Machine learning (eight) polynomial regression and model generalization (i)

I. What is polynomial regression

Linear regression is a regression problem between a dependent variable and an independent variable, however, in many practical problems in the field of livestock and fishery science, the independent variables that influence dependent variables tend to be more than one, but many, such as the wool yield of sheep is affected by many variables, such as weight, bust, body length, etc. Therefore, it is necessary to make a regression analysis between the dependent variable and several independent variables, namely multivariate regression analysis. In this paper, a regression analysis method for polynomial regression between a dependent variable and one or more independent variables is studied, which is called polynomial return (polynomial Regression). If the argument is only one, it is called a unary polynomial regression, and if there are multiple arguments, it is called multivariate polynomial regression. In a unary regression analysis, if the relationship between the variable y and the argument x is nonlinear, but the proper function curve can not be found to fit, then the unary polynomial regression may be used. The unary m polynomial regression equation is:. The quadratic two polynomial regression equation is:. The most important advantage of polynomial regression is that the measured points can be approximated by increasing the higher order of x, until they are satisfied. In fact, polynomial regression can deal with quite a class of nonlinear problems, it occupies an important position in regression analysis, because any function can be segmented by polynomial approximation. Therefore, in the usual practical problems, we can always use polynomial regression to analyze the relationship between the dependent variable and other independent variables. The polynomial regression problem can be solved by transforming the variables into multiple linear regression problems. For the unary m polynomial regression equation, the unary m-polynomial is transformed into the M-element linear regression equation. Therefore, the polynomial regression problem can be solved by using the regression method of multivariate linear function. It should be pointed out that in the polynomial regression analysis, the test of the regression coefficient is significant, in essence, to determine whether the I-th of the independent variable x has a significant effect on the dependent variable Y. For the two-yuan two-time polynomial regression equation, the two-yuan two-time polynomial function is transformed into a linear regression equation of five yuan. But as the number of independent variables increases, the computational amount of multivariate polynomial regression analysis increases sharply. Multivariate polynomial regression is a multi-dimensional nonlinear regression problem. [2]A model is called a unary polynomial regression model in the following form:

Polynomial regression and pipeline in Scikit-learn

Three, over-fitting and under-fitting

Iv. Why there are training datasets and test data sets

Five, learning curve

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