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Learning notes of statistical learning methods -- Chapter 1 Introduction to statistical learning methods
2022-07-05 21:25:00 【Raymond。】
Statistical learning methods learning notes -- Chapter one Introduction to statistical learning methods
- 1.1 Statistical learning
- 1.1.1 Basic steps of statistical learning
- 1.1.2 Statistical learning classification
- 1.1.3 Three elements of statistical learning method
- 1.1.4 Model evaluation and model selection
- 1.1.5 Regularization and cross validation -- Prevent over fitting
- 1.1.6 Generalization ability
- 1.1.7 Generation model and discrimination model
- 1.2 Supervised learning
1.1 Statistical learning
1.1.1 Basic steps of statistical learning
Steps to achieve statistical learning methods :
- Get a limited set of training data
- Determine the hypothetical space containing all possible models , That is, the set of learning models
- Determine the criteria for model selection , Learning strategies
- Determine the algorithm for solving the optimal model , Learning algorithm
- Choosing the best model by learning method
- Use the learned optimal model to predict and analyze new data
1.1.2 Statistical learning classification
Statistical learning includes supervised learning , Unsupervised learning , Semi supervised learning and intensive learning . Focus on supervised learning .
1.1.3 Three elements of statistical learning method
Statistical learning method = Model + Strategy + Algorithm
Model
A set of all possible mappings from input variables to output variablesStrategy
The optimal model .
How to measure the quality of the model : Loss function L(Y, f(X))( Measure the quality of a forecast ) And risk function ( The prediction of the model is good or bad in the average sense ).Algorithm
The calculation method of solving the optimal model .
1.1.4 Model evaluation and model selection
Training error and test error
Over fitting
The training error is small , The test error is large .( The noise is also studied and predicted )
1.1.5 Regularization and cross validation -- Prevent over fitting
Regularization
Add regularization term or penalty term to empirical risk , Measure the complexity of the model .Cross validation
When the data is enough , Divide the data into training sets , Verification set ( For model selection ) And test set .
1.1.6 Generalization ability
1.1.7 Generation model and discrimination model
- Generate models
Joint distribution by data learning P(X,Y), Find the conditional probability distribution P(Y|X).
Common generation models : Naive Bayes and hidden Markov model - Discriminant model
Learning decision function directly from data f(X) Or conditional probability distribution P(Y|X).
Common discriminant models :k a near neighbor , perceptron , Decision tree , Logistic regression model , Maximum entropy model , Support vector machine , Lifting method and condition random field .
1.2 Supervised learning
1.2.1 Basic concepts
- input space , Feature space and output space
Input ( Output ) Space is input ( Output ) All possible values . Each specific input is an instance , Usually represented by eigenvectors , The space where all eigenvectors exist is the eigenspace . - Classification of prediction problems
The problem that input and output are continuous variables is called regression problem .
The output variables are finite discrete variables, which is called classification problem .
The prediction problem in which both input and output variables are variable sequences is called marking problem . - Hypothetical space
The purpose of supervised learning is to learn a mapping from input to output , A map is represented by a model , The set of all mappings is called the hypothesis space . - Supervised learning model classification
It can be divided into probability models ( By conditional probability distribution P(Y|X) Express ) And non probabilistic models ( Decision function Y=f(X) Express ). The specific model is determined by the specific learning method .
1.2.2 Formalization of problems
- The process
The learning process ( Completed by the learning system ) And the prediction process ( Completed by the prediction system )
1.2.3 Application of supervised learning
Classification problem
The model is a classifier .AEC Dimension
The return question
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