# partialDependence

Compute partial dependence

## Description

example

pd = partialDependence(RegressionMdl,Vars) computes the partial dependence pd between the predictor variables listed in Vars and the responses predicted by using the regression model RegressionMdl, which contains predictor data.

example

pd = partialDependence(ClassificationMdl,Vars,Labels) computes the partial dependence pd between the predictor variables listed in Vars and the scores for the classes specified in Labels by using the classification model ClassificationMdl, which contains predictor data.

pd = partialDependence(___,Data) uses new predictor data in Data. You can specify Data in addition to any of the input argument combinations in the previous syntaxes.

example

pd = partialDependence(fun,Vars,Data) computes the partial dependence between the predictor variables listed in Vars and the outputs returned by the custom model fun, using the predictor data Data.

example

pd = partialDependence(___,Name,Value) uses additional options specified by one or more name-value arguments. For example, if you specify "UseParallel","true", the partialDependence function uses parallel computing to perform the partial dependence calculations.

[pd,x,y] = partialDependence(___) also returns x and y, which contain the query points of the first and second predictor variables in Vars, respectively. If you specify one variable in Vars, then partialDependence returns an empty matrix ([]) for y.

## Examples

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Train a naive Bayes classification model with the fisheriris data set, and compute partial dependence values that show the relationship between the predictor variable and the predicted scores (posterior probabilities) for multiple classes.

Load the fisheriris data set, which contains species (species) and measurements (meas) on sepal length, sepal width, petal length, and petal width for 150 iris specimens. The data set contains 50 specimens from each of three species: setosa, versicolor, and virginica.

Train a naive Bayes classification model with species as the response and meas as predictors.

Mdl = fitcnb(meas,species,"PredictorNames",["Sepal Length","Sepal Width","Petal Length","Petal Width"]);

Compute partial dependence values on the third predictor variable (petal length) of the scores predicted by Mdl for all three classes of species. Specify the class labels by using the ClassNames property of Mdl.

[pd,x] = partialDependence(Mdl,3,Mdl.ClassNames);

pd contains the partial dependence values for the query points x. You can plot the computed partial dependence values by using plotting functions such as plot and bar. Plot pd against x by using the bar function.

bar(x,pd)
legend(Mdl.ClassNames)
xlabel("Petal Length")
ylabel("Scores")
title("Partial Dependence Plot")

According to this model, the probability of virginica increases with petal length. The probability of setosa is about 0.33, from where petal length is 0 to around 2.5, and then the probability drops to almost 0.

Alternatively, you can use the plotPartialDependence function to compute and plot partial dependence values.

plotPartialDependence(Mdl,3,Mdl.ClassNames)

Train an ensemble of classification models and compute partial dependence values on two variables for multiple classes. Then plot the partial dependence values for each class.

Load the census1994 data set, which contains US yearly salary data, categorized as <=50K or >50K, and several demographic variables.

Extract a subset of variables to analyze from the table adultdata.

X = adultdata(1:500,["age","workClass","education_num","marital_status","race", ...
"sex","capital_gain","capital_loss","hours_per_week","salary"]);

Train a random forest of classification trees by using fitcensemble and specifying Method as "Bag". For reproducibility, use a template of trees created by using templateTree with the Reproducible option.

rng("default")
t = templateTree("Reproducible",true);
Mdl = fitcensemble(X,"salary","Method","Bag","Learners",t);

Inspect the class names in Mdl.

Mdl.ClassNames
ans = 2x1 categorical
<=50K
>50K

Compute partial dependence values of the scores on the predictors age and education_num for both classes (<=50K and >50K). Specify the number of observations to sample as 100.

[pd,x,y] = partialDependence(Mdl,["age","education_num"],Mdl.ClassNames,"NumObservationsToSample",100);

Create a surface plot of the partial dependence values for the first class (<=50K) by using the surf function.

figure
surf(x,y,squeeze(pd(1,:,:)))
xlabel("age")
ylabel("education\_num")
zlabel("Score of class <=50K")
title("Partial Dependence Plot")
view([130 30]) % Modify the viewing angle

Create a surface plot of the partial dependence values for the second class (>50K).

figure
surf(x,y,squeeze(pd(2,:,:)))
xlabel("age")
ylabel("education\_num")
zlabel("Score of class >50K")
title("Partial Dependence Plot")
view([130 30]) % Modify the viewing angle

The two plots show different partial dependence patterns depending on the class.

Train a support vector machine (SVM) regression model using the carsmall data set, and compute the partial dependence on two predictor variables. Then, create a figure that shows the partial dependence on the two variables along with the histogram on each variable.

Load the carsmall data set.

Create a table that contains Weight, Cylinders, Displacement, and Horsepower.

Tbl = table(Weight,Cylinders,Displacement,Horsepower);

Train an SVM regression model using the predictor variables in Tbl and the response variable MPG. Use a Gaussian kernel function with an automatic kernel scale.

Mdl = fitrsvm(Tbl,MPG,"ResponseName","MPG", ...
"CategoricalPredictors","Cylinders","Standardize",true, ...
"KernelFunction","gaussian","KernelScale","auto");

Compute the partial dependence of the predicted response (MPG) on the predictor variables Weight and Horsepower. Specify query points to compute the partial dependence by using the QueryPoints name-value argument.

numPoints = 10;
ptX = linspace(min(Weight),max(Weight),numPoints)';
ptY = linspace(min(Horsepower),max(Horsepower),numPoints)';
[pd,x,y] = partialDependence(Mdl,["Weight","Horsepower"],"QueryPoints",[ptX ptY]);

Create a figure that contains a 5-by-5 tiled chart layout. Plot the partial dependence on the two variables by using the imagesc function. Then draw the histogram for each variable by using the histogram function. Specify the edges of the histograms so that the centers of the histogram bars align with the query points. Change the axes properties to align the axes of the plots.

t = tiledlayout(5,5,"TileSpacing","compact");

ax1 = nexttile(2,[4,4]);
imagesc(x,y,pd)
title("Partial Dependence Plot")
colorbar("eastoutside")
ax1.YDir = "normal";

ax2 = nexttile(22,[1,4]);
dX = diff(ptX(1:2));
edgeX = [ptX-dX/2;ptX(end)+dX];
histogram(Weight,edgeX);
xlabel("Weight")
xlim(ax1.XLim);

ax3 = nexttile(1,[4,1]);
dY = diff(ptY(1:2));
edgeY = [ptY-dY/2;ptY(end)+dY];
histogram(Horsepower,edgeY)
xlabel("Horsepower")
xlim(ax1.YLim);
ax3.XDir = "reverse";
camroll(-90)

Each element of pd specifies the color for one pixel of the image plot. The histograms aligned with the axes of the image show the distribution of the predictors.

Compute the partial dependence of label scores on predictor variables for a SemiSupervisedSelfTrainingModel object. You cannot pass a SemiSupervisedSelfTrainingModel object directly to the partialDependence function. Instead, define a custom function that returns label scores for the object, and then pass the function to partialDependence.

Randomly generate 15 observations of labeled data, with five observations in each of three classes.

rng("default") % For reproducibility
labeledX = [randn(5,2)*0.25 + ones(5,2);
randn(5,2)*0.25 - ones(5,2);
randn(5,2)*0.5];
Y = [ones(5,1); ones(5,1)*2; ones(5,1)*3];

Randomly generate 300 additional observations of unlabeled data, with 100 observations per class.

unlabeledX = [randn(100,2)*0.25 + ones(100,2);
randn(100,2)*0.25 - ones(100,2);
randn(100,2)*0.5];

Fit labels to the unlabeled data by using a semi-supervised self-training method. The function fitsemiself returns a SemiSupervisedSelfTrainingModel object.

Mdl = fitsemiself(labeledX,Y,unlabeledX);

Define the custom function myLabelScores, which returns label scores computed by the predict function of SemiSupervisedSelfTrainingModel; the custom function definition appears at the end of this example.

Compute the partial dependence of the scores for unlabeledX on each variable for all classes. partialDependence accepts a custom model in the form of a function handle. The function represented by the function handle must accept predictor data and return a column vector or matrix with one row for each observation. Specify the custom model as @(X)myLabelScores(Mdl,X) so that the custom function uses the trained model Mdl and accepts predictor data.

[pd1,x1] = partialDependence(@(X)myLabelScores(Mdl,X),1,unlabeledX);
[pd2,x2] = partialDependence(@(X)myLabelScores(Mdl,X),2,unlabeledX);

You can plot the computed partial dependence values by using plotting functions such as plot and bar. Alternatively, you can use the plotPartialDependence function to compute and plot partial dependence values.

Create partial dependence plots for the first variable and all classes.

plotPartialDependence(@(X)myLabelScores(Mdl,X),1,unlabeledX)
xlabel("1st Variable of unlabeledX")
ylabel("Scores")
legend("Class 1","Class 2","Class 3")

Custom Function myLabelScores

function scores = myLabelScores(Mdl,X)
[~,scores] = predict(Mdl,X);
end

## Input Arguments

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Regression model, specified as a full or compact regression model object, as given in the following tables of supported models.

ModelFull or Compact Model Object
Generalized linear modelGeneralizedLinearModel, CompactGeneralizedLinearModel
Generalized linear mixed-effect modelGeneralizedLinearMixedModel
Linear regressionLinearModel, CompactLinearModel
Linear mixed-effect modelLinearMixedModel
Nonlinear regressionNonLinearModel
Ensemble of regression modelsRegressionEnsemble, RegressionBaggedEnsemble, CompactRegressionEnsemble
Generalized additive model (GAM)RegressionGAM, CompactRegressionGAM
Gaussian process regressionRegressionGP, CompactRegressionGP
Gaussian kernel regression model using random feature expansionRegressionKernel
Linear regression for high-dimensional dataRegressionLinear
Neural network regression modelRegressionNeuralNetwork, CompactRegressionNeuralNetwork
Support vector machine (SVM) regressionRegressionSVM, CompactRegressionSVM
Regression treeRegressionTree, CompactRegressionTree
Bootstrap aggregation for ensemble of decision treesTreeBagger, CompactTreeBagger

If RegressionMdl is a model object that does not contain predictor data (for example, a compact model), you must provide the input argument Data.

partialDependence does not support a model object trained with a sparse matrix. When you train a model, use a full numeric matrix or table for predictor data where rows correspond to individual observations.

Classification model, specified as a full or compact classification model object, as given in the following tables of supported models.

ModelFull or Compact Model Object
Discriminant analysis classifierClassificationDiscriminant, CompactClassificationDiscriminant
Multiclass model for support vector machines or other classifiersClassificationECOC, CompactClassificationECOC
Ensemble of learners for classificationClassificationEnsemble, CompactClassificationEnsemble, ClassificationBaggedEnsemble
Generalized additive model (GAM)ClassificationGAM, CompactClassificationGAM
Gaussian kernel classification model using random feature expansionClassificationKernel
k-nearest neighbor classifierClassificationKNN
Linear classification modelClassificationLinear
Multiclass naive Bayes modelClassificationNaiveBayes, CompactClassificationNaiveBayes
Neural network classifierClassificationNeuralNetwork, CompactClassificationNeuralNetwork
Support vector machine (SVM) classifier for one-class and binary classificationClassificationSVM, CompactClassificationSVM
Binary decision tree for multiclass classificationClassificationTree, CompactClassificationTree
Bagged ensemble of decision treesTreeBagger, CompactTreeBagger

If ClassificationMdl is a model object that does not contain predictor data (for example, a compact model), you must provide the input argument Data.

partialDependence does not support a model object trained with a sparse matrix. When you train a model, use a full numeric matrix or table for predictor data where rows correspond to individual observations.

Custom model, specified as a function handle. The function handle fun must represent a function that accepts the predictor data Data and returns an output in the form of a column vector or matrix. Each row of the output must correspond to each observation (row) in the predictor data.

By default, partialDependence uses all output columns of fun for the partial dependence computation. You can specify which output columns to use by setting the OutputColumns name-value argument.

If the predictor data (Data) is in a table, partialDependence assumes that a variable is categorical if it is a logical vector, categorical vector, character array, string array, or cell array of character vectors. If the predictor data is a matrix, partialDependence assumes that all predictors are continuous. To identify any other predictors as categorical predictors, specify them by using the CategoricalPredictors name-value argument.

Data Types: function_handle

Predictor variables, specified as a vector of positive integers, character vector, string scalar, string array, or cell array of character vectors. You can specify one or two predictor variables, as shown in the following tables.

One Predictor Variable

ValueDescription
positive integerIndex value corresponding to the column of the predictor data.
character vector or string scalar

Name of the predictor variable. The name must match the entry in the PredictorNames property for RegressionMdl and ClassificationMdl or the variable name of Data in a table for a custom model fun.

Two Predictor Variables

ValueDescription
vector of two positive integersIndex values corresponding to the columns of the predictor data.
string array or cell array of character vectors

Names of the predictor variables. Each element in the array is the name of a predictor variable. The names must match the entries in the PredictorNames property for RegressionMdl and ClassificationMdl or the variable names of Data in a table for a custom model fun.

Example: ["x1","x3"]

Data Types: single | double | char | string | cell

Class labels, specified as a categorical or character array, logical or numeric vector, or cell array of character vectors. The values and data types in Labels must match those of the class names in the ClassNames property of ClassificationMdl (ClassificationMdl.ClassNames).

You can specify one or multiple class labels.

This argument is valid only when you specify a classification model object ClassificationMdl.

Example: ["red","blue"]

Example: ClassificationMdl.ClassNames([1 3]) specifies Labels as the first and third classes in ClassificationMdl.

Data Types: single | double | logical | char | cell | categorical

Predictor data, specified as a numeric matrix or table. Each row of Data corresponds to one observation, and each column corresponds to one variable.

For both a regression model (RegressionMdl) and a classification model (ClassificationMdl), Data must be consistent with the predictor data that trained the model, stored in either the X or Variables property.

• If you trained the model using a numeric matrix, then Data must be a numeric matrix. The variables that make up the columns of Data must have the same number and order as the predictor variables that trained the model.

• If you trained the model using a table (for example, Tbl), then Data must be a table. All predictor variables in Data must have the same variable names and data types as the names and types in Tbl. However, the column order of Data does not need to correspond to the column order of Tbl.

• Data must not be sparse.

If you specify a regression or classification model that does not contain predictor data, you must provide Data. If the model is a full model object that contains predictor data and you specify the Data argument, then partialDependence ignores the predictor data in the model and uses Data only.

If you specify a custom model fun, you must provide Data.

Data Types: single | double | table

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: partialDependence(Mdl,Vars,Data,"NumObservationsToSample",100,"UseParallel",true) computes the partial dependence values by using 100 sampled observations in Data and executing for-loop iterations in parallel.

Flag to include interaction terms of the generalized additive model (GAM) in the partial dependence computation, specified as true or false. This argument is valid only for a GAM. That is, you can specify this argument only when RegressionMdl is RegressionGAM or CompactRegressionGAM, or ClassificationMdl is ClassificationGAM or CompactClassificationGAM.

The default IncludeInteractions value is true if the model contains interaction terms. The value must be false if the model does not contain interaction terms.

Example: "IncludeInteractions",false

Data Types: logical

Flag to include an intercept term of the generalized additive model (GAM) in the partial dependence computation, specified as true or false. This argument is valid only for a GAM. That is, you can specify this argument only when RegressionMdl is RegressionGAM or CompactRegressionGAM, or ClassificationMdl is ClassificationGAM or CompactClassificationGAM.

Example: "IncludeIntercept",false

Data Types: logical

Number of observations to sample, specified as a positive integer. The default value is the number of total observations in Data or the model (RegressionMdl or ClassificationMdl). If you specify a value larger than the number of total observations, then partialDependence uses all observations.

partialDependence samples observations without replacement by using the datasample function and uses the sampled observations to compute partial dependence.

Example: "NumObservationsToSample",100

Data Types: single | double

Points to compute partial dependence for numeric predictors, specified as a numeric column vector, a numeric two-column matrix, or a cell array of two numeric column vectors.

• If you select one predictor variable in Vars, use a numeric column vector.

• If you select two predictor variables in Vars:

• Use a numeric two-column matrix to specify the same number of points for each predictor variable.

• Use a cell array of two numeric column vectors to specify a different number of points for each predictor variable.

The default value is a numeric column vector or a numeric two-column matrix, depending on the number of selected predictor variables. Each column contains 100 evenly spaced points between the minimum and maximum values of the sampled observations for the corresponding predictor variable.

You cannot modify QueryPoints for a categorical variable. The partialDependence function uses all categorical values in the selected variable.

If you select one numeric variable and one categorical variable, you can specify QueryPoints for a numeric variable by using a cell array consisting of a numeric column vector and an empty array.

Example: "QueryPoints",{pt,[]}

Data Types: single | double | cell

Flag to run in parallel, specified as true or false. If you specify "UseParallel",true, the partialDependence function executes for-loop iterations in parallel by using parfor when predicting responses or scores for each observation and averaging them. This option requires Parallel Computing Toolbox™.

Example: "UseParallel",true

Data Types: logical

Categorical predictors list for the custom model fun, specified as one of the values in this table.

ValueDescription
Vector of positive integers

Each entry in the vector is an index value indicating that the corresponding predictor is categorical. The index values are between 1 and p, where p is the number of variables in Data.

Logical vector

A true entry means that the corresponding predictor is categorical. The length of the vector is p.

Character matrixEach row of the matrix is the name of a predictor variable. The names must match the variable names of the predictor data Data in a table. Pad the names with extra blanks so each row of the character matrix has the same length.
String array or cell array of character vectorsEach element in the array is the name of a predictor variable. The names must match the variable names of the predictor data Data in a table.
"all"All predictors are categorical.

By default, if the predictor data Data is in a table, partialDependence assumes that a variable is categorical if it is a logical vector, categorical vector, character array, string array, or cell array of character vectors. If the predictor data is a matrix, partialDependence assumes that all predictors are continuous. To identify any other predictors as categorical predictors, specify them by using the CategoricalPredictors name-value argument.

This argument is valid only when you specify a custom model by using fun.

Example: "CategoricalPredictors","all"

Data Types: single | double | logical | char | string | cell

Output columns of the custom model fun to use for the partial dependence computation, specified as one of the values in this table.

ValueDescription
Vector of positive integers

Each entry in the vector is an index value indicating that partialDependence uses the corresponding output column for the partial dependence computation. The index values are between 1 and q, where q is the number of columns in the output matrix returned by the custom model fun.

Logical vector

A true entry means that partialDependence uses the corresponding output column for the partial dependence computation. The length of the vector is q.

"all"partialDependence uses all output columns for the partial dependence computation.

This argument is valid only when you specify a custom model by using fun.

Example: "OutputColumns",[1 2]

Data Types: single | double | logical | char | string

## Output Arguments

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Partial dependence values, returned as a numeric array.

The dimension of pd depends on the type of model (regression, classification or custom), number of variables specified in Vars, number of classes specified in Labels (classification model only), and number of columns specified in OutputColumns (custom model only).

For a regression model (RegressionMdl), the following conditions apply:

• If you specify two variables in Vars, pd is a numY-by-numX matrix, where numY and numX are the number of query points of the second and first variables in Vars, respectively. The value in pd(i,j) is the partial dependence value of the query point corresponding to y(i) and x(j). y(i) is the ith query point of the second predictor variable, and x(j) is the jth query point of the first predictor variable.

• If you specify one variable in Vars, pd is a 1-by-numX vector.

For a classification model (ClassificationMdl), the following conditions apply:

• If you specify two variables in Vars, pd is a num-by-numY-by-numX array, where num is the number of class labels in Labels. The value in pd(i,j,k) is the partial dependence value of the query point y(j) and x(k) for the ith class label in Labels.

• If you specify one variable in Vars, pd is a num-by-numX matrix.

• If you specify one class in Labels, pd is a numY-by-numX matrix.

• If you specify one variable and one class, pd is a 1-by-numX vector.

For a custom model (fun), the following conditions apply:

• If you specify two variables in Vars, pd is a num-by-numY-by-numX array, where num is the number of output columns in OutputColumns. The value in pd(i,j,k) is the partial dependence value of the query point y(j) and x(k) for the ith column in OutputColumns.

• If you specify one variable in Vars, pd is a num-by-numX matrix.

• If you specify one column in OutputColumns, pd is a numY-by-numX matrix.

• If you specify one variable and one column, pd is a 1-by-numX vector.

Query points of the first predictor variable in Vars, returned as a numeric or categorical column vector.

If the predictor variable is numeric, then you can specify the query points by using the QueryPoints name-value argument.

Data Types: single | double | categorical

Query points of the second predictor variable in Vars, returned as a numeric or categorical column vector. This output argument is empty ([]) if you specify only one variable in Vars.

If the predictor variable is numeric, then you can specify the query points by using the QueryPoints name-value argument.

Data Types: single | double | categorical

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### Partial Dependence for Regression Models

Partial dependence[1] represents the relationships between predictor variables and predicted responses in a trained regression model. partialDependence computes the partial dependence of predicted responses on a subset of predictor variables by marginalizing over the other variables.

Consider partial dependence on a subset XS of the whole predictor variable set X = {x1, x2, …, xm}. A subset XS includes either one variable or two variables: XS = {xS1} or XS = {xS1, xS2}. Let XC be the complementary set of XS in X. A predicted response f(X) depends on all variables in X:

f(X) = f(XS, XC).

The partial dependence of predicted responses on XS is defined by the expectation of predicted responses with respect to XC:

${f}^{S}\left({X}^{S}\right)={E}_{C}\left[f\left({X}^{S},{X}^{C}\right)\right]=\int f\left({X}^{S},{X}^{C}\right){p}_{C}\left({X}^{C}\right)d{X}^{C},$

where pC(XC) is the marginal probability of XC, that is, ${p}_{C}\left({X}^{C}\right)\approx \int p\left({X}^{S},{X}^{C}\right)d{X}^{S}$. Assuming that each observation is equally likely, and the dependence between XS and XC and the interactions of XS and XC in responses is not strong, partialDependence estimates the partial dependence by using observed predictor data as follows:

 ${f}^{S}\left({X}^{S}\right)\approx \frac{1}{N}\sum _{i=1}^{N}f\left({X}^{S},{X}_{i}{}^{C}\right),$ (1)

where N is the number of observations and Xi = (XiS, XiC) is the ith observation.

When you call the partialDependence function, you can specify a trained model (f(·)) and select variables (XS) by using the input arguments RegressionMdl and Vars, respectively. partialDependence computes the partial dependence at 100 evenly spaced points of XS or the points that you specify by using the QueryPoints name-value argument. You can specify the number (N) of observations to sample from given predictor data by using the NumObservationsToSample name-value argument.

### Partial Dependence Classification Models

In the case of classification models, partialDependence computes the partial dependence in the same way as for regression models, with one exception: instead of using the predicted responses from the model, the function uses the predicted scores for the classes specified in Labels.

### Weighted Traversal Algorithm

The weighted traversal algorithm[1] is a method to estimate partial dependence for a tree-based model. The estimated partial dependence is the weighted average of response or score values corresponding to the leaf nodes visited during the tree traversal.

Let XS be a subset of the whole variable set X and XC be the complementary set of XS in X. For each XS value to compute partial dependence, the algorithm traverses a tree from the root (beginning) node down to leaf (terminal) nodes and finds the weights of leaf nodes. The traversal starts by assigning a weight value of one at the root node. If a node splits by XS, the algorithm traverses to the appropriate child node depending on the XS value. The weight of the child node becomes the same value as its parent node. If a node splits by XC, the algorithm traverses to both child nodes. The weight of each child node becomes a value of its parent node multiplied by the fraction of observations corresponding to each child node. After completing the tree traversal, the algorithm computes the weighted average by using the assigned weights.

For an ensemble of bagged trees, the estimated partial dependence is an average of the weighted averages over the individual trees.

## Algorithms

For both a regression model (RegressionMdl) and a classification model (ClassificationMdl), partialDependence uses a predict function to predict responses or scores. partialDependence chooses the proper predict function according to the model and runs predict with its default settings. For details about each predict function, see the predict functions in the following two tables. If the specified model is a tree-based model (not including a boosted ensemble of trees), then partialDependence uses the weighted traversal algorithm instead of the predict function. For details, see Weighted Traversal Algorithm.

Regression Model Object

Model TypeFull or Compact Regression Model ObjectFunction to Predict Responses
Bootstrap aggregation for ensemble of decision treesCompactTreeBaggerpredict
Bootstrap aggregation for ensemble of decision treesTreeBaggerpredict
Ensemble of regression modelsRegressionEnsemble, RegressionBaggedEnsemble, CompactRegressionEnsemblepredict
Gaussian kernel regression model using random feature expansionRegressionKernelpredict
Gaussian process regressionRegressionGP, CompactRegressionGPpredict
Generalized additive modelRegressionGAM, CompactRegressionGAMpredict
Generalized linear mixed-effect modelGeneralizedLinearMixedModelpredict
Generalized linear modelGeneralizedLinearModel, CompactGeneralizedLinearModelpredict
Linear mixed-effect modelLinearMixedModelpredict
Linear regressionLinearModel, CompactLinearModelpredict
Linear regression for high-dimensional dataRegressionLinearpredict
Neural network regression modelRegressionNeuralNetwork, CompactRegressionNeuralNetworkpredict
Nonlinear regressionNonLinearModelpredict
Regression treeRegressionTree, CompactRegressionTreepredict
Support vector machineRegressionSVM, CompactRegressionSVMpredict

Classification Model Object

Model TypeFull or Compact Classification Model ObjectFunction to Predict Labels and Scores
Discriminant analysis classifierClassificationDiscriminant, CompactClassificationDiscriminantpredict
Multiclass model for support vector machines or other classifiersClassificationECOC, CompactClassificationECOCpredict
Ensemble of learners for classificationClassificationEnsemble, CompactClassificationEnsemble, ClassificationBaggedEnsemblepredict
Gaussian kernel classification model using random feature expansionClassificationKernelpredict
Generalized additive modelClassificationGAM, CompactClassificationGAMpredict
k-nearest neighbor modelClassificationKNNpredict
Linear classification modelClassificationLinearpredict
Naive Bayes modelClassificationNaiveBayes, CompactClassificationNaiveBayespredict
Neural network classifierClassificationNeuralNetwork, CompactClassificationNeuralNetworkpredict
Support vector machine for one-class and binary classificationClassificationSVM, CompactClassificationSVMpredict
Binary decision tree for multiclass classificationClassificationTree, CompactClassificationTreepredict
Bagged ensemble of decision treesTreeBagger, CompactTreeBaggerpredict

## References

[1] Friedman, Jerome. H. “Greedy Function Approximation: A Gradient Boosting Machine.” The Annals of Statistics 29, no. 5 (2001): 1189-1232.

[2] Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learning. New York, NY: Springer New York, 2009.

## Version History

Introduced in R2020b