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Multivariate linear regression model: y = b1x1 + b2x2 + b3x3 + ... +bnxn;We are based on a set of data: similar to arr_x = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]]; Arr_y = [5, 10, 15]; The last we asked for was an array that contained the B1 to Bn;Methods: Using least squares methodFormula: We only use the first half of the formula, that is, the matrix to calculateThe x in the formula is a
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
') plt.ylabel (' Ratio_sugar ') plt.title (' LDA ') plt.show () W=calulate_w () plot (W)The results are as follows: The corresponding W value is:[ -6.62487509e-04, -9.36728168e-01]Because of the relationship between data distribution, LDA's effect is not obvious. So I changed the number of samples of several label=0, rerun the program to get the result as follows:The result is obvious, the corresponding W value is:[-0.60311161,-0.67601433]Transferred from: http://cache.baiducontent.com/c?m= 9d7
The importance of database in PHP
There is a lack of a powerful tool in the PHP field: a language-based math library. In this two-part series, Paul Meagher wants to inspire PHP developers to develop and implement a PHP-based math library by providing an example of how to develop an analytics model library. In the 1th part, he demonstrates how to use PHP as an implementation language to develop and implement the core part of the simple linear
,-2.68076.5479,0.296787.5386,3.88455.0365,5.701410.274,6.75265.1077,2.05765.7292,0.479535.1884,0.204216.3557,0.678619.7687,7.54356.5159,5.34368.5172,4.24159.1802,6.79816.002,0.926955.5204,0.1525.0594,2.82145.7077,1.84517.6366,4.29595.8707,7.20295.3054,1.98698.2934,0.1445413.394,9.05515.4369,0.61705Third, the code implementationClear all; Clc;data = Load (' ex1data1.txt '); X = Data (:, 1); y = data (:, 2); m = length (y); % Number of training Examplesplot (x, y, ' Rx '), percent ================
This article will cover:
(1) Another Linear Regression Method: normal equation; (2) Advantages and Disadvantages of gradient descent and normal equation;
Previously we used the Gradient Descent Method for linear regression, but gradient descent has the following features: (1) learning rate needs to be selected in a
Example of the 2D regression linear scatter effect implemented by jQuery plug-in HighCharts [with demo source code download], jqueryhighcharts
The example in this article describes the 2D regression linear scatter effect implemented by the jQuery plug-in HighCharts. We will share this with you for your reference. The d
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 than the original (1-αλ⁄m)
Normal equation
Witho
# Linear regression least squaresFrom Sklearn import Linear_modelImport SysImport Tushare as TSImport Matplotlib.pyplot as PltImport Pandas as PDImport Sklearn.metrics as SMSh=ts.get_hist_data (' sh '). Sort_index () #获取上证指数每日数据 and sorted by time indexPf=ts.get_hist_data (' 600000 '). Sort_index () #获取浦发银行数据 and sorted by time indexsh[' re ']=np.log (sh[' close ']/sh[' Close '].shift (1)) #计算上证指数收益率pf[' re
(https://mirrors.tuna.tsinghua.edu.cn/CRAN/) After download good R open, you can enter the command, as below, I enter> Y=c (61,57,58,40,90,35,68) indicates that a y vector is created, and the value of the vector is the content after C> y echo y[1] 61 57 58 40 90 35 68> X=c (170,168,175,153,185,135,172) create an x vector> x Echo X[1] 170 168 175 153 185 135 172>> Plot (x, y), y to the left ordinate, and scatter plot.> Z=lm (y~x+1) a linear
In this lesson, we talk about the example of the regression of the downline, and introduce several common optimization algorithms.
After the linear fitting of the data, it is found that the error is large, so Huber loss is proposed.Huber loss is in robust regress (robust regression. ) is used in the loss function, compared to the square error, the discrete value
R Language Generalized linear Model GLM () functionGLM (formula, family=family.generator, Data,control = List (...))Formula data relationships, such as y~x1+x2+x3Family: Each response distribution (exponential distribution family) allows various correlation functions to correlate the mean with the linear predictor.Common family:
Binomal (link= ' logit ')--the response variable is subject to two distributio
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
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 "
linear regression is discussed, then the form of the assumed function can be written as hθ (x) =θ0+θ1x H_\theta (x) =\theta_0+\theta_1x, in order to hθ (x) H_\theta (x) for analysis, we introduce the loss function . loss functions (cost function)
The introduction of the loss function is derived from the evaluation of the assumption function.Assuming we've got a hypothetical function hθ (x) =θ0+θ1x H_\theta
Simple linear regression implemented using PHP: (1 ). The importance of databases in PHP The PHP field lacks a powerful tool: a language-based mathematical library. In this two-part series, PaulMeagher wants to use the importance of databases in PHP
PHP lacks a powerful tool: a language-based mathematical library. In this two-part series, Paul Meagher hopes to inspire PHP developers to develop and implement
The importance of databases in PHP
A powerful tool in the field of PHP is missing: A language based math library. In this two-part series, Paul Meagher hopes to inspire PHP developers to develop and implement a PHP based math library by providing an example of how to develop an analysis model library. In part 1th, he demonstrates how to use PHP as the implementation language to develop and implement a core part of a simple linear
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
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