In the past, there was a regression analysis in statistics learning. If only one independent variable and one dependent variable are included, and the relationship between them can be expressed in a straight line, this regression analysis is called a one-dimensional linear regression analysis, the least square method c
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 Descent:
Algorithm Implementation:Computecost function:
function J = computeCost(X, y, theta)m = length(y); % number of training examplesJ = 0
This article mainly introduces the multi-linear regression simulation curve algorithm based on PHP implementation, and analyzes the principle of the multivariate linear regression simulation curve algorithm and the relevant PHP implementation skills with the specific instance form, and the friends who need can refer to
Must do:[*] warmupexercise.m-simple example function in Octave/matlab[*] plotdata.m-function to display the dataset[*] computecost.m-function to compute the cost of linear regression[*] gradientdescent.m-function to run gradient descent1.warmupexercise.mA = Eye (5);2.plotdata.m' Rx ' ' markersize ' Ten % Plot The Dataylabel ('Profit in $10,000s'% Set the y-axis labelXlabel ('Populationof city in 10,000s'
what is linear regression. The so-called linear regression (taking a single variable as an example) is to give you a bunch of points, and you need to find a straight line from this pile of points. Figure below
This screenshot is from Andrew Ng's What you can do when you find this line. Let's say we find A and b that re
process above。。。 return x, YData processing, above #2. Linear regressionRead data:Data1=pd.read_csv (' Train.csv ')X_train=sz (DATA1) [0]Y_train=sz (DATA1) [1]Data2=pd.read_csv (' Test1.csv ')X_test=sz (DATA2) [0]Y_test=sz (DATA2) [1]The linear regression of the data in train, the linear coefficients, and the x_te
[Cpp]// Average annual traffic trend test. h// Trend analysis of average annual traffic using the Mann-Kendall MethodVoid MannKendall (){Using namespace std;Int S = 0; // The Statistical variable for the testDouble VarS, // returns the variance of variable S.Z; // standard normal statistical variable varianceS = 0;For (int I = 0; I For (int j = I + 1; j {If (YearQ [j]> YearQ [I]) S ++;If (YearQ [j] }VarS = 0;VarS = Y * (Y-1) * (2 * Y + 5)/18.0;If (S> 0) Z = (S-1)/pow (VarS, 0.5 );If (S Cout Cin>
1 reviews1.1 Supervised learningDefinition: Machine learning algorithm for given correct answerClassification:(1) Regression algorithm: Predicting the output of successive values, such as the prediction of house prices(2) Classification algorithm: The output of discrete values, such as determining whether the disease is a certain type of cancer1.2 Non-supervised learningDefinition: The relationship between data is analyzed without the information of t
as, if you add n-k more instrument, then you can fully determine the value of B based on the resulting equations, and no least squares are required.2. Main component Analysis thought:From the above analysis, we know that we are actually using a given instrument composition to simulate y this portfolio. So, can you use other instrument to replace the original, and then also get y? The answer is yes.This is a bit of orthogonal decomposition, as in the above example, if there are 3 instrument, the
piecewise linear regression: It is the influence of explanatory variables with virtual variables to estimate the different amount of levels. In economic relations , there is a linear relationship with the interpreted variable before the value of the explanatory variable x reaches a certain level x′, and when the value of the explanatory variable x reaches or exce
Warm-up ExerciseFollow the instruction, type the code in WARMUPEXERCISE.M file:A = Eye (5);Computing cost (for one Variable)By the formula to cost function (for one Variable):J (θ0,θ1) = 1/(2m) *∑i=1~m (hθ (x (i)-y (i)) 2We can implement it in COMPUTECOST.M file by these steps: function J = Computecost (x, Y, theta)%computecost Compute cost for linear regression% J = Computecost (x, Y, theta) Computes the c
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
gradient descent algorithm: linear regression Model: Linear hypothesis:Squared difference cost function:By substituting each formula, the θ0 and θ1 are respectively biased:By substituting the partial derivative into the gradient descent algorithm, we can realize the process of finding the local optimal solution.The cost function of
. The Getstudentprob method is used to evaluate the degree of coincidence of the linear model; The Getinversestudentprob method returns an intermediate value that calculates the confidence interval for each predicted y value.
Because of the limited space, I cannot explain all the functions in this class one-by-one, so if you want to understand the terms and procedures involved in simple linear
to evaluate the degree of coincidence of the linear model; The Getinversestudentprob method returns an intermediate value that calculates the confidence interval for each predicted y value.
Because of the limited space, I cannot explain all the functions in this class one-by-one, so if you want to understand the terms and procedures involved in simple linear regression
A linear/Nonlinear regression fitting example using R language (1)
1. Generate a set of data
vector
vector
Ofstreamfout ("Data2.txt");
for (int i =1;i
{
float x =i*0.8;
Float randdnum= rand ()%10 * 10;
Floatrandomflag = (rand ()%10)%2==0? (1):(-1);
Float y = 3 *x*x + 2*x + 5 + randomflag*randdnum;
fout
Xxvec.push_back (x);
Yyvec.push_back (y);
}
Fout.close ();
Save the generated data as a TXT file, named "
generally divided into regression and classification. If we predict that the value is discrete, then such learning tasks are called classifications, and if the prediction is continuous, such a learning task is called regression.
Unsupervised Learning: Clustering is non - supervised learning a representation algorithm that, without the given attribute characteristics, divides the given dataset into the req
I. Linear Logistic Regression
The Code is as follows:
Import numpy as npimport pandas as pdimport matplotlib. pyplot as pltimport scipy. optimize as optimport Seaborn as SNS # Read the dataset Path = 'ex2data1.txt 'Data = PD. read_csv (path, header = none, names = ['expired', 'expired', 'admitted']) # Separate Positive and Negative datasets positive = data [DATA ['admitted']. ISIN ([1])] Negative = data [DA
1650 sq-ft, 3 BR House ' ... ' (using gradient descent): \ n $%f\n '], price); percent ================ part 3:normal equations ================data = Csvread (' Ex1data2.txt '); X = Data (:, 1:2); y = data (:, 3); m = length (y);% Add intercept term to XX = [Ones (M, 1) x];% Calculate the parameters from The normal Equationtheta = normaleqn (X, y);% Display normal equation ' s resultfprintf (' Theta computed from the normal equat Ions: \ n '); fprintf ('%f \ n ', theta); fprintf (' \
- on - in if(1= = Alpha (alpha_i))%The result of the experiment is that the alpha 1 o'clock is the best, then the theta value after the iteration is the desired value -Theta_grad_descent =Theta to End + End -Legend'0.01','0.03','0.1','0.3','1','1.3'); theXlabel ('Number of iterations') *Ylabel ('Cost function') $ Panax Notoginseng%here is the prediction formula -Price_grad_descend = Theta_grad_descent'*[1 (1650-meanx (2))/sigmax (2) (3-meanx (3)/sigmax (3))]' the
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