There are three main categories of artificial intelligence machine learning: 1) classification; 2) regression; 3) clustering. Today we focus on the regression model (RM).

Regression is not a single supervised learning technique, but the entire category to which many technologies belong. The purpose of the regression is to predict numerical target values, such as forecasting commodity prices, PM2.5 for the next few days, and so on. The most straightforward way is to write a calculation formula for the target value based on the input, which is called the regression equation (regressionequaTIon). The process of finding the regression coefficients in the regression equation is regression. Regression is an approximation of the true value. Regression is one of the most powerful algorithms in statistics.

Regression concept:

Regression is a mathematical term that refers to a statistical analysis of the relationship between a set of random variables (Y1, Y2, ..., Yi) and another set of (X1, X2, ..., Xk) variables, also known as multiple regression analysis. Among them, X1, X2, ..., Xk are independent variables, Y1, Y2, ..., and Yi are dependent variables.

Regression model:

Regression Model A mathematical model that quantitatively describes statistical relationships. It is a predictive modeling technique that studies the relationship between dependent variables (targets) and independent variables (predictors). This technique is commonly used for predictive analysis, time series models, and causal relationships between variables.

regression analysis:

The important basis or method of the regression model is regression analysis. Regression analysis is a computational method and theory for studying the specific dependence of a variable (interpreted variable) on another variable (interpreted variable) and is an important tool for modeling and analyzing data. Regression analysis is to estimate the parameters of unknown formulas with known samples, give a set of points D, use a function to fit the set of points, and minimize the error between the set of points and the fitted function.

Regression classification:

In statistics, regression analysis refers to a statistical analysis method that determines the quantitative relationship between two or more variables. Regression analysis is divided into one-way regression and multiple regression analysis according to the variables involved; according to the number of dependent variables, it can be divided into simple regression analysis and multiple regression analysis; according to the relationship between independent variables and dependent variables, it can be divided into linear Regression analysis and nonlinear regression analysis.

Common regression types are: linear regression, curve regression, logistic regression, and so on.

Linear regression:

If the fitting function is a linear function with unknown parameters, that is, the dependent variable and the independent variable are linear, it is called linear regression.

Through a lot of training, you can get a model that works best with the data. You can use some algorithms (such as least squares, gradient descent, etc.) and tools (SPSS) to train the applicable linear regression model faster and better. The essence is to solve the weight θ of each feature independent variable.

In the training process, feature selection, fitting optimization, etc. need to be considered.

The ultimate goal is to determine each weight (parameter) θ or to approximate the real weight (parameter) θ by an algorithm.

It should be noted that linear regression does not refer to the linearity of the sample. The sample can be nonlinear, but refers to the linearity of the parameter θ.

Linear regression problems: Under-fitting, non-full-rank matrix problems, etc. may occur.

Solution: To solve the under-fitting problem, local weighted linear regression LWLR (Locally Weighted Linear Regression) can be used. To solve the problem of non-full rank matrices, ridge regression (RR), Lasso method, forward stepwise regression, etc. can be used.

Algorithm advantages:

1) One of the most interpretable machine learning algorithms, understanding and interpretation are very intuitive;

2) Easy to use because minimal tuning is required;

3) Fast operation and high efficiency;

4) The most widely used machine learning technology.

Nonlinear regression:

If the fitting function is a nonlinear function with unknown parameters, it is called nonlinear or curve regression. The solution of nonlinear functions can be generally divided into two categories: nonlinear transformation into linear and non-transformable into linear.

1) Transform into linear: the basic method of dealing with nonlinear regression. By nonlinear transformation, the nonlinear regression is linearized and then processed by linear regression. Linear iterative methods, piecewise regression methods, iterative least squares methods, etc. are generally used.

2) Cannot be transformed into linear: Based on the least squares method of regression problem, a mathematical solution to the unconstrained extremum problem in the optimization method is applied to the extremum problem with the smallest squared error. The algorithm is relatively simple, and the convergence effect and convergence speed are ideal.

Common nonlinear regression models: 1) hyperbolic model; 2) power function model; 3) exponential function model; 4) logarithmic function model; 5) polynomial model.

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