To start with, we are going to discuss one of thesimplest regression i.e. linear regressionandwe will code a simple machine learning programme to predict the relationship between the head size and the brain wei
temp=x*theta'-y;sqrerrors=temp.^2;theta=theta-learning_rate*(1/m)*(temp'*x);Jcost(step)=(1/2*m)*sum(sqrerrors);disp(step),disp(Jcost(step))end figure;plot(Jcost)title('The relation between J and iteration ');ylabel('J')xlabel('iteration')legend('\alpha = 0.07')figureplot(...
优化代码如下: 通过循环迭代,我们发现,当迭代次数达到200时,函数就已经收敛,作图如下: 曲线表示损失函数的值随着迭代次数的变化趋势,完成200次迭代之后,曲线已经收敛。 计算出的theta值如下: 根据迭代求得的theta值得到房价关于标准化后的数值的函数关系式,做出图像如下: 可以看到,根据theta值得到一个平面如上图所示,...
Python has methods for finding a relationship between data-points and to draw a line of linear regression. We will show you how to use these methods instead of going through the mathematic formula. In the example below, the x-axis represents age, and the y-axis represents speed. We have ...
Machine learning is the study of how to make computers learn better from historical data, to produce an excellent model that can improve the performance of a system. It is widely used to solve complex problems in practical engineering applications, business analysis, other fields. With the ...
三、Robust regression鲁棒线性回归(Laplace/Student似然+均匀先验) 因为先验服从均匀分布,所以求鲁棒线性回归即求Laplace/Student最大似然。在heavy tail(奇异点较多)情况下用鲁棒线性回归,因为Laplace/Student分布比高斯分布更鲁棒。 似然函数为: 由于零点不可微,所以求解析解困难,无法使用梯度下降法。引入Huber损失函数解...
多项式回归(Polynomial Regression): 形如h(x)=theta0+theta1*x1+theta2*(x2^2)+theta3*(x3^3) 或者h(x)=ttheta0+theta1*x1+theta2*sqr(x2) 但是我们可以令x2=x2^2,x3=x3^3,于是又将其转化为了线性回归模型。虽然不能说多项式回归问题属于线性回归问题,但是一般我们就是这么做的。
import numpy as np import matplotlib.pyplot as plt from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression # 构造模拟数据,X特征(一维) , y真值 x = np.random.uniform(-3, 3, size=100) X = x.reshape(-1, 1) y = 0.5 * x**2 + x + 2 + ...
Linear regression in machine learning is defined as a statistical model that analyzes the linear relationship between a dependent variable and a given set of independent variables. The linear relationship between variables means that when the value of one or more independent variables will change (...
多元线性回归(Multivariate Linear Regression): 上面说的是最简单的一元线性回归,那么如果特征不止一个呢?这时就要用到多元线性回归,此时目标方程式表示如下: (x1~xp表示p个特征) 参数a,b,特征x以及目标y可以用向量和矩阵的方式表示出来。 首先将特征表示为 n行p+1列的矩阵,每行对应一个样本,每列对应一个特征...