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loss

Classification loss for classification tree model

Description

L = loss(tree,Tbl,ResponseVarName) returns the classification loss L for the trained classification tree model tree using the predictor data in table Tbl and the true class labels in Tbl.ResponseVarName. The interpretation of L depends on the loss function (LossFun) and weighting scheme (Weights). In general, better classifiers yield smaller classification loss values.

L = loss(tree,Tbl,Y) uses the predictor data in table Tbl and the true class labels in Y.

L = loss(tree,X,Y) uses the predictor data in matrix X and the true class labels in Y.

example

L = loss(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in the previous syntaxes. For example, you can specify the loss function or observation weights.

example

[L,SE,Nleaf,BestLevel] = loss(___) also returns the standard errors of the classification loss, number of leaf nodes in the trees of the pruning sequence, and best pruning level as defined in the TreeSize name-value argument.

Examples

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Compute the resubstituted classification error for the ionosphere data set.

load ionosphere
tree = fitctree(X,Y);
L = loss(tree,X,Y)
L = 
0.0114

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 Fisher's iris data set. Partition the data into training (50%) and validation (50%) sets.

load fisheriris
n = size(meas,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 classification tree using the training set.

Mdl = fitctree(meas(idxTrn,:),species(idxTrn));

View the classification tree.

view(Mdl,'Mode','graph');

Figure Classification tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 18 objects of type line, text. One or more of the lines displays its values using only markers

The classification tree has four pruning levels. Level 0 is the full, unpruned tree (as displayed). Level 3 is just the root node (i.e., no splits).

Examine the training sample classification error for each subtree (or pruning level) excluding the highest level.

m = max(Mdl.PruneList) - 1;
trnLoss = resubLoss(Mdl,'Subtrees',0:m)
trnLoss = 3×1

    0.0267
    0.0533
    0.3067

  • The full, unpruned tree misclassifies about 2.7% of the training observations.

  • The tree pruned to level 1 misclassifies about 5.3% of the training observations.

  • The tree pruned to level 2 (i.e., a stump) misclassifies about 30.6% of the training observations.

Examine the validation sample classification error at each level excluding the highest level.

valLoss = loss(Mdl,meas(idxVal,:),species(idxVal),'Subtrees',0:m)
valLoss = 3×1

    0.0369
    0.0237
    0.3067

  • The full, unpruned tree misclassifies about 3.7% of the validation observations.

  • The tree pruned to level 1 misclassifies about 2.4% of the validation observations.

  • The tree pruned to level 2 (i.e., a stump) misclassifies about 30.7% of the validation observations.

To balance model complexity and out-of-sample performance, consider pruning Mdl to level 1.

pruneMdl = prune(Mdl,'Level',1);
view(pruneMdl,'Mode','graph')

Figure Classification tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 12 objects of type line, text. One or more of the lines displays its values using only markers

Input Arguments

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Trained classification tree, specified as a ClassificationTree model object trained with fitctree, or a CompactClassificationTree model object created with compact.

Sample data, specified as a table. Each row of Tbl corresponds to one observation, and each column corresponds to one predictor variable. Optionally, Tbl can contain additional columns for the response variable and observation weights. Tbl must contain all the predictors used to train tree. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

If Tbl contains the response variable used to train tree, then you do not need to specify ResponseVarName or Y.

If you train tree using sample data contained in a table, then the input data for loss must also be in a table.

Data Types: table

Response variable name, specified as the name of a variable in Tbl. If Tbl contains the response variable used to train tree, then you do not need to specify ResponseVarName.

You must specify ResponseVarName as a character vector or string scalar. For example, if the response variable is stored as Tbl.Response, then specify it as "Response". Otherwise, the software treats all columns of Tbl, including Tbl.Response, as predictors.

The response variable must be a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. If the response variable is a character array, then each element must correspond to one row of the array.

Data Types: char | string

Class labels, specified as a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. Y must be of the same type as the class labels used to train tree, and its number of elements must equal the number of rows of X.

Data Types: categorical | char | string | logical | single | double | cell

Predictor data, specified as a numeric matrix. Each column of X represents one variable, and each row represents one observation.

X must have the same number of columns as the data used to train tree. X must have the same number of rows as the number of rows in Y.

Data Types: single | double

Name-Value Arguments

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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 = loss(tree,X,Y,LossFun="exponential") specifies to use an exponential loss function.

Loss function, specified as a built-in loss function name or a function handle.

The following table describes the values for the built-in loss functions.

ValueDescription
"binodeviance"Binomial deviance
"classifcost"Observed misclassification cost
"classiferror"Misclassified rate in decimal
"exponential"Exponential loss
"hinge"Hinge loss
"logit"Logistic loss
"mincost"Minimal expected misclassification cost (for classification scores that are posterior probabilities)
"quadratic"Quadratic loss

"mincost" is appropriate for classification scores that are posterior probabilities. Classification trees return posterior probabilities as classification scores by default (see predict).

Specify your own function using function handle notation. Suppose that n is the number of observations in X, and K is the number of distinct classes (numel(tree.ClassNames)). Your function must have the signature

lossvalue = lossfun(C,S,W,Cost)
where:

  • The output argument lossvalue is a scalar.

  • You specify the function name (lossfun).

  • C is an n-by-K logical matrix with rows indicating the class to which the corresponding observation belongs. The column order corresponds to the class order in tree.ClassNames.

    Create C by setting C(p,q) = 1, if observation p is in class q, for each row. Set all other elements of row p to 0.

  • S is an n-by-K numeric matrix of classification scores. The column order corresponds to the class order in tree.ClassNames. S is a matrix of classification scores, similar to the output of predict.

  • W is an n-by-1 numeric vector of observation weights. If you pass W, the software normalizes the weights to sum to 1.

  • Cost is a K-by-K numeric matrix of misclassification costs. For example, Cost = ones(K) - eye(K) specifies a cost of 0 for correct classification and 1 for misclassification.

For more details on the loss functions, see Classification Loss.

Example: LossFun="binodeviance"

Example: LossFun=@lossfun

Data Types: char | string | function_handle

Observation weights, specified as a numeric vector or the name of a variable in Tbl.

If you specify Weights as a numeric vector, then the size of Weights must be equal to the number of rows in X or Tbl.

If you specify Weights as the name of a variable in Tbl, then the name must be a character vector or string scalar. For example, if the weights are stored as Tbl.W, then specify it as "W". Otherwise, the software treats all columns of Tbl, including Tbl.W, as predictors.

loss normalizes the weights so that the observation weights in each class sum to the prior probability of that class. When you specify Weights, loss computes the weighted classification loss.

Example: Weights="W"

Data Types: single | double | char | string

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 loss operates on all subtrees (in other words, the entire pruning sequence). This specification is equivalent to using 0:max(tree.PruneList).

loss 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.

Example: Subtrees="all"

Data Types: single | double | char | string

Tree size, specified as one of these values:

  • "se"loss 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, where L and se relate to the smallest value in Subtrees).

  • "min"loss returns the best pruning level, which corresponds to the element of Subtrees with the smallest loss. This element is usually the smallest element of Subtrees.

Example: TreeSize="min"

Data Types: char | string

Output Arguments

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Classification loss, returned as a numeric vector that has the same length as Subtrees. The meaning of the error depends on the values in Weights and LossFun.

Standard error of loss, returned as a numeric vector that has the same length as Subtrees.

Number of leaf nodes in the pruned subtrees, returned as a vector of integer values that has the same length as Subtrees. Leaf nodes are terminal nodes, which give responses, not splits.

Best pruning level, returned as a numeric scalar whose value depends on TreeSize:

  • When TreeSize is "se", the loss function returns the highest pruning level whose loss is within one standard deviation of the minimum (L+se, where L and se relate to the smallest value in Subtrees).

  • When TreeSize is "min", the loss function returns the element of Subtrees with the smallest loss, usually the smallest element of Subtrees.

More About

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Extended Capabilities

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Version History

Introduced in R2011a