margin
Syntax
Description
returns the Classification Margin (m
= margin(Mdl
,Tbl
,ResponseVarName
)m
)
for the generalized additive model Mdl
using the predictor data in
Tbl
and the true class labels in
Tbl.ResponseVarName
.
m
is returned as an n-by-1 numeric column
vector, where n is the number of observations in the predictor
data.
specifies whether to include interaction terms in computations. You can specify
m
= margin(___,'IncludeInteractions',includeInteractions
)includeInteractions
in addition to any of the input argument
combinations in the previous syntaxes.
Examples
Estimate Test Sample Classification Margins and Edge
Estimate the test sample classification margins and edge of a generalized additive model. The test sample margins are the observed true class scores minus the false class scores, and the test sample edge is the mean of the margins.
Load the fisheriris
data set. Create X
as a numeric matrix that contains two sepal and two petal measurements for versicolor and virginica irises. Create Y
as a cell array of character vectors that contains the corresponding iris species.
load fisheriris inds = strcmp(species,'versicolor') | strcmp(species,'virginica'); X = meas(inds,:); Y = species(inds,:);
Randomly partition observations into a training set and a test set with stratification, using the class information in Y
. Specify a 30% holdout sample for testing.
rng('default') % For reproducibility cv = cvpartition(Y,'HoldOut',0.30);
Extract the training and test indices.
trainInds = training(cv); testInds = test(cv);
Specify the training and test data sets.
XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);
Train a GAM using the predictors XTrain
and class labels YTrain
. A recommended practice is to specify the class names.
Mdl = fitcgam(XTrain,YTrain,'ClassNames',{'versicolor','virginica'});
Mdl
is a ClassificationGAM
model object.
Estimate the test sample classification margins and edge.
m = margin(Mdl,XTest,YTest); e = edge(Mdl,XTest,YTest)
e = 0.8000
Display the histogram of the test sample classification margins.
histogram(m,length(unique(m)),'Normalization','probability') xlabel('Test Sample Margins') ylabel('Probability') title('Probability Distribution of the Test Sample Margins')
Compare GAMs by Examining Test Sample Margins and Edge
Compare a GAM with linear terms to a GAM with both linear and interaction terms by examining the test sample margins and edge. Based solely on this comparison, the classifier with the highest margins and edge is the best model.
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere
Randomly partition observations into a training set and a test set with stratification, using the class information in Y
. Specify a 30% holdout sample for testing.
rng('default') % For reproducibility cv = cvpartition(Y,'Holdout',0.30);
Extract the training and test indices.
trainInds = training(cv); testInds = test(cv);
Specify the training and test data sets.
XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);
Train a GAM that contains both linear and interaction terms for predictors. Specify to include all available interaction terms whose p-values are not greater than 0.05.
Mdl = fitcgam(XTrain,YTrain,'Interactions','all','MaxPValue',0.05)
Mdl = ClassificationGAM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: 'logit' Intercept: 3.0398 Interactions: [561x2 double] NumObservations: 246
Mdl
is a ClassificationGAM
model object. Mdl
includes all available interaction terms.
Estimate the test sample margins and edge for Mdl
.
M = margin(Mdl,XTest,YTest); E = edge(Mdl,XTest,YTest)
E = 0.7848
Estimate the test sample margins and edge for Mdl
without including interaction terms.
M_nointeractions = margin(Mdl,XTest,YTest,'IncludeInteractions',false); E_nointeractions = edge(Mdl,XTest,YTest,'IncludeInteractions',false)
E_nointeractions = 0.7871
Display the distributions of the margins using box plots.
boxplot([M M_nointeractions],'Labels',{'Linear and Interaction Terms','Linear Terms Only'}) title('Box Plots of Test Sample Margins')
The margins M
and M_nointeractions
have a similar distribution, but the test sample edge of the classifier with only linear terms is larger. Classifiers that yield relatively large margins are preferred.
Input Arguments
Mdl
— Generalized additive model
ClassificationGAM
model object | CompactClassificationGAM
model object
Generalized additive model, specified as a ClassificationGAM
or CompactClassificationGAM
model object.
Tbl
— Sample data
table
Sample data, specified as a table. Each row of Tbl
corresponds to one observation, and each column corresponds to one predictor variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.
Tbl
must contain all the predictors used to train
Mdl
. Optionally, Tbl
can contain a column
for the response variable and a column for the observation weights.
The response variable must have the same data type as
Mdl.Y
. (The software treats string arrays as cell arrays of character vectors.) If the response variable inTbl
has the same name as the response variable used to trainMdl
, then you do not need to specifyResponseVarName
.The weight values must be a numeric vector. You must specify the observation weights in
Tbl
by using'Weights'
.
If you trained Mdl
using sample data contained in a table, then the input data for margin
must also be in a table.
Data Types: table
ResponseVarName
— Response variable name
name of variable in Tbl
Response variable name, specified as a character vector or string scalar containing the name
of the response variable in Tbl
. For example, if the response
variable Y
is stored in Tbl.Y
, then specify it as
'Y'
.
Data Types: char
| string
Y
— Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
Class labels, specified as a categorical, character, or string array, a logical or
numeric vector, or a cell array of character vectors. Each row of Y
represents the classification of the corresponding row of X
or
Tbl
.
Y
must have the same data type as Mdl.Y
. (The software treats string arrays as cell arrays of character
vectors.)
Data Types: single
| double
| categorical
| logical
| char
| string
| cell
X
— Predictor data
numeric matrix
Predictor data, specified as a numeric matrix. Each row of X
corresponds to one observation, and each column corresponds to one predictor variable.
If you trained Mdl
using sample data contained in a matrix, then the input data for margin
must also be in a matrix.
Data Types: single
| double
includeInteractions
— Flag to include interaction terms
true
| false
Flag to include interaction terms of the model, specified as true
or
false
.
The default includeInteractions
value is true
if
the model contains interaction terms. The value must be false
if the model
does not contain interaction terms.
Example: includeInteractions=false
Data Types: logical
More About
Classification Margin
The classification margin for binary classification is, for each observation, the difference between the classification score for the true class and the classification score for the false class.
If the margins are on the same scale (that is, the score values are based on the same score transformation), then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.
Version History
Introduced in R2021a
See Also
predict
| loss
| edge
| resubMargin
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