Performing linear regression using Scikit-Learn: from sklearn.linear_model import LinearRegression lin_reg = LinearRegression() lin_reg.fit(X, y) lin_reg.intercept_, lin_reg.coef_ lin_reg.predict(X_new) based on thescipy.linalg.lstsq()(the name stands for "least squares") theta_best_svd...
"x"是原始数据,蓝线是用Matlab的polyfit()方法算出来的linear regression。红圈就是用normal method计算出来的预测值,可以看到他们全部都完美的对齐在蓝线上。 不记得在哪里看到的了,有人说,当数据量过大的时候normal equation method会变得不稳定。QR Factorization是一种更好的方法。我还没研究过,以后懂了再更新...
%COMPUTECOST Compute cost for linear regression % J = COMPUTECOST(X, y, theta) computes the cost of using theta as the % parameter for linear regression to fit the data points in X and y % Initialize some useful values m = length(y); % number of training examples % You need to ret...
(3)需要Feature Scaling; 因此可能会比较麻烦,这里介绍一种适用于Feature数量较少时使用的方法:Normal Equation; 当Feature数量小于100000时使用Normal Equation; 当Feature数量大于100000时使用Gradient Descent; Normal Equation的特点:简单、方便、不需要Feature Scaling; 其中Normal Equation的公式: Normal Equation 举个课...
Linear Regression 中 Normal Equation 的推导 设$X$ 是训练数据组成的矩阵,每一行代表一条训练数据,每一列代表一种特征。设 $Y$ 是训练数据的“正确答案”组成的向量,再设 $\theta$ 是每种特征的权值组成的向量,linear regression 的目的就是通过让代价函数 $J(\theta) = \frac{1}{2}(X\theta-Y)^T(...
Derivation of the Normal Equation for Linear Regression(by Eli Bendersky) First, some terminology. The following symbols are compatible with the machine learning course, not with the exposition of the normal equation on Wikipedia and other sites - semantically it's all the same, just the symbols...
当Feature数量小于100000时使用Normal Equation; 当Feature数量大于100000时使用Gradient Descent; Normal Equation的特点:简单、方便、不需要Feature Scaling; 其中Normal Equation的公式: 其中 表示第i个training example; 表示第i个training example里的第j个feature的值; ...
The normal equation is a closed-form solution used to find the value of θ that minimizes the cost function for ordinary least squares linear regression. Another way to describe the normal equation is as an analytical approach to find the coefficients that minimize the loss function. Both descrip...
Linear regression is one of the most basic and commonly used type of predictive models. It dates back to 1805, when Legendre and Gauss used linear regression to predict the movement of the planets. The goal in regression problems is to predict the value of one variable based on the values ...
1单变量线性回归Linear Regression with One Variable 1.1模型表达Model Representation 一个实际问题,我们可以对其进行数据建模。在机器学习中模型函数一般称为hypothsis。这里假设h为: 我们从简单的单变量线性回归模型开始学习。 1.2代价函数Cost Function 代价函数也有很多种,下面的是平方误差Squared error function: ...