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# margin

Classification margins for naive Bayes classifiers

## Syntax

``m = margin(Mdl,tbl,ResponseVarName)``
``m = margin(Mdl,tbl,Y)``
``m = margin(Mdl,X,Y)``

## Description

````m = margin(Mdl,tbl,ResponseVarName)` returns the classification margins (`m`) for the trained naive Bayes classifier `Mdl` using the predictor data in table `tbl` and the class labels in `tbl.ResponseVarName`.```
````m = margin(Mdl,tbl,Y)` returns the classification margins (`m`) for the trained naive Bayes classifier `Mdl` using the predictor data in table `tbl` and the class labels in vector `Y`.```

example

````m = margin(Mdl,X,Y)` returns the classification margins (`m`) for the trained naive Bayes classifier `Mdl` using the predictor data `X` and class labels `Y`.```

## Input Arguments

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Naive Bayes classifier, specified as a `ClassificationNaiveBayes` model or `CompactClassificationNaiveBayes` model returned by `fitcnb` or `compact`, respectively.

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 `Mdl`. Multi-column variables and cell arrays other than cell arrays of character vectors are not allowed.

If you trained `Mdl` using sample data contained in a `table`, then the input data for this method must also be in a table.

Data Types: `table`

Response variable name, specified as the name of a variable in `tbl`.

You must specify `ResponseVarName` as a character vector or string scalar. For example, if the response variable `y` is stored as `tbl.y`, then specify it as `'y'`. Otherwise, the software treats all columns of `tbl`, including `y`, as predictors when training the model.

The response variable must be a categorical, character, or string array, logical or numeric vector, or 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`

Predictor data, specified as a numeric matrix.

Each row of `X` corresponds to one observation (also known as an instance or example), and each column corresponds to one variable (also known as a feature). The variables making up the columns of `X` should be the same as the variables that trained `Mdl`.

The length of `Y` and the number of rows of `X` must be equal.

Data Types: `double` | `single`

Class labels, specified as a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. `Y` must be the same as the data type of `Mdl.ClassNames`. (The software treats string arrays as cell arrays of character vectors.)

The length of `Y` and the number of rows of `tbl` or `X` must be equal.

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

## Output Arguments

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Classification margins, returned as a numeric vector.

`m` has the same length equal to `size(X,1)`. Each entry of `m` is the classification margin of the corresponding observation (row) of `X` and element of `Y`.

## Examples

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```load fisheriris X = meas; % Predictors Y = species; % Response rng(1);```

Train a naive Bayes classifier. Specify a 30% holdout sample for testing. It is good practice to specify the class order. Assume that each predictor is conditionally normally distributed given its label.

```CVMdl = fitcnb(X,Y,'Holdout',0.30,... 'ClassNames',{'setosa','versicolor','virginica'}); CMdl = CVMdl.Trained{1}; ... % Extract the trained, compact classifier testInds = test(CVMdl.Partition); % Extract the test indices XTest = X(testInds,:); YTest = Y(testInds);```

`CVMdl` is a `ClassificationPartitionedModel` classifier. It contains the property `Trained`, which is a 1-by-1 cell array holding a `CompactClassificationNaiveBayes` classifier that the software trained using the training set.

Estimate the test sample classification margins. Display the distribution of the margins using a boxplot.

```m = margin(CMdl,XTest,YTest); figure; boxplot(m); title 'Distribution of the Test-Sample Margins';```

An observation margin is the observed true class score minus the maximum false class score among all scores in the respective class. Classifiers that yield relatively large margins are desirable.

The classifier margins measure, for each observation, the difference between the true class observed score and the maximal false class score for a particular class. One way to perform feature selection is to compare test sample margins from multiple models. Based solely on this criterion, the model with the highest margins is the best model.

```load fisheriris X = meas; % Predictors Y = species; % Response rng(1);```

Partition the data set into training and test sets. Specify a 30% holdout sample for testing.

```Partition = cvpartition(Y,'Holdout',0.30); testInds = test(Partition); % Indices for the test set XTest = X(testInds,:); YTest = Y(testInds);```

Partition defines the data set partition.

Define these two data sets:

• `fullX` contains all predictors.

• `partX` contains the last 2 predictors.

```fullX = X; partX = X(:,3:4);```

Train naive Bayes classifiers for each predictor set. Specify the partition definition.

```FCVMdl = fitcnb(fullX,Y,'CVPartition',Partition); PCVMdl = fitcnb(partX,Y,'CVPartition',Partition); FCMdl = FCVMdl.Trained{1}; PCMdl = PCVMdl.Trained{1};```

`FullCVMdl` and `PartCVMdl` are `ClassificationPartitionedModel` classifiers. They contain the property `Trained`, which is a 1-by-1 cell array holding a `CompactClassificationNaiveBayes` classifier that the software trained using the training set.

Estimate the test sample margins for each classifier. Display the distributions of the margins for each model using boxplots.

```fullM = margin(FCMdl,XTest,YTest); partM = margin(PCMdl,XTest(:,3:4),YTest); figure; boxplot([fullM partM],'Labels',{'All Predictors','Two Predictors'}) h = gca; h.YLim = [0.98 1.01]; % Modify axis to see boxes. title 'Boxplots of Test-Sample Margins';```

The margins have a similar distribution, but `PCMdl` is less complex.

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