resubPredict

Predict response of regression tree by resubstitution

Syntax

Yfit = resubPredict(tree)

Yfit = resubPredict(tree,Subtrees=subtrees)

[Yfit,node] = resubPredict(___)

Description

Yfit = resubPredict(tree) returns a vector of tree.X elements containing the responses predicted by tree for the data tree.X. Yfit contains the predictions of tree on the data used by fitrtree to create tree.

Yfit = resubPredict(tree,Subtrees=subtrees) also prunes tree to the level specified by subtrees, before predicting responses.

[Yfit,node] = resubPredict(___) also returns the node numbers of tree for the resubstituted data, using any of the input argument combinations in the previous syntaxes.

Examples

Compute the In-Sample MSE

Load the carsmall data set. Consider Displacement, Horsepower, and Weight as predictors of the response MPG.

load carsmall
X = [Displacement Horsepower Weight];

Grow a regression tree using all observations.

Mdl = fitrtree(X,MPG);

Compute the resubstitution MSE.

Yfit = resubPredict(Mdl);
mean((Yfit - Mdl.Y).^2)

ans = 
4.8952

You can get the same result using resubLoss.

resubLoss(Mdl)

ans = 
4.8952

Estimate In-Sample Responses for Each Subtree

Load the carsmall data set. Consider Weight as a predictor of the response MPG.

load carsmall
idxNaN = isnan(MPG + Weight);
X = Weight(~idxNaN);
Y = MPG(~idxNaN);
n = numel(X);

Grow a regression tree using all observations.

Mdl = fitrtree(X,Y);

Compute resubstitution fitted values for the subtrees at several pruning levels.

m = max(Mdl.PruneList);
pruneLevels = 1:4:m; % Pruning levels to consider
z = numel(pruneLevels);
Yfit = resubPredict(Mdl,Subtrees=pruneLevels);

Yfit is an n-by-z matrix of fitted values in which the rows correspond to observations and the columns correspond to a subtree.

Plot several columns of Yfit and Y against X.

sortDat = sortrows([X Y Yfit],1); % Sort all data with respect to X
plot(repmat(sortDat(:,1),1,size(Yfit,2)+1),sortDat(:,2:end)) % Vectorize for efficiency
lev = num2str((pruneLevels)',"Level %d MPG");
legend(["Observed MPG"; lev])
title("In-Sample Fitted Responses")
xlabel("Weight (lbs)")
ylabel("MPG")
h = findobj(gcf);
set(h(4:end),LineWidth=3) % Widen all lines

The values of Yfit for lower pruning levels tend to follow the data more closely than higher levels. Higher pruning levels tend to be flat for large X intervals.

Input Arguments

tree — Regression tree model

RegressionTree model object

Regression tree model, specified as a RegressionTree model object trained with fitrtree.

subtrees — Pruning level

0 (default) | vector of nonnegative integers | "all"

Pruning level, specified as a vector of nonnegative integers in ascending order or "all".

If you specify a vector, then all elements must be at least 0 and at most max(tree.PruneList). 0 indicates the full, unpruned tree, and max(tree.PruneList) indicates the completely pruned tree (in other words, just the root node).

If you specify "all", then resubPredict operates on all subtrees (in other words, the entire pruning sequence). This specification is equivalent to using 0:max(tree.PruneList).

resubPredict prunes tree to each level specified by subtrees, and then estimates the corresponding output arguments. The size of subtrees determines the size of some output arguments.

For the function to invoke subtrees, the properties PruneList and PruneAlpha of tree must be nonempty. In other words, grow tree by setting Prune="on" when you use fitrtree, or by pruning tree using prune.

Data Types: single | double | char | string

Output Arguments

Yfit — Predicted resubstitution response values

numeric vector | numeric matrix

Predicted resubstitution response values for the training data, returned as a numeric vector or a numeric matrix. Yfit has the same data type as the training response data tree.Y.

If subtrees is a numeric scalar, then Yfit is returned as a numeric column vector. Otherwise, Yfit is returned as a numeric matrix with m columns, where m is the number of subtrees. Each column represents the predictions of the corresponding subtree.

node — Node numbers

numeric column vector | numeric matrix

Node numbers for the predicted classes, returned as a numeric column vector or numeric matrix.

If subtrees is a scalar or is not specified, then resubPredict returns node as a numeric column vector with n rows, the same number of rows as tree.X.

If subtrees contains m > 1 entries, then node is an n-by-m numeric matrix. Each column represents the node predictions of the corresponding subtree.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2011a