coursera machine learning andrew ng cost

Gradient descent algorithm minimization of cost function J gradient descent Using the whole machine learning minimization first look at the General J () function problem We have J (θ0,θ1) we want to get min J (θ0,θ1) gradient drop for more general functions J (Θ0,θ1,θ2 .....) θn) min J (θ0,θ1,θ2 .....) Θn) How this algorithm works. : Starting from the initial ass

Overview Cost Function and BackPropagation Cost Function BackPropagation algorithm BackPropagation Intuition Back propagation in practice Implementation Note:unrolling Parameters Gradient Check Random initialization Put It together Application of Neural Networks Autonomous Driving Review Log

Before the machine learning is very interested in the holiday cannot to see Coursera machine learning all the courses, collated notes in order to experience repeatedly.I. Introduction (Week 1)-What's machine learningThere is no un

different lambda, the calculated training error and cross-validation error are as follows:Lambda Train error Validation error 0.000000 0.173616 22.066602 0.001000 0.156653 18.597638 0.003000 0.190298 19.981503 0.010000 0.221975 16.969087 0.030000 0.281852 12.829003 0.100000 0.459318 7.587013 0.300000 0.921760 1.000000 2.076188 4.260625 3.000000 4.901351 3.822907 10.000000 16.092213 9.945508The graphic is represented as follows:As

First, how to learn a large-scale data set?In the case of a large training sample set, we can take a small sample to learn the model, such as m=1000, and then draw the corresponding learning curve. If the model is found to be of high deviation according to the learning curve, the model should continue to be adjusted on the existing sample, and the adjustment strategy should refer to the High deviation of se

m>=10n and uses multiple Gaussian distributions.In practical applications, the original model is more commonly used, the average person will manually add additional variables.If the σ matrix is found to be irreversible in practical applications, there are 2 possible reasons for this:1. The condition of M greater than N is not satisfied.2. There are redundant variables (at least 2 variables are exactly the same, XI=XJ,XK=XI+XJ). is actually caused by the linear correlation of the characteristic

-Gradient descentThe gradient descent algorithm is an algorithm for calculating the minimum value of a function, and here we will use the gradient descent algorithm to find the minimum value of the cost function.The idea of a gradient descent is that we randomly select a combination of parameters and calculate the cost function at the beginning, and then we look for the next combination of parameters that w

use of MATLAB. *.4.gradientdescent.mfunction [Theta, j_history] =gradientdescent (X, y, theta, Alpha, num_iters)%gradientdescent performs gradient descent to learn theta% theta = gradientdescent (X, y, theta, Alpha, num_iters) up Dates theta by% taking num_iters gradient steps with learning rate alpha% Initialize Some useful valuesm= Length (y);%Number of training examplesj_history= Zeros (Num_iters,1); forITER =1: Num_iters% ======================

-Learning RateIn the gradient descent algorithm, the number of iterations required for the algorithm convergence varies according to the model. Since we cannot predict in advance, we can plot the corresponding graphs of iteration times and cost functions to observe when the algorithm tends to converge.Of course, there are some ways to automatically detect convergence, for example, we compare the change valu

, i.e., all of our training examples lie perfectly on some straigh T line. If J (θ0,θ1) =0, that means the line defined by the equation "y=θ0+θ1x" perfectly fits all of our data. For the To is true, we must has Y (i) =0 for every value of i=1,2,..., m. So long as any of our training examples lie on a straight line, we'll be able to findθ0 andθ1 so, J (θ0,θ1) =0. It is not a necessary that Y (i) =0 for all of our examples. We can perfectly predict the value o

)/∂ (θ (1) JK) is tested for gradients. After the partial derivative code does not have a problem, close the Gradient check section code.6. Use gradient descent or other advanced algorithms to perform reverse propagation to find the θ values for minimizing j (θ).This paper describes the gradient descent algorithm in neural networks: starting from the random initial point, descending step by step, until the local optimal value is obtained. Algorithms such as gradient descent can at least guarante

, the weight of the high-weighted data is increased by 1000 times times the probability, which is equivalent to replication. However, if you are traversing the entire test set (not sampling) to calculate the error, there is no need to modify the call probability, just add the weights of the corresponding errors and divide by N. So far, we have expanded the VC Bound, which is also set up on the issue of multiple classifications!SummaryFor more discussion and exchange on

-Cost functionFor the training set and our assumptions, we will consider how to determine the coefficients in the assumptions.What we are going to do now is to choose the right parameters, and the selection of parameters directly affects the accuracy of the resulting straight line for the training set description. The difference between the predicted value and the actual value in the training set is the modeling error (Modeling error).the

-Gradient descent for linear regressionHere we apply the gradient descent algorithm to the linear regression model, we first review the gradient descent algorithm and the linear regression model:We then expand the slope of the gradient descent algorithm to the partial derivative:In most cases, the linear regression model cost function is shaped like a convex body, so the local minimum value is equivalent to the global minimum:The following is the enti

-Normal equationSo far, the gradient descent algorithm has been used in linear regression problems, but for some linear regression problems, the normal equation method is a better solution.The normal equation is solved by solving the following equations to find the parameters that make the cost function least:Assuming our training set feature matrix is x, our training set results are vector y, then the normal equation is used to solve the vector:The f

general, multiplication does not satisfy the exchange law: $ \ Matrix {A} \ times \ matrix {B} \ not = \ matrix {B} \ times \ matrix {A} $Special Matrix $ \ Matrix {I }=\ matrix {I _ {n \ times N }}=\ begin {bmatrix} 1 0 \ cdots 0 0 \ Cr0 1 \ cdots 0 0 \ Cr \ vdots \ vdots \ Cr0 0 \ cdots 1 0 \ Cr0 0 \ cdots 0 1 \ Cr \ end {bmatrix} $ For any matrix $ \ matrix {A} $: $ \ Matrix {A} \ times \ matrix {I }=\ matrix {I} \ times \ matrix {A }=\ matrix {A} $Inverse Matrix and inverte

Mainly for the week content: large-scale machine learning, cases, summary(i) Random gradient descent methodIf there is a large-scale training set, the normal batch gradient descent method needs to calculate the sum of squares of errors across the entire training set, which is a very large computational cost if the learning