Predict Out-of-Sample Responses of Subtrees
This example shows how to predict out-of-sample responses of regression trees, and then plot the results.
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);
Partition the data into training (50%) and validation (50%) sets.
rng(1) % For reproducibility idxTrn = false(n,1); idxTrn(randsample(n,round(0.5*n))) = true; % Training set logical indices idxVal = idxTrn == false; % Validation set logical indices
Grow a regression tree using the training observations.
Mdl = fitrtree(X(idxTrn),Y(idxTrn)); view(Mdl,'Mode','graph')
Compute fitted values of the validation observations for each of several subtrees.
m = max(Mdl.PruneList); pruneLevels = 0:2:m; % Pruning levels to consider z = numel(pruneLevels); Yfit = predict(Mdl,X(idxVal),'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 Yfit
and Y
against X
.
figure; sortDat = sortrows([X(idxVal) Y(idxVal) Yfit],1); % Sort all data with respect to X plot(sortDat(:,1),sortDat(:,2),'*'); hold on; plot(repmat(sortDat(:,1),1,size(Yfit,2)),sortDat(:,3:end)); lev = cellstr(num2str((pruneLevels)','Level %d MPG')); legend(['Observed MPG'; lev]) title 'Out-of-Sample Predictions' xlabel 'Weight (lbs)'; ylabel 'MPG'; h = findobj(gcf); axis tight; 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.