculate J
theta0_vals = linspace(-3, 3, 100);
theta1_vals = linspace(-1, 1, 100); % initialize J_vals to a matrix of 0's
J_vals = zeros(length(theta0_vals), length(theta1_vals)); for i = 1:length(theta0_vals)
for j = 1:length(theta1_vals)
t = [theta0_vals(i); theta1_vals(j)];
J_vals(i,j) = (0.5/m) .* (x * t - y)' * (x * t - y);
end
end % Because of the way meshgrids work in the surf command, we need to
% transpose J_vals before calling surf, or else the axes will be flipped
J_vals = J_vals';
% Surface plot
figure;
surf(theta0_vals, theta1_vals, J_vals)
xlabel('\theta_0'); ylabel('\theta_1'); % Contour plot
figure;
% Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 2, 15))%画出等高线
xlabel('\theta_0'); ylabel('\theta_1');%类似于转义字符,但是最多只能是到参数0~9

参考资料:

http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=DeepLearning&doc=exercises/ex2/ex2.html

作者:tornadomeet 出处:http://www.cnblogs.com/tornadomeet 欢迎转载或分享,但请务必声明文章出处。

转载 Deep learning:二(linear regression练习)的更多相关文章

  1. 转载 Deep learning:三(Multivariance Linear Regression练习)

    前言: 本文主要是来练习多变量线性回归问题(其实本文也就3个变量),参考资料见网页:http://openclassroom.stanford.edu/MainFolder/DocumentPage. ...

  2. Machine Learning #Lab1# Linear Regression

    Machine Learning Lab1 打算把Andrew Ng教授的#Machine Learning#相关的6个实验一一实现了贴出来- 预计时间长度战线会拉的比較长(毕竟JOS的7级浮屠还没搞 ...

  3. 转载 Deep learning:六(regularized logistic回归练习)

    前言: 在上一讲Deep learning:五(regularized线性回归练习)中已经介绍了regularization项在线性回归问题中的应用,这节主要是练习regularization项在lo ...

  4. [转载]Deep Learning(深度学习)学习笔记整理

    转载自:http://blog.csdn.net/zouxy09/article/details/8775360 感谢原作者:zouxy09@qq.com 八.Deep learning训练过程 8. ...

  5. 【Coursera - machine learning】 Linear regression with one variable-quiz

    Question 1 Consider the problem of predicting how well a student does in her second year of college/ ...

  6. 转载 deep learning:八(SparseCoding稀疏编码)

    转载 http://blog.sina.com.cn/s/blog_4a1853330102v0mr.html Sparse coding: 本节将简单介绍下sparse coding(稀疏编码),因 ...

  7. CheeseZH: Stanford University: Machine Learning Ex1:Linear Regression

    (1) How to comput the Cost function in Univirate/Multivariate Linear Regression; (2) How to comput t ...

  8. machine learning (2)-linear regression with one variable

    machine learning- linear regression with one variable(2) Linear regression with one variable = univa ...

  9. 转载 Deep learning:四(logistic regression练习)

    前言: 本节来练习下logistic regression相关内容,参考的资料为网页:http://openclassroom.stanford.edu/MainFolder/DocumentPage ...

随机推荐

  1. SpringFramework_module

    org.springframework : spring-aop:基于代理的AOP spring-aspects:基于切面的AspectJ spring-beans:beans spring-cont ...

  2. 【实验室笔记】C#的Socket客户端接收和发送数据

    采用socket发送和接收数据的实验中,服务器采用的是网络助手作为模拟服务器端. 客户端程序流程: 应用的命名空间: using System.Net; using System.Net.Socket ...

  3. 初始go语言

    一.创建第一个go语言程序:打印hello world! package main import "fmt" func main() { fmt.Println("Hel ...

  4. List集合对象中的排序,随机显示

    List<User> students = new ArrayList<User>(); User user1 = new User(); user1.setAge(112); ...

  5. java练习 - 字符串反转

    思路: 1. 首先将字符串转换成数组,一个数组元素放一个字符. 2. 循环遍历字符串,将所有字符串前后字符调换位置,比如:第一个和最后一个调换,第二个和倒数第三调换,第三个和倒数第三调换,直到所有字符 ...

  6. mysql修改编码

    1.查看当前编码 2.设置utf8mb4编码(也可以是其他),修改my.cnf或my.ini

  7. Angularjs directive全面解读(1.4.5)

    说到Angularjs directive即指令,可以这么说Angularjs的灵魂就是指令,学会Angularjs指令那么你的Angularjs的武功就修炼了一半了,当然这只是鄙人的一点点独到见解, ...

  8. B/S、C/S区别

    [B/S.C/S C/S (Client/Server客户端服务器) B/S (Brower/Server浏览器服务器)  区别 1.硬件环境不同: C/S 一般建立在专用的网络上, 小范围里的网络环 ...

  9. Golang--计算文件的MD5值

    参考: http://blog.csdn.net/u014029783/article/details/53762363 用法: $ go run 01.go -f 1.txt b9d228f114d ...

  10. Tomcat下log4j设置文件路径和temp目录

    转自:http://www.cnblogs.com/dkblog/archive/2007/07/27/1980873.html 在Web应用中的如何设置日志文件的路径呢?最笨的方法是写绝对路径,但很 ...