gradient descent linear regression

and can quickly converge to the near truth. While the off-line algorithm is accurate to solve the linear equations, no data preprocessing is needed, only the feature vector x is needed to expand a intercept term.But-------off-line algorithm needs to solve the inverse of the matrix, when the amount of data is large, this method is not suitable.CLC Clear All;close all;x= Load ('Ex3x.dat');%Load Data y= Load ('Ex3y.dat');%%%%--------------------Data pre

From the previous article, the most important thing in supervised learning is to determine the imaginary function h (θ), which is to determine the H (θ) by making the cost function J (θ) the smallest.The last one is to find the smallest J (θ) by the gradient descent method, which we will use to explain the matrix.1, ordinary least squaresUsing a matrix, the M training set (x, y) can be represented as follow

follows:The MATLAB code is implemented as follows: The cost function here is implemented by vector (matrix) multiplication .The concrete proof can refer to: Linear Regression---realizes a linear regression2:length (theta) ) ) ' * Theta (2:length (theta))); J = SUM ((x*theta-y). ^2)/(2*m) + reg;Note: Since θ0 does not participate in regularization, the above MATL

I. Algorithm ImplementationFrom the previous theory, we know the formula for Solving Linear Regression with Gradient Descent: the idea of Solving Linear Regression with Gradient

Reference: openclassroomLinear Regression)To fit the relationship between age (x1) and height (y) of children under 10 years old, we assume a function h (x) for x ):H (x) = Theta; 0 + Theta; 1 * x1 = Theta; 0 * x0 + Theta; 1 * x1 = Theta; T * x (x0 = 1, x = [x0, x1])Our goal is to find Theta; so that h (x) is close to y.Therefore, we need to minimize the square error between h (x) and y on m training samples (x, y.That is, to minimize J ( Theta;

Phi's model of X. now we've got Phi's model for x, the parameters are theta, and we're going to create a hypothetical model of our classification:This means that if we get the parameter theta, for a given x can get y=1 probability, then the probability of y=0 can also find out, the problem is solved, the following is how to solve the parameter theta. Iv. objective functions and gradientsNow that we know the form of the logistic regression model, we u

distribution of this noise random variable E. The process of solving the maximum likelihood problem Here, the problem can be solved, that is, for the existing data D (x,y) and any one parameter F (X), find the best parameters we need, Select a model f (x), and initialize its parameters Estimate the distribution of the noise random variable e (e.g. uniform distribution, Gaussian distribution ...), get likelihood expression Calculates the likelihood function and adjusts the likelihood to achieve

Logistic regression is used to classify, and linear regression is used to return.Linear regression is the addition of the properties of the sample to the front plus the coefficients. The cost function is the sum of squared errors. Therefore, in the minimization of the cost function, you can directly derivative, so that

, 1)) A #Pre-valuation atPreY = w * x +b - - #loss value: The mean variance between the pre-estimate and the actual value -Loss = Tf.reduce_mean (Tf.square (PreY-y)) - #Optimizer: Gradient Descent method -Optimizer =Tf.train.GradientDescentOptimizer (learnrate) in #Training: Minimizing loss function -Trainer =optimizer.minimize (loss) to + With TF. Session () as Sess: - Sess.run (Tf.global

equation, so we're going to expand the X into a column of 1. 9W=INV (x'*x) *x'*yTen on APlot (X (:,2),0.0639*x (:,2)+0.7502The 0.7502 here is the first value of the W vector to be obtained, that is, the Wx+b b,w the second value is Wx+b W.Method Two:1 clear all, close all, CLC2x = Load ('Ex2x.dat'); y = Load ('Ex2y.dat');3m = Length (y); %Number of training examples4%Plot the training data5Figure % Open aNewFigure Window This figure also can not write, no influence6Plot (x, Y,'o');%use a circl

its parameters Estimate the distribution of the noise random variable e (e.g. uniform distribution, Gaussian distribution ...) to get likelihood expression Calculate the likelihood function and adjust the likelihood to achieve maximum The method of adjustment can be used as described in the previous chapter "derivative Descent Method", of course, you can also directly find the extremum point (derivative of 0) to obtain its maximum minimum value. The

Gradient descent in Practice-feature ScalingMake sure features is on a similar scale.The smaller the range of Features, the less likely the total is, and the faster the calculation will be.Dividing by the rangeBy Feature/range each feature within the range of [-1, 1]The next question is an example:Mean NormalizationChanges the value to close to 0. Except for x0, because the value of x0 is 1.MU1 is average v

Linear regression is the basis of machine learning and is very useful in daily work.1. What is linear regressionOne-dimensional linear regression can be accomplished by finding the curve of the function with multiple points.2. Mathematical representationis the Intercept valu

price of a house is whether the area is more important or the room orientation is more important. We make x0 = 1, we can use vectors to represent In the above formula, once Theta is determined, then our straight line is determined, and we are able to forecast the house price. So the job we're going to do is to determine theta. The value of θ can have countless, how should we choose θ? 3. Model Establishment-least squares O

Supervised Learning Learn a function H: X → y H is called a hypothesis. 1. Linear Regression In this example, X is a two-dimensional vector, x1 represents living area, and x2 represents bedrooms. Functions/hypotheses H Set X0 = 1. Now, given a training set, how do we pick, or learn, the parameters θ? Now it is used to evaluate the θ parameter. One reasonable method seems to be to make h (x)

* len (Matrixx)) # Gradient descent iterative function def gradientdescent (Matrixx, Matrixy, Matrixtheta, Falpha, nitercounts): Matrixthetatemp = Np.matrix (Np.zeros (matrixtheta.shape)) nparameters = Int (Matrixtheta.ravel (). Shap E[1]) Arraycost = Np.zeros (nitercounts) for I in Xrange (nitercounts): Matrixerror = (Matrixx * Matrixthet A.T)-Matrixy for J in Xrange (nparameters): Matrixsumte

This section begins with the basic linear regression algorithm.(1) The hypothetical space of Linear regression becomes the real field(2) The goal of Linear regression is to find the dividing line (super plane) that makes the resid

technical thing. I have been talking about this problem with the department boss during outing. Machine Learning is definitely not isolated one by one.AlgorithmIt is an undesirable way to read machine learning like an introduction to algorithms. There are several things in machine learning that keep going through the book, for example, data distribution, maximum likelihood (and several methods for extreme values, but this is more mathematical), deviation and variance trade-offs, and knowledge a

Machine learning (--regularization:regularized) Linear regression Gradient descent Without regularization With regularization Θ0 is the same as the original, no regularization. The θ1-n is slightly smaller

In fact, the method of multivariate linear regression is similar to that of single-variable linear regression. The algorithm is provided here:Computecostmulti Function function J = computeCostMulti(X, y, theta)m = length(y); % number of training examplesJ = 0;predictions = X * theta;J = 1/(2*m)*(predictions - y)' * (pr