edge
Classification edge for naive Bayes classifier
Syntax
Description
returns the Classification Edge (e
= edge(Mdl
,tbl
,ResponseVarName
)e
) for the naive
Bayes classifier Mdl
using the predictor data in table
tbl
and the class labels in
tbl.ResponseVarName
.
The classification edge (e
) is a scalar value that
represents the weighted mean of the Classification Margins.
Examples
Estimate Test Sample Edge of Naive Bayes Classifier
Estimate the test sample edge (the classification margin average) of a naive Bayes classifier. The test sample edge is the average test sample difference between the estimated posterior probability for the predicted class and the posterior probability for the class with the next lowest posterior probability.
Load the fisheriris
data set. Create X
as a numeric matrix that contains four measurements for 150 irises. Create Y
as a cell array of character vectors that contains the corresponding iris species.
load fisheriris X = meas; Y = species; rng('default') % for reproducibility
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.
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 naive Bayes classifier using the predictors XTrain
and class labels YTrain
. A recommended practice is to specify the class names. fitcnb
assumes that each predictor is conditionally and normally distributed.
Mdl = fitcnb(XTrain,YTrain,'ClassNames',{'setosa','versicolor','virginica'})
Mdl = ClassificationNaiveBayes ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 105 DistributionNames: {'normal' 'normal' 'normal' 'normal'} DistributionParameters: {3x4 cell}
Mdl
is a trained ClassificationNaiveBayes
classifier.
Estimate the test sample edge.
e = edge(Mdl,XTest,YTest)
e = 0.8658
The margin average is approximately 0.87
. This result suggests that the classifier labels predictors with high confidence.
Estimate Test Sample Weighted Edge of Naive Bayes Classifier
Estimate the test sample weighted edge (the weighted margin average) of a naive Bayes classifier. The test sample edge is the average test sample difference between the estimated posterior probability for the predicted class and the posterior probability for the class with the next lowest posterior probability. The weighted sample edge estimates the margin average when the software assigns a weight to each observation.
Load the fisheriris
data set. Create X
as a numeric matrix that contains four measurements for 150 irises. Create Y
as a cell array of character vectors that contains the corresponding iris species.
load fisheriris X = meas; Y = species; rng('default') % for reproducibility
Suppose that some of the measurements are lower quality because they were measured with older technology. To simulate this effect, add noise to a random subset of 20 measurements.
idx = randperm(size(X,1),20); X(idx,:) = X(idx,:) + 2*randn(20,size(X,2));
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.
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 naive Bayes classifier using the predictors XTrain
and class labels YTrain
. A recommended practice is to specify the class names. fitcnb
assumes that each predictor is conditionally and normally distributed.
Mdl = fitcnb(XTrain,YTrain,'ClassNames',{'setosa','versicolor','virginica'});
Mdl
is a trained ClassificationNaiveBayes
classifier.
Estimate the test sample edge.
e = edge(Mdl,XTest,YTest)
e = 0.5920
The average margin is approximately 0.59.
One way to reduce the effect of the noisy measurements is to assign them less weight than the other observations. Define a weight vector that gives the better quality observations twice the weight of the other observations.
n = size(X,1); weights = ones(size(X,1),1); weights(idx) = 0.5; weightsTrain = weights(trainInds); weightsTest = weights(testInds);
Train a naive Bayes classifier using the predictors XTrain
, class labels YTrain
, and weights weightsTrain
.
Mdl_W = fitcnb(XTrain,YTrain,'Weights',weightsTrain,... 'ClassNames',{'setosa','versicolor','virginica'});
Mdl_W
is a trained ClassificationNaiveBayes
classifier.
Estimate the test sample weighted edge using the weighting scheme.
e_W = edge(Mdl_W,XTest,YTest,'Weights',weightsTest)
e_W = 0.6816
The weighted average margin is approximately 0.69. This result indicates that, on average, the weighted classifier labels predictors with higher confidence than the noise corrupted predictors.
Select Naive Bayes Classifier Features by Comparing Test Sample Edges
The classifier edge measures the average of the classifier margins. One way to perform feature selection is to compare test sample edges from multiple models. Based solely on this criterion, the classifier with the highest edge is the best classifier.
Load the ionosphere
data set. Remove the first two predictors for stability.
load ionosphere X = X(:,3:end); rng('default') % for reproducibility
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.
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);
Define these two training data sets:
fullXTrain
contains all predictors.partXTrain
contains the 10 most important predictors.
fullXTrain = XTrain; idx = fscmrmr(XTrain,YTrain); partXTrain = XTrain(:,idx(1:10));
Train a naive Bayes classifier for each predictor set.
fullMdl = fitcnb(fullXTrain,YTrain); partMdl = fitcnb(partXTrain,YTrain);
fullMdl
and partMdl
are trained ClassificationNaiveBayes
classifiers.
Estimate the test sample edge for each classifier.
fullEdge = edge(fullMdl,XTest,YTest)
fullEdge = 0.5831
partEdge = edge(partMdl,XTest(:,idx(1:10)),YTest)
partEdge = 0.7593
The test sample edge of the classifier using the 10 most important predictors is larger.
Input Arguments
Mdl
— Naive Bayes classification model
ClassificationNaiveBayes
model object | CompactClassificationNaiveBayes
model object
Naive Bayes classification model, specified as a ClassificationNaiveBayes
model object or CompactClassificationNaiveBayes
model object returned by fitcnb
or compact
,
respectively.
tbl
— Sample data
table
Sample data used to train the model, specified as a table. Each row of
tbl
corresponds to one observation, and each column corresponds
to one predictor variable. tbl
must contain all the predictors used
to train Mdl
. Multicolumn variables and cell arrays other than cell
arrays of character vectors are not allowed. Optionally, tbl
can
contain additional columns for the response variable and observation weights.
If you train Mdl
using sample data contained in a table, then the input
data for edge
must also be in a table.
ResponseVarName
— Response variable name
name of a variable in tbl
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.
If tbl
contains the response variable used to train
Mdl
, then you do not need to specify
ResponseVarName
.
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
X
— Predictor data
numeric matrix
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 in the
columns of X
must be the same as the
variables that trained the Mdl
classifier.
The length of Y
and the number of rows of X
must
be equal.
Data Types: double
| single
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, logical or numeric
vector, or cell array of character vectors. Y
must have the same data
type as Mdl.ClassNames
. (The software treats string arrays as cell arrays of character
vectors.)
The length of Y
must be equal to the number of rows of
tbl
or X
.
Data Types: categorical
| char
| string
| logical
| single
| double
| cell
Weights
— Observation weights
ones(size(X,1),1)
(default) | numeric vector | name of a variable in tbl
Observation weights, specified as a numeric vector or the name of a
variable in tbl
. The software weighs the observations
in each row of X
or tbl
with the
corresponding weights in Weights
.
If you specify Weights
as a numeric vector, then the
size of Weights
must be equal to the number of rows of
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 Weights
as
'w'
. Otherwise, the software treats all columns of
tbl
, including tbl.w
, as
predictors.
Data Types: double
| char
| string
More About
Classification Edge
The classification edge is the weighted mean of the classification margins.
If you supply weights, then the software normalizes them to sum to the prior probability of their respective class. The software uses the normalized weights to compute the weighted mean.
When choosing among multiple classifiers to perform a task such as feature section, choose the classifier that yields the highest edge.
Classification Margins
The classification margin for each observation is the difference between the score for the true class and the maximal score for the false classes. Margins provide a classification confidence measure; among multiple classifiers, those that yield larger margins (on the same scale) are better.
Posterior Probability
The posterior probability is the probability that an observation belongs in a particular class, given the data.
For naive Bayes, the posterior probability that a classification is k for a given observation (x1,...,xP) is
where:
is the conditional joint density of the predictors given they are in class k.
Mdl.DistributionNames
stores the distribution names of the predictors.π(Y = k) is the class prior probability distribution.
Mdl.Prior
stores the prior distribution.is the joint density of the predictors. The classes are discrete, so
Prior Probability
The prior probability of a class is the assumed relative frequency with which observations from that class occur in a population.
Classification Score
The naive Bayes score is the class posterior probability given the observation.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
The
edge
function fully supports tall arrays. For more information,
see Tall Arrays.
Version History
Introduced in R2014b
See Also
ClassificationNaiveBayes
| CompactClassificationNaiveBayes
| predict
| fitcnb
| loss
| resubLoss
| margin
| resubEdge
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