Mathematical modeling (i)--Mathematical Model Overview _ machine learning

I. Model 1. Prototype and model prototype refer to the actual object that people care about, study or engage in production and management in the real world.        A model is a prototype substitute that constructs a part of the prototype's information for a specific purpose, abbreviated and refining it. The model can be divided into the material model (image model) and the ideal model (abstract model) according to the mode of replacing the prototype.        The former includes visual model, physical model and so on, the latter includes thinking model, symbolic model, mathematical model and so on. A mathematical model can be described as a mathematical structure for a particular object in the real world that, for a particular purpose, makes some necessary simplification assumptions, using appropriate mathematical tools, according to specific intrinsic laws. 2. Modeling methods can be divided into two types: mechanism analysis and test analysis. Mechanism analysis is based on the understanding of the characteristics of the objective things, to find out the number of internal mechanism of the law, the model is often clear physical or practical significance. Test analysis is to treat the object as a "black box" system, through the system input, output data measurement and statistical analysis, according to certain criteria to find the best model of data fitting. 3. Modeling steps according to the mechanism analysis method of modeling steps are as follows 4. In the process of modeling, the mathematical modeling process is divided into several stages, such as formulation, solution, explanation and verification, and the cycle of the mathematical model to the real object is realized through these stages.
5. Model classification According to the mathematical method of establishing the model: Elementary model, geometrical model, statistical regression model, mathematical programming model and so on.         According to the model's performance characteristics: Deterministic model and stochastic model, static model and dynamic model, linear model and non-linear model, discrete model and continuous model.         According to the modeling purpose: Describe the model, forecast model, optimization model, decision model and so on. According to the understanding of the model structure: White box model, gray box model, and black box model. Two. System identification in scientific research and engineering practice, experiment and observation is one of the important means.         The result of the experiment is the data of input and output, and the mathematical model is established by the system identification.         System identification is: Select a system based on input and output data in a specified class of systems, and this system is equivalent to the practical system studied. The general steps of system identification are: Selection of ① model class, ② experiment design, ③ parameter estimation, ④ model verification and validation.
Three. Machine Learning machine learning is to transform the disordered data into useful information, its main task is to classify, which involves several key concepts: ① Training set is used for training machine learning algorithm data sample geometry; ② target variable is the predictive result of machine learning algorithm, in the classification algorithm,         The result type of the target variable is usually a nominal type, and in the regression algorithm it is usually continuous; ③ knowledge representation can take the form of a rule set, or it can be in the form of a probability distribution. Another task of machine learning is regression, which is mainly used to predict numerical data. Classification and regression belong to supervised learning because such algorithms must know what to predict, that is, the classification information of the target variable. The corresponding to supervised learning is unsupervised learning, at which time there is no category information and no target value is given. In unsupervised learning, the process of dividing data sets into multiple classes consisting of similar objects is called clustering; the process of looking for descriptive data statistics is called density estimation. Machine learning algorithms for performing classification, regression, clustering, and density estimation
The steps of machine learning program design: ① Collect data, ② prepare input data, ③ analysis input data, ④ training algorithm, ⑤ test algorithm, ⑥ use algorithm.
Reference documents: 1. Mathematical Model (fourth edition). Kang Qiyuan 2. System modeling and identification. Wang Xiufeng 3. Machine Learning (Nineth edition)