# 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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