Definition: A decision tree is a tree structure that guides the decision-making process through a series of questions or conditions.

Visual explanation: It can be compared to the decision-making process in our daily life, where a decision is finally made through layers of screening.

The decision tree is like a wise "guiding tree". It stands in the forest of data and helps us guide the direction and find the answers we want. Imagine you are standing at an unfamiliar intersection and want to go to a specific destination but don't know where to go. At this time, if a "guiding tree" appears in front of you, what will it do?

(1) Decision node: The node that determines the next branch.

(2) Plan branch: The branch derived from the decision node represents different decision plans.

(3) Status node: A node that represents the decision result or status, which can be an intermediate result or a final result.

(4) Probability branch: Connects state nodes and represents the probability of different states occurring.

The first step is to draw a tree diagram and arrange each scheme and the various natural states of each scheme according to the known conditions.

In the second step, mark the probability and profit and loss value of each state on the probability branch.

The third step is to calculate the expected value of each plan and mark it on the state node corresponding to the plan.

The fourth step is to perform pruning (pruning is one of the ways to stop branching in a decision tree. In order to avoid overfitting, the generated tree needs to be pruned to remove some unnecessary nodes), compare the expected values ​​of each solution, and Mark it on the plan branch, and the last remaining plan with a small expected value (i.e., pruning out inferior plans) is the best plan.

Advantages: Intuitive, easy to understand, highly interpretable, and can handle numerical and categorical data.

Disadvantages: prone to overfitting, sensitive to outliers, lack of smoothness and bias towards selecting features with more eigenvalues.

In practical applications, it is necessary to choose whether to use a decision tree and how to optimize it based on specific scenarios and needs.

Scope of application: Suitable for classification and prediction problems, especially when the feature selection is clear and the data size is moderate.

Commonly used methods:

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Regression analysis is a method of statistically analyzing data. It mainly studies how one or more independent variables (also called predictor variables, explanatory variables or independent variables) affect the dependent variable (also called the response variable, explained variable or changes in the dependent variable).

Simply put, regression analysis attempts to find a mathematical relationship or model between the independent variables and the dependent variable so that the value of the dependent variable can be predicted based on the value of the independent variable.

Regression analysis is widely used in various fields, such as economics, sociology, medicine, engineering, etc. For example:

(1) Linear regression: There is a linear relationship between the independent variable and the dependent variable, which is the simplest and most commonly used type.

(2) Logistic regression: Mainly used for classification problems, predicting the probability of an event, and mapping the results of linear regression to between 0-1 to express probability.

(3) Polynomial regression: The data relationship between the independent variable and the dependent variable is not linear, but has a polynomial relationship, and the data can be fitted by polynomials.

(4) Stepwise regression: By gradually introducing or eliminating independent variables, important independent variables are automatically selected to avoid multicollinearity and select the optimal regression model.

(5) Ridge regression: An improved linear regression method that processes high-dimensional data, reduces model complexity, prevents overfitting, and is used to solve multicollinearity problems.

(1) Linear regression model: y = ax b, where a is the slope and b is the intercept.

(2) Nonlinear regression model: There is a nonlinear relationship between independent variables and dependent variables, such as exponential functions, logarithmic functions, etc.

(3) Logistic regression model: Used to predict the probability of an event occurring, such as predicting whether a user will click on an advertisement.

(4) Ridge regression model: Add regularization terms to the loss function to avoid overfitting.

(5) Principal component regression: Reduce the number of independent variables and improve model efficiency through dimensionality reduction. First perform principal component analysis on the independent variables, and then use the principal components to perform regression.

(1) Determine the independent variables and dependent variables: Clarify the questions and objectives to be studied.

(2) Collect data: Collect relevant independent variable and dependent variable data.

(3) Select regression model: Select an appropriate model based on the characteristics of the data and research objectives.

(4) Model fitting: Use data to estimate model parameters.

(5) Model evaluation: Evaluate the fitting effect and prediction ability of the model.

(6) Model application: Use models for prediction and analysis.