resubLoss
Resubstitution loss for regression tree model
Description
L = resubLoss(
specifies additional options using one or more tree
,Name=Value
)name-value
arguments.
For example, you can specify the loss function, the pruning level, and the tree size that
resubLoss
uses to calculate the loss.
[
also returns the standard error of the loss, the number of leaf nodes in the trees of the
pruning sequence, and the best pruning level as defined in the L
,SE
,Nleaf
,BestLevel
] = resubLoss(___)TreeSize
name-value argument. By default, BestLevel
is the pruning level that
gives the loss within one standard deviation of the minimal loss.
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.
resubLoss(Mdl)
ans = 4.8952
Examine the MSE for Each Subtree
Unpruned decision trees tend to overfit. One way to balance model complexity and out-of-sample performance is to prune a tree (or restrict its growth) so that in-sample and out-of-sample performance are satisfactory.
Load the carsmall
data set. Consider Displacement
, Horsepower
, and Weight
as predictors of the response MPG
.
load carsmall
X = [Displacement Horsepower Weight];
Y = MPG;
Partition the data into training (50%) and validation (50%) sets.
n = size(X,1); 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 set.
Mdl = fitrtree(X(idxTrn,:),Y(idxTrn));
View the regression tree.
view(Mdl,Mode="graph");
The regression tree has seven pruning levels. Level 0 is the full, unpruned tree (as displayed). Level 7 is just the root node (i.e., no splits).
Examine the training sample MSE for each subtree (or pruning level) excluding the highest level.
m = max(Mdl.PruneList) - 1; trnLoss = resubLoss(Mdl,SubTrees=0:m)
trnLoss = 7×1
5.9789
6.2768
6.8316
7.5209
8.3951
10.7452
14.8445
The MSE for the full, unpruned tree is about 6 units.
The MSE for the tree pruned to level 1 is about 6.3 units.
The MSE for the tree pruned to level 6 (i.e., a stump) is about 14.8 units.
Examine the validation sample MSE at each level excluding the highest level.
valLoss = loss(Mdl,X(idxVal,:),Y(idxVal),Subtrees=0:m)
valLoss = 7×1
32.1205
31.5035
32.0541
30.8183
26.3535
30.0137
38.4695
The MSE for the full, unpruned tree (level 0) is about 32.1 units.
The MSE for the tree pruned to level 4 is about 26.4 units.
The MSE for the tree pruned to level 5 is about 30.0 units.
The MSE for the tree pruned to level 6 (i.e., a stump) is about 38.5 units.
To balance model complexity and out-of-sample performance, consider pruning Mdl
to level 4.
pruneMdl = prune(Mdl,Level=4);
view(pruneMdl,Mode="graph")
Input Arguments
tree
— Regression tree model
RegressionTree
model object
Regression tree model, specified as a RegressionTree
model object trained with fitrtree
.
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: L = resubloss(tree,Subtrees="all")
prunes all
subtrees.
LossFun
— Loss function
"mse"
(default) | function handle
Loss function, specified as "mse"
(mean squared error) or as a
function handle. If you pass a function handle fun
, resubLoss
calls it as
fun(Y,Yfit,W)
where Y
, Yfit
, and W
are
numeric vectors of the same length.
Y
is the observed response.Yfit
is the predicted response.W
is the observation weights.
The returned value of fun(Y,Yfit,W)
must be a scalar.
Example: LossFun="mse"
Example: LossFun=@
Lossfun
Data Types: char
| string
| function_handle
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 resubLoss
operates on all subtrees, meaning the entire pruning sequence. This specification is
equivalent to using 0:max(tree.PruneList)
.
resubLoss
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
.
Example: Subtrees="all"
Data Types: single
| double
| char
| string
TreeSize
— Tree size
"se"
(default) | "min"
Tree size, specified as one of these values:
"se"
—resubLoss
returns the best pruning level (BestLevel
), which corresponds to the highest pruning level with the loss within one standard deviation of the minimum (L
+se
, whereL
andse
relate to the smallest value inSubtrees
)."min"
—resubLoss
returns the best pruning level, which corresponds to the element ofSubtrees
with the smallest loss. This element is usually the smallest element ofSubtrees
.
Example: TreeSize="min"
Data Types: char
| string
Output Arguments
SE
— Standard error of loss
numeric vector of positive values
Standard error of loss, returned as a numeric vector of positive values that has the
same length as Subtrees
.
Nleaf
— Number of leaf nodes
numeric vector of nonnegative integers
Number of leaf nodes in the pruned subtrees, returned as a numeric vector of
nonnegative integers that has the same length as Subtrees
. Leaf
nodes are terminal nodes, which give responses, not splits.
BestLevel
— Best pruning level
numeric scalar
Best pruning level, returned as a numeric scalar whose value depends on
TreeSize
:
When
TreeSize
is"se"
, theloss
function returns the highest pruning level whose loss is within one standard deviation of the minimum (L
+se
, whereL
andse
relate to the smallest value inSubtrees
).When
TreeSize
is"min"
, theloss
function returns the element ofSubtrees
with the smallest loss, usually the smallest element ofSubtrees
.
More About
Loss Functions
The built-in loss function is "mse"
, meaning mean squared
error.
To write your own loss function, create a function file of the form
function loss = lossfun(Y,Yfit,W)
N
is the number of rows oftree
.X
.Y
is anN
-element vector representing the observed response.Yfit
is anN
-element vector representing the predicted responses.W
is anN
-element vector representing the observation weights.The output
loss
should be a scalar.
Pass the function handle @
as the
value of the lossfun
LossFun
name-value argument.
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
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