Choose Regression Model Options

Choose Regression Model Type

You can use the Regression Learner app to automatically train a selection of different models on your data. Use automated training to quickly try a selection of model types, and then explore promising models interactively. To get started, try these options first

Get Started Regression Model Buttons	Description
All Quick-To-Train	Try the All Quick-To-Train button first. The app trains all model types that are typically quick to train.
All	Use the All button to train all available nonoptimizable model types. Trains every type regardless of any prior trained models. Can be time-consuming.

To learn more about automated model training, see Automated Regression Model Training.

If you want to explore models one at a time, or if you already know what model type you want, you can select individual models or train a group of the same type. To see all available regression model options, on the Regression Learner tab, click the arrow in the Model Type section to expand the list of regression models. The nonoptimizable model options in the gallery are preset starting points with different settings, suitable for a range of different regression problems. To use optimizable model options and tune model hyperparameters automatically, see Hyperparameter Optimization in Regression Learner App.

For help choosing the best model type for your problem, see the tables showing typical characteristics of different regression model types. Decide on the tradeoff you want in speed, flexibility, and interpretability. The best model type depends on your data.

Tip

To avoid overfitting, look for a less flexible model that provides sufficient accuracy. For example, look for simple models such as regression trees that are fast and easy to interpret. If the models are not accurate enough predicting the response, choose other models with higher flexibility, such as ensembles. To control flexibility, see the details for each model type.

Characteristics of Regression Model Types

Regression Model Type	Interpretability
Linear Regression Models	Easy
Regression Trees	Easy
Support Vector Machines	Easy for linear SVMs. Hard for other kernels.
Gaussian Process Regression Models	Hard
Ensembles of Trees	Hard

To read a description of each model in Regression Learner, switch to the details view in the list of all model presets.

Tip

The nonoptimizable models in the Model Type gallery are preset starting points with different settings. After you choose a model type, such as regression trees, try training all the nonoptimizable presets to see which one produces the best model with your data.

For workflow instructions, see Train Regression Models in Regression Learner App.

Categorical Predictor Support

In Regression Learner, all model types support categorical predictors.

Tip

If you have categorical predictors with many unique values, training linear models with interaction or quadratic terms and stepwise linear models can use a lot of memory. If the model fails to train, try removing these categorical predictors.

Linear Regression Models

Linear regression models have predictors that are linear in the model parameters, are easy to interpret, and are fast for making predictions. These characteristics make linear regression models popular models to try first. However, the highly constrained form of these models means that they often have low predictive accuracy. After fitting a linear regression model, try creating more flexible models, such as regression trees, and compare the results.

Tip

In the Model Type gallery, click All Linear to try each of the linear regression options and see which settings produce the best model with your data. Select the best model in the History list and try to improve that model by using feature selection and changing some advanced options.

Regression Model Type	Interpretability	Model Flexibility
Linear	Easy	Very low
Interactions Linear	Easy	Medium
Robust Linear	Easy	Very low. Less sensitive to outliers, but can be slow to train.
Stepwise Linear	Easy	Medium

Tip

For a workflow example, see Train Regression Trees Using Regression Learner App.

Advanced Linear Regression Options

Regression Learner uses the fitlm function to train Linear, Interactions Linear, and Robust Linear models. The app uses the stepwiselm function to train Stepwise Linear models.

For Linear, Interactions Linear, and Robust Linear models you can set these options:

Terms
Specify which terms to use in the linear model. You can choose from:
- Linear. A constant term and linear terms in the predictors
- Interactions. A constant term, linear terms, and interaction terms between the predictors
- Pure Quadratic. A constant term, linear terms, and terms that are purely quadratic in each of the predictors
- Quadratic. A constant term, linear terms, and quadratic terms (including interactions)
Robust option
Specify whether to use a robust objective function and make your model less sensitive to outliers. With this option, the fitting method automatically assigns lower weights to data points that are more likely to be outliers.

Stepwise linear regression starts with an initial model and systematically adds and removes terms to the model based on the explanatory power of these incrementally larger and smaller models. For Stepwise Linear models, you can set these options:

Initial terms
Specify the terms that are included in the initial model of the stepwise procedure. You can choose from Constant,Linear, Interactions, Pure Quadratic, and Quadratic.
Upper bound on terms
Specify the highest order of the terms that the stepwise procedure can add to the model. You can choose from Linear, Interactions, Pure Quadratic, and Quadratic.
Maximum number of steps
Specify the maximum number of different linear models that can be tried in the stepwise procedure. To speed up training, try reducing the maximum number of steps. Selecting a small maximum number of steps decreases your chances of finding a good model.

Tip

Regression Trees

Regression trees are easy to interpret, fast for fitting and prediction, and low on memory usage. Try to grow smaller trees with fewer larger leaves to prevent overfitting. Control the leaf size with the Minimum leaf size setting.

Tip

In the Model Type gallery, click All Trees to try each of the nonoptimizable regression tree options and see which settings produce the best model with your data. Select the best model in the History list, and try to improve that model by using feature selection and changing some advanced options.

Regression Model Type	Interpretability	Model Flexibility
Fine Tree	Easy	High Many small leaves for a highly flexible response function (Minimum leaf size is 4.)
Medium Tree	Easy	Medium Medium-sized leaves for a less flexible response function (Minimum leaf size is 12.)
Coarse Tree	Easy	Low Few large leaves for a coarse response function (Minimum leaf size is 36.)

To predict a response of a regression tree, follow the tree from the root (beginning) node down to a leaf node. The leaf node contains the value of the response.

Statistics and Machine Learning Toolbox™ trees are binary. Each step in a prediction involves checking the value of one predictor variable. For example, here is a simple regression tree

This tree predicts the response based on two predictors, x1 and x2. To make a prediction, start at the top node. At each node, check the values of the predictors to decide which branch to follow. When the branches reach a leaf node, the response is set to the value corresponding to that node.

You can visualize your regression tree model by exporting the model from the app, and then entering:

view(trainedModel.RegressionTree,'Mode','graph')

Tip

For a workflow example, see Train Regression Trees Using Regression Learner App.

Advanced Regression Tree Options

The Regression Learner app uses the fitrtree function to train regression trees. You can set these options:

Minimum leaf size
Specify the minimum number of training samples used to calculate the response of each leaf node. When you grow a regression tree, consider its simplicity and predictive power. To change the minimum leaf size, click the buttons or enter a positive integer value in the Minimum leaf size box.
- A fine tree with many small leaves is usually highly accurate on the training data. However, the tree might not show comparable accuracy on an independent test set. A very leafy tree tends to overfit, and its validation accuracy is often far lower than its training (or resubstitution) accuracy.
- In contrast, a coarse tree with fewer large leaves does not attain high training accuracy. But a coarse tree can be more robust in that its training accuracy can be near that of a representative test set.
Tip
Decrease the Minimum leaf size to create a more flexible model.
Surrogate decision splits — For missing data only.
Specify surrogate use for decision splits. If you have data with missing values, use surrogate splits to improve the accuracy of predictions.
When you set Surrogate decision splits to On, the regression tree finds at most 10 surrogate splits at each branch node. To change the number of surrogate splits, click the buttons or enter a positive integer value in the Maximum surrogates per node box.
When you set Surrogate decision splits to Find All, the regression tree finds all surrogate splits at each branch node. The Find All setting can use considerable time and memory.

Alternatively, you can let the app choose some of these model options automatically by using hyperparameter optimization. See Hyperparameter Optimization in Regression Learner App.

Support Vector Machines

You can train regression support vector machines (SVMs) in Regression Learner. Linear SVMs are easy to interpret, but can have low predictive accuracy. Nonlinear SVMs are more difficult to interpret, but can be more accurate.

Tip

In the Model Type gallery, click All SVMs to try each of the nonoptimizable SVM options and see which settings produce the best model with your data. Select the best model in the History list, and try to improve that model by using feature selection and changing some advanced options.

Regression Model Type	Interpretability	Model Flexibility
Linear SVM	Easy	Low
Quadratic SVM	Hard	Medium
Cubic SVM	Hard	Medium
Fine Gaussian SVM	Hard	High Allows rapid variations in the response function. Kernel scale is set to `sqrt(P)/4`, where `P` is the number of predictors.
Medium Gaussian SVM	Hard	Medium Gives a less flexible response function. Kernel scale is set to `sqrt(P)`.
Coarse Gaussian SVM	Hard	Low Gives a rigid response function. Kernel scale is set to `sqrt(P)*4`.

Statistics and Machine Learning Toolbox implements linear epsilon-insensitive SVM regression. This SVM ignores prediction errors that are less than some fixed number ε. The support vectors are the data points that have errors larger than ε. The function the SVM uses to predict new values depends only on the support vectors. To learn more about SVM regression, see Understanding Support Vector Machine Regression.

Tip

For a workflow example, see Train Regression Trees Using Regression Learner App.

Advanced SVM Options

Regression Learner uses the fitrsvm function to train SVM regression models.

You can set these options in the app:

Kernel function
The kernel function determines the nonlinear transformation applied to the data before the SVM is trained. You can choose from:
- Gaussian or Radial Basis Function (RBF) kernel
- Linear kernel, easiest to interpret
- Quadratic kernel
- Cubic kernel
Box constraint mode
The box constraint controls the penalty imposed on observations with large residuals. A larger box constraint gives a more flexible model. A smaller value gives a more rigid model, less sensitive to overfitting.
When Box constraint mode is set to Auto, the app uses a heuristic procedure to select the box constraint.
Try to fine-tune your model by specifying the box constraint manually. Set Box constraint mode to Manual and specify a value. Change the value by clicking the buttons or entering a positive scalar value in the Manual box constraint box. The app automatically preselects a reasonable value for you. Try to increase or decrease this value slightly and see if this improves your model.
Tip
Increase the box constraint value to create a more flexible model.
Epsilon mode
Prediction errors that are smaller than the epsilon (ε) value are ignored and treated as equal to zero. A smaller epsilon value gives a more flexible model.
When Epsilon mode is set to Auto, the app uses a heuristic procedure to select the kernel scale.
Try to fine-tune your model by specifying the epsilon value manually. Set Epsilon mode to Manual and specify a value. Change the value by clicking the buttons or entering a positive scalar value in the Manual epsilon box. The app automatically preselects a reasonable value for you. Try to increase or decrease this value slightly and see if this improves your model.
Tip
Decrease the epsilon value to create a more flexible model.
Kernel scale mode
The kernel scale controls the scale of the predictors on which the kernel varies significantly. A smaller kernel scale gives a more flexible model.
When Kernel scale mode is set to Auto, the app uses a heuristic procedure to select the kernel scale.
Try to fine-tune your model by specifying the kernel scale manually. Set Kernel scale mode to Manual and specify a value. Change the value by clicking the buttons or entering a positive scalar value in the Manual kernel scale box. The app automatically preselects a reasonable value for you. Try to increase or decrease this value slightly and see if this improves your model.
Tip
Decrease the kernel scale value to create a more flexible model.
Standardize
Standardizing the predictors transforms them so that they have mean 0 and standard deviation 1. Standardizing removes the dependence on arbitrary scales in the predictors and generally improves performance.

Alternatively, you can let the app choose some of these model options automatically by using hyperparameter optimization. See Hyperparameter Optimization in Regression Learner App.

Gaussian Process Regression Models

You can train Gaussian process regression (GPR) models in Regression Learner. GPR models are often highly accurate, but can be difficult to interpret.

Tip

In the Model Type gallery, click All GPR Models to try each of the nonoptimizable GPR model options and see which settings produce the best model with your data. Select the best model in the History list, and try to improve that model by using feature selection and changing some advanced options.

Regression Model Type	Interpretability	Model Flexibility
Rational Quadratic	Hard	Automatic
Squared Exponential	Hard	Automatic
Matern 5/2	Hard	Automatic
Exponential	Hard	Automatic

In Gaussian process regression, the response is modeled using a probability distribution over a space of functions. The flexibility of the presets in the Model Type gallery is automatically chosen to give a small training error and, simultaneously, protection against overfitting. To learn more about Gaussian process regression, see Gaussian Process Regression Models.

Tip

For a workflow example, see Train Regression Trees Using Regression Learner App.

Advanced Gaussian Process Regression Options

Regression Learner uses the fitrgp function to train GPR models.

You can set these options in the app:

Basis function
The basis function specifies the form of the prior mean function of the Gaussian process regression model. You can choose from Zero, Constant, and Linear. Try to choose a different basis function and see if this improves your model.
Kernel function
The kernel function determines the correlation in the response as a function of the distance between the predictor values. You can choose from Rational Quadratic, Squared Exponential, Matern 5/2, Matern 3/2, and Exponential.
To learn more about kernel functions, see Kernel (Covariance) Function Options.
Use isotropic kernel
If you use an isotropic kernel, the correlation length scales are the same for all the predictors. With a nonisotropic kernel, each predictor variable has its own separate correlation length scale.
Using a nonisotropic kernel can improve the accuracy of your model, but can make the model slow to fit.
To learn more about nonisotropic kernels, see Kernel (Covariance) Function Options.
Kernel mode
You can manually specify initial values of the kernel parameters Kernel scale and Signal standard deviation. The signal standard deviation is the prior standard deviation of the response values. By default the app locally optimizes the kernel parameters starting from the initial values. To use fixed kernel parameters, clear the Optimize numeric parameters check box in the advanced options.
When Kernel scale mode is set to Auto, the app uses a heuristic procedure to select the initial kernel parameters.
If you set Kernel scale mode to Manual, you can specify the initial values. Click the buttons or enter a positive scalar value in the Kernel scale box and the Signal standard deviation box.
If you clear the Use isotropic kernel check box, you cannot set initial kernel parameters manually.
Sigma mode
You can specify manually the initial value of the observation noise standard deviation Sigma. By default the app optimizes the observation noise standard deviation, starting from the initial value. To use fixed kernel parameters, clear the Optimize numeric parameters check box in the advanced options.
When Sigma mode is set to Auto, the app uses a heuristic procedure to select the initial observation noise standard deviation.
If you set Sigma mode to Manual, you can specify the initial values. Click the buttons or enter a positive scalar value in the Sigma box.
Standardize
Standardizing the predictors transforms them so that they have mean 0 and standard deviation 1. Standardizing removes the dependence on arbitrary scales in the predictors and generally improves performance.
Optimize numeric parameters
With this option, the app automatically optimizes numeric parameters of the GPR model. The optimized parameters are the coefficients of the Basis function, the kernel parameters Kernel scale and Signal standard deviation, and the observation noise standard deviation Sigma.

Alternatively, you can let the app choose some of these model options automatically by using hyperparameter optimization. See Hyperparameter Optimization in Regression Learner App.

Ensembles of Trees

You can train ensembles of regression trees in Regression Learner. Ensemble models combine results from many weak learners into one high-quality ensemble model.

Tip

In the Model Type gallery, click All Ensembles to try each of the nonoptimizable ensemble options and see which settings produce the best model with your data. Select the best model in the History list, and try to improve that model by using feature selection and changing some advanced options.

Regression Model Type	Interpretability	Ensemble Method	Model Flexibility
Boosted Trees	Hard	Least-squares boosting (`LSBoost`) with regression tree learners.	Medium to high
Bagged Trees	Hard	Bootstrap aggregating or bagging, with regression tree learners.	High

Tip

For a workflow example, see Train Regression Trees Using Regression Learner App.

Advanced Ensemble Options

Regression Learner uses the fitrensemble function to train ensemble models. You can set these options:

Minimum leaf size
Specify the minimum number of training samples used to calculate the response of each leaf node. When you grow a regression tree, consider its simplicity and predictive power. To change the minimum leaf size, click the buttons or enter a positive integer value in the Minimum leaf size box.
- A fine tree with many small leaves is usually highly accurate on the training data. However, the tree might not show comparable accuracy on an independent test set. A very leafy tree tends to overfit, and its validation accuracy is often far lower than its training (or resubstitution) accuracy.
- In contrast, a coarse tree with fewer large leaves does not attain high training accuracy. But a coarse tree can be more robust in that its training accuracy can be near that of a representative test set.
Tip
Decrease the Minimum leaf size to create a more flexible model.
Number of learners
Try changing the number of learners to see if you can improve the model. Many learners can produce high accuracy, but can be time consuming to fit.

Tip
Increase the Number of learners to create a more flexible model.
Learning rate
For boosted trees, specify the learning rate for shrinkage. If you set the learning rate to less than 1, the ensemble requires more learning iterations but often achieves better accuracy. 0.1 is a popular initial choice.

Alternatively, you can let the app choose some of these model options automatically by using hyperparameter optimization. See Hyperparameter Optimization in Regression Learner App.

Documentation