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found by gradient descent: '); fprintf ('%f%f \ n ', theta (1), Theta (2));% Plot the Lin Ear fithold on; % Keep previous plot visibleplot (X (:, 2), X*theta, '-') Legend (' Training data ', ' Linear regression ') hold off% don ' t overlay Any more plots on the figure% Predict values for population sizes of 35,000 and 70,000predict1 = [1, 3.5] *theta;fprintf (' for population = 35,000, we predict a profit of%f\n ',... predict1*10000);p redict2 =
calculate the cost function value at this timeEnd% observe the change in cost function value with the number of iterations% plot (J);% observed fitting conditionsStem (x1,y);P2=x*theta;Hold on;Plot (X1,P2);7. Actual UseWhen you actually use linear regression, the input data is optimized first. Includes: 1. Remove redundant and unrelated variables; 2. For nonlinear relationships, polynomial fitting is used to change a variable into multiple variables;
regression problem. If it is a discrete value, it is a classification problem. Unlike supervised learning,Unsupervised learningDuring training, I did not know the correct results. I went on to give the above example a bunch of fruits to the children, such as apples, oranges, and pears. At the beginning, the children did not know what the fruits were, let the children classify these fruits. After the child classifies the child, give him an apple. He s
Machine learning Notes (iii) multivariable linear regression
Note: This content resource is from Andrew Ng's machine learning course on Coursera, which pays tribute to Andrew Ng.
One, multiple characteristics (multiple Features)The housing price problem discus
A brief introduction of linear regression algorithmlinear regression is a statistical analysis method using regression analysis in mathematical statistics to determine the quantitative relationship between two or more variables, which is widely used. Its expression is y = W ' x+e,e is a normal distribution where the error obeys the mean value of 0. In regression analysis, only one argument and one dependent variable are included, and the relationship
root '
def rmse (Y_test, y):
return Sp.sqrt (Sp.mean ((y_test-y) * * 2))
"' issuperior to the mean, between [0~1]. 0 is not equal to the mean value. 1 means perfect predictions. This version of the implementation is the reference Scikit-learn official website document "'
def R2 (Y_test, y_true):
return 1-((y_test-y_true) * *2). SUM ()/((Y_true-y_true.mean ()) * *2). SUM ()
"This is the version of Conwaywhite" Machine
each parameter corresponding to 44 is the value of J_vals (i,j) end46 end47 j_vals = J_vals ';% Surface plot49 Figure;50 Surf (theta0_vals, theta1_vals, j_vals)% draws an image of the parameter and loss function. Pay attention to use this surf compare egg ache, surf (x, y, z) is such, Wuyi%x,y is a vector, Z is a matrix, with X, Y paved grid (100*100 point) and Z of each point 52 to form a graph, but how to correspond to where, the egg hurts is, The second element of your x with the first eleme
Blog has migrated to Marcovaldo's blog (http://marcovaldong.github.io/)
Machine learning Cornerstone Tenth introduces the linear regression problem (linear regression problem), starting with this lecture to introduce specific machine lea
-variable linear regression model.The process of solving this problem with the machine learning method is actually using the training algorithm to process the data in the training set, get our regression equation h, and then with the new data, we can use the regression equation h to calculate the value of the corresponding output y when we only know the input x.
NormalizationBy looking at the values, note this House sizes is about the number of bedrooms. When features differ by orders of magnitude, first performing feature scaling can make gradient descent converge much more QuicklyThat is, when there is a large difference between features, such as the size of the house and the number of bedrooms, this will cause the gradient descent convergence is relatively slow, as shown in (left) , when the characteristics are normal, gradient descent convergence f
Tags: probability gradient drop RAM log directory UNC measure between playFinishing the Machine Learnig course from Andrew Ng Week1Directory:
What is machine learning
Supervised learning
Non-supervised learning
Unary
ensure reversible ( reversible Sufficient condition : matrix X columns linearly independent )In retrospect, our approach is to use iterative methods to find out the value of the cost function, and not to find the cost function. That is to say, whether the so-called optimal solution can be obtained, either by iteration or by other means, in line with the above conditions.But the reality of the data is not so ideal.If not reversible, how to solve?1, to seek pseudo-inverse (statistics solution )2.
Machine learning notes (b) univariate linear regression
Note: This content resource is from Andrew Ng's machine learning course on Coursera, which pays tribute to Andrew Ng.
Model representationHow to solve the problem of house price in note (a), this will be
of finding the best fitting line is actually looking for the best b b and M M. In order to find the best fit line, here we first define what line is the best line. We define error (cost function): Error function errors (b,m) =1n∑1n ((B+MXI) −yi) 2 error functions \ error_{(b, M)}=\frac{1}{n}\sum_{1}^{n} ((b+mx_i)-y_i) ^{2}
The Python code that calculates the loss function is as follows:
# y = b + mx
def compute_error_for_line_given_points (b, M, points):
totalerror = SUM ((((b + M * point[
From a statistical point of view, most of the methods of machine learning are statistical classification and regression method to the field of engineering extension.The term "regression" (Regression) was the origin of the British scientist Francis Galton (1822-1911) in a 1886 paper [1] to study the relationship between height and parental height of a child. After observing 1087 couples, the adult son was
build the model.In the exponential distribution family expression of the Bernoulli distribution we have known:, thus obtained.Three assumptions for building a generalized linear model:
Assuming that the Bernoulli distribution is met,
, in Bernoulli distribution
The derivation process is as follows:As with the least squares model, the next work is done by gradient descent or Newton's method.Note the above push to the result, rec
http://blog.csdn.net/ppn029012/article/details/8908104
Machine Learning---2. From maximum likelihood to view linear regression classification: Mathematics machine Study 2013-05-10 00:34 3672 people read comments (15) Collection Report MLE machine
based on the minimum mean variance. The closer to the predicted point, the heavier the weight, which is to use the points near the check to give higher weights. The most common is the Gaussian nucleus. The weights corresponding to the Gaussian nuclei are as follows:In (Formula 2), the only thing we need to make sure is that it's a user-specified parameter that determines how much weight is given to nearby points.Therefore, as shown in (Equation 3), local weighted
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