resubPredict
Classify observations in classification tree by resubstitution
Syntax
Description
Examples
Compute Number of Misclassified Observations
Find the total number of misclassifications of the Fisher iris data for a classification tree.
load fisheriris tree = fitctree(meas,species); Ypredict = resubPredict(tree); % The predictions Ysame = strcmp(Ypredict,species); % True when == sum(~Ysame) % How many are different?
ans = 3
Compare In-Sample Posterior Probabilities for Each Subtree
Load Fisher's iris data set. Partition the data into training (50%)
load fisheriris
Grow a classification tree using the all petal measurements.
Mdl = fitctree(meas(:,3:4),species); n = size(meas,1); % Sample size K = numel(Mdl.ClassNames); % Number of classes
View the classification tree.
view(Mdl,'Mode','graph');
The classification tree has four pruning levels. Level 0 is the full, unpruned tree (as displayed). Level 4 is just the root node (i.e., no splits).
Estimate the posterior probabilities for each class using the subtrees pruned to levels 1 and 3.
[~,Posterior] = resubPredict(Mdl,'Subtrees',[1 3]);
Posterior
is an n
-by- K
-by- 2 array of posterior probabilities. Rows of Posterior
correspond to observations, columns correspond to the classes with order Mdl.ClassNames
, and pages correspond to pruning level.
Display the class posterior probabilities for iris 125 using each subtree.
Posterior(125,:,:)
ans = ans(:,:,1) = 0 0.0217 0.9783 ans(:,:,2) = 0 0.5000 0.5000
The decision stump (page 2 of Posterior
) has trouble predicting whether iris 125 is versicolor or virginica.
Posterior Probability Definition for Classification Tree
Classify a predictor X
as true when X < 0.15
or X > 0.95
, and as false otherwise.
Generate 100 uniformly distributed random numbers between 0 and 1, and classify them using a tree model.
rng("default") % For reproducibility X = rand(100,1); Y = (abs(X - 0.55) > 0.4); tree = fitctree(X,Y); view(tree,"Mode","graph")
Prune the tree.
tree1 = prune(tree,"Level",1); view(tree1,"Mode","graph")
The pruned tree correctly classifies observations that are less than 0.15 as true
. It also correctly classifies observations from 0.15 to 0.95 as false
. However, it incorrectly classifies observations that are greater than 0.95 as false
. Therefore, the score for observations that are greater than 0.15 should be about 0.05/0.85=0.06 for true
, and about 0.8/0.85=0.94 for false
.
Compute the prediction scores (posterior probabilities) for the first 10 rows of X
.
[~,score] = resubPredict(tree1); [score(1:10,:) X(1:10)]
ans = 10×3
0.9059 0.0941 0.8147
0.9059 0.0941 0.9058
0 1.0000 0.1270
0.9059 0.0941 0.9134
0.9059 0.0941 0.6324
0 1.0000 0.0975
0.9059 0.0941 0.2785
0.9059 0.0941 0.5469
0.9059 0.0941 0.9575
0.9059 0.0941 0.9649
Indeed, every value of X
(the right-most column) that is less than 0.15 has associated scores (the left and center columns) of 0 and 1, while the other values of X
have associated scores of approximately 0.91 and 0.09. The difference (score of 0.09 instead of the expected 0.06) is due to a statistical fluctuation: there are 8 observations in X
in the range (0.95,1) instead of the expected 5 observations.
sum(X > 0.95)
ans = 8
Input Arguments
tree
— Classification tree model
ClassificationTree
model object
Classification tree model, specified as a ClassificationTree
model object trained with fitctree
.
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 (that is, just the root node).
If you specify "all"
, then resubPredict
operates on all subtrees (that is, 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
fitctree
, or by pruning tree
using prune
.
Data Types: single
| double
| char
| string
Output Arguments
label
— Predicted class labels
categorical array | character array | logical vector | vector of numeric values | cell array of character vectors
Predicted class labels for the training data, returned as a categorical or character
array, logical or numeric vector, or cell array of character vectors.
label
has the same data type as the training response data
tree.Y
.
If subtrees
contains m
>
1
entries, then label
is returned as a matrix
with m
columns, each of which represents the predictions of the
corresponding subtree. Otherwise, label
is returned as a
vector.
posterior
— Posterior probabilities
numeric matrix | numeric array
Posterior probabilities for the classes predicted by tree
,
returned as a numeric matrix or numeric array.
If subtrees
is a scalar or is not specified, then
resubPredict
returns posterior
as an
n
-by-k
numeric matrix, where
n
is the number of rows in the training data
tree.X
, and k
is the number of classes.
If subtrees
contains m
>
1
entries, then resubPredict
returns
posterior
as an
n
-by-k
-by-m
numeric array,
where the matrix for each m
gives posterior probabilities for 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.
cnum
— Predicted class numbers for resubstituted data
numeric column vector | numeric matrix
Predicted class numbers for resubstituted data, returned as a numeric column vector or numeric matrix.
If subtrees
is a scalar or is not specified, then
cnum
is a numeric column vector with n
rows,
the same number of rows as tree.X
.
If subtrees
contains m
>
1
entries, then cnum
is an
n
-by-m
numeric matrix. Each column represents
the class predictions of the corresponding subtree.
More About
Posterior Probability
The posterior probability of the classification at a node is the number of training sequences that lead to that node with this classification, divided by the number of training sequences that lead to that node.
For an example, see Posterior Probability Definition for Classification Tree.
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
See Also
resubEdge
| resubMargin
| resubLoss
| predict
| fitctree
| ClassificationTree
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