In the process of data analysis and modeling, choosing the appropriate fitting technique is an important step to enhance the accuracy of the model. This article will introduce several common fitting techniques in detail, including linear and polynomial fitting, special curve fitting, and machine learning models.
1.Linear and Polynomial Fitting
Linear Fitting: Suitable for data with linear relationships, using a simple first-degree function.
Polynomial Fitting: Suitable for more complex nonlinear relationships by selecting an appropriate polynomial degree.
--------------------------
Data Visualization Examples: 2D Data Table-Simple Linear Regression Analysis
(Click to view AI+Python_Data Visualization Examples)
2.Exponential, Logarithmic, and Power Law
Exponential Fitting: Deals with data with exponential relationships, such as financial growth and decay processes.
Logarithmic Fitting: Used for data with logarithmic relationships, can linearize nonlinear relationships.
Power Law Fitting: Commonly used for natural phenomena, like landforms and economic distribution.
--------------------------
Data Visualization Examples: 2D Data Table-Volcano Plot
(Click to view AI+Python_Data Visualization Examples)
3.Special Curve Fitting
Logistic Fitting: Suitable for data with S-shaped curves, such as population growth.
Sine Fitting: Handles periodic data, commonly seen in signal processing.
Gaussian Curve Fitting: Suitable for data with normal distribution characteristics, such as measurement errors and natural phenomenon distributions.
--------------------------
Data Visualization Examples: 2D Data Table-Simple Logistic Regression
(Click to view AI+Python_Data Visualization Examples)
4.Piecewise, Spline, and Smoothing
Piecewise Linear Fitting: Handles segments of data with different linear characteristics.
Spline Interpolation: Connects multiple polynomial segments to ensure smooth transitions.
Smoothing Spline: Adjusts the flexibility of the fitting through smoothing parameters.
--------------------------
Data Visualization Examples: 2D Table-Standard Curve Analysis Interpolation
(Click to view AI+Python_Data Visualization Examples)
5.Machine Learning and Advanced Models
Nonlinear Regression: Suitable for complex nonlinear relationships.
Machine Learning Regression: Includes decision trees, random forests, SVR, neural networks, suitable for high-dimensional complex data.
Mixed Effects Model: Used for multilevel data structures or modeling random effects.
--------------------------
Data Visualization Examples: 2D Data Table-Nonlinear Regression Analysis
(Click to view AI+Python_Data Visualization Examples)
6.Regularization and Robustness
Ridge, Lasso, Elastic Net Regression: Use regularization to control model complexity and prevent overfitting.
Robust Regression: Insensitive to outliers, suitable for data with outliers.
7.Time Series and Hidden State Models
Moving Average: Smooths time series data, removing short-term fluctuations.
Hidden Markov Model: Analyzes time series with hidden states.
--------------------------
Data Visualization Examples: Time Series Analysis (ARIMA)
(Click to view AI+Python_Data Visualization Examples)
8.Bayesian and Nonparametric Methods
Bayesian Fitting: Uses Bayesian updating of parameter probability distribution to handle uncertainty.
Kernel Regression: A nonparametric method, suitable for analyzing local trends.
Locally Weighted Regression: Applies weighted linear regression locally to fit the data.
9.High-Dimensional and Covariate Analysis
Principal Component Regression, Partial Least Squares Regression: Handle high-dimensional data and collinearity problems.
Analysis of Covariance (ANCOVA): Combines regression and variance analysis to describe the relationship between the dependent variable and covariates.
10.Regression Under Special Conditions
Quantile Regression: Analyzes specific quantiles of data distribution.
Nonlinear Least Squares: Deals with complex nonlinear relationships by minimizing residuals to adjust parameters.
Generalized Additive Models (GAMs): The response variable is the sum of smooth functions of several predictors.
These are some common fitting models introduced. Thank you for reading this installment.
About Bayeslab
Bayeslab: Website
The AI First Data Workbench
X: @BayeslabAI
Documents:
https://bayeslab.gitbook.io/docs
Blogs:
