predict

Predict labels using naive Bayes classification model

Syntax

label = predict(Mdl,X)

[label,Posterior,Cost]
= predict(Mdl,X)

Description

example

label = predict(Mdl,X) returns a vector of predicted class labels for the predictor data in the table or matrix X, based on the trained, full or compact naive Bayes classifier Mdl.

example

[label,Posterior,Cost] = predict(Mdl,X) also returns:

A matrix of posterior probabilities (Posterior) indicating the likelihood that a label comes from a particular class.
A matrix of misclassification costs (Cost). For each observation in X, the predicted class label corresponds to the minimum expected classification costs among all classes.

Input Arguments

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`Mdl` — Naive Bayes classifier
`ClassificationNaiveBayes` model | `CompactClassificationNaiveBayes` model

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

`X` — Predictor data to be classified
numeric matrix | table

Predictor data to be classified, specified as a numeric matrix or table.

Each row of X corresponds to one observation, and each column corresponds to one variable.

For a numeric matrix:
- The variables making up the columns of X must have the same order as the predictor variables that trained Mdl.
- If you trained Mdl using a table (for example, Tbl), then X can be a numeric matrix if Tbl contains all numeric predictor variables. To treat numeric predictors in Tbl as categorical during training, identify categorical predictors using the CategoricalPredictors name-value pair argument of fitcnb. If Tbl contains heterogeneous predictor variables (for example, numeric and categorical data types) and X is a numeric matrix, then predict throws an error.
For a table:
- predict does not support multi-column variables and cell arrays other than cell arrays of character vectors.
- If you trained Mdl using a table (for example, Tbl), then all predictor variables in X must have the same variable names and data types as those that trained Mdl (stored in Mdl.PredictorNames). However, the column order of X does not need to correspond to the column order of Tbl. Tbl and X can contain additional variables (response variables, observation weights, etc.), but predict ignores them.
- If you trained Mdl using a numeric matrix, then the predictor names in Mdl.PredictorNames and corresponding predictor variable names in X must be the same. To specify predictor names during training, see the PredictorNames name-value pair argument of fitcnb. All predictor variables in X must be numeric vectors. X can contain additional variables (response variables, observation weights, etc.), but predict ignores them.

Data Types: table | double | single

Notes:

If Mdl.DistributionNames is 'mn', then the software returns NaNs corresponding to rows of X containing at least one NaN.
If Mdl.DistributionNames is not 'mn', then the software ignores NaN values when estimating misclassification costs and posterior probabilities. Specifically, the software computes the conditional density of the predictors given the class by leaving out the factors corresponding to missing predictor values.
For predictor distribution specified as 'mvmn', if X contains levels that are not represented in the training data (i.e., not in Mdl.CategoricalLevels for that predictor), then the conditional density of the predictors given the class is 0. For those observations, the software returns the corresponding value of Posterior as a NaN. The software determines the class label for such observations using the class prior probability, stored in Mdl.Prior.

Output Arguments

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`label` — Predicted class labels
categorical vector | character array | logical vector | numeric vector | cell array of character vectors

Predicted class labels, returned as a categorical vector, character array, logical or numeric vector, or cell array of character vectors.

label:

Is the same data type as the observed class labels (Mdl.Y) that trained Mdl
Has length equal to the number of rows of Mdl.X
Is the class yielding the lowest expected misclassification cost (Cost)

`Posterior` — Class posterior probabilities
numeric matrix

Class posterior probabilities, returned as a numeric matrix. Posterior has rows equal to the number of rows of X and columns equal to the number of distinct classes in the training data (size(Mdl.ClassNames,1)).

Posterior(j,k) is the predicted posterior probability of class k (i.e., in class Mdl.ClassNames(k)) given the observation in row j of X.

Data Types: double

`Cost` — Expected misclassification costs
numeric matrix

Expected misclassification costs, returned as a numeric matrix. Cost has rows equal to the number of rows of X and columns equal to the number of distinct classes in the training data (size(Mdl.ClassNames,1)).

Cost(j,k) is the expected misclassification cost of the observation in row j of X being predicted into class k (i.e., in class Mdl.ClassNames(k)).

Examples

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Label Test Sample Observations of Naive Bayes Classifiers

Open Live Script

Load Fisher's iris data set.

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

Train a naive Bayes classifier and specify to holdout 30% of the data for a test sample. 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 trained, compact classifier
testIdx = test(CVMdl.Partition); % Extract the test indices
XTest = X(testIdx,:);
YTest = Y(testIdx);

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.

Label the test sample observations. Display the results for a random set of 10 observations in the test sample.

idx = randsample(sum(testIdx),10);
label = predict(CMdl,XTest);
table(YTest(idx),label(idx),'VariableNames',...
    {'TrueLabel','PredictedLabel'})

ans=10×2 table
      TrueLabel       PredictedLabel
    ______________    ______________

    {'setosa'    }    {'setosa'    }
    {'versicolor'}    {'versicolor'}
    {'setosa'    }    {'setosa'    }
    {'virginica' }    {'virginica' }
    {'versicolor'}    {'versicolor'}
    {'setosa'    }    {'setosa'    }
    {'virginica' }    {'virginica' }
    {'virginica' }    {'virginica' }
    {'setosa'    }    {'setosa'    }
    {'setosa'    }    {'setosa'    }

Estimate Posterior Probabilities and Misclassification Costs

Open Live Script

A goal of classification is to estimate posterior probabilities of new observations using a trained algorithm. Many applications train algorithms on large data sets, which can use resources that are better used elsewhere. This example shows how to efficiently estimate posterior probabilities of new observations using a Naive Bayes classifier.

Load Fisher's iris data set.

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

Partition the data set into two sets: one in the training set, and the other is new unobserved data. Reserve 10 observations for the new data set.

n = size(X,1);
newInds = randsample(n,10);
inds = ~ismember(1:n,newInds);
XNew = X(newInds,:);
YNew = Y(newInds);

Train a naive Bayes classifier. It is good practice to specify the class order. Assume that each predictor is conditionally, normally distributed given its label. Conserve memory by reducing the size of the trained SVM classifier.

Mdl = fitcnb(X(inds,:),Y(inds),...
    'ClassNames',{'setosa','versicolor','virginica'});
CMdl = compact(Mdl);
whos('Mdl','CMdl')

  Name      Size            Bytes  Class                                                        Attributes

  CMdl      1x1              5238  classreg.learning.classif.CompactClassificationNaiveBayes              
  Mdl       1x1             12539  ClassificationNaiveBayes

The CompactClassificationNaiveBayes classifier (CMdl) uses less space than the ClassificationNaiveBayes classifier (Mdl) because the latter stores the data.

Predict the labels, posterior probabilities, and expected class misclassification costs. Since true labels are available, compare them with the predicted labels.

CMdl.ClassNames

ans = 3x1 cell
    {'setosa'    }
    {'versicolor'}
    {'virginica' }

[labels,PostProbs,MisClassCost] = predict(CMdl,XNew);
table(YNew,labels,PostProbs,'VariableNames',...
    {'TrueLabels','PredictedLabels',...
    'PosteriorProbabilities'})

ans=10×3 table
      TrueLabels      PredictedLabels             PosteriorProbabilities          
    ______________    _______________    _________________________________________

    {'setosa'    }    {'setosa'    }               1     4.1259e-16     1.1846e-23
    {'versicolor'}    {'versicolor'}      1.0373e-60        0.99999     5.8053e-06
    {'virginica' }    {'virginica' }     4.8708e-211     0.00085645        0.99914
    {'setosa'    }    {'setosa'    }               1     1.4053e-19     2.2672e-26
    {'versicolor'}    {'versicolor'}      2.9308e-75        0.99987     0.00012869
    {'setosa'    }    {'setosa'    }               1      2.629e-18     4.4297e-25
    {'versicolor'}    {'versicolor'}      1.4238e-67        0.99999      9.733e-06
    {'versicolor'}    {'versicolor'}     2.0667e-110        0.94237       0.057625
    {'setosa'    }    {'setosa'    }               1     4.3779e-19     3.5139e-26
    {'setosa'    }    {'setosa'    }               1     1.1792e-17     2.2912e-24

MisClassCost

MisClassCost = 10×3

    0.0000    1.0000    1.0000
    1.0000    0.0000    1.0000
    1.0000    0.9991    0.0009
    0.0000    1.0000    1.0000
    1.0000    0.0001    0.9999
    0.0000    1.0000    1.0000
    1.0000    0.0000    1.0000
    1.0000    0.0576    0.9424
    0.0000    1.0000    1.0000
    0.0000    1.0000    1.0000

PostProbs and MisClassCost are 15-by- 3 numeric matrices, where each row corresponds to a new observation and each column corresponds to a class. The order of the columns corresponds to the order of CMdl.ClassNames.

Plot Posterior Probability Regions for Naive Bayes Classifiers

Open Live Script

Load Fisher's iris data set. Train the classifier using the petal lengths and widths.

load fisheriris
X = meas(:,3:4);
Y = species;

Train a naive Bayes classifier. It is good practice to specify the class order. Assume that each predictor is conditionally, normally distributed given its label.

Mdl = fitcnb(X,Y,...
    'ClassNames',{'setosa','versicolor','virginica'});

Mdl is a ClassificationNaiveBayes model. You can access its properties using dot notation.

Define a grid of values in the observed predictor space. Predict the posterior probabilities for each instance in the grid.

xMax = max(X);
xMin = min(X);
h = 0.01;
[x1Grid,x2Grid] = meshgrid(xMin(1):h:xMax(1),xMin(2):h:xMax(2));

[~,PosteriorRegion] = predict(Mdl,[x1Grid(:),x2Grid(:)]);

Plot the posterior probability regions and the training data.

figure;
% Plot posterior regions 
scatter(x1Grid(:),x2Grid(:),1,PosteriorRegion);
% Adjust color bar options
h = colorbar;
h.Ticks = [0 0.5 1];
h.TickLabels = {'setosa','versicolor','virginica'};
h.YLabel.String = 'Posterior';
h.YLabel.Position = [-0.5 0.5 0];
% Adjust color map options
d = 1e-2;
cmap = zeros(201,3);
cmap(1:101,1) = 1:-d:0;
cmap(1:201,2) = [0:d:1 1-d:-d:0];
cmap(101:201,3) = 0:d:1;
colormap(cmap);
% Plot data
hold on
gh = gscatter(X(:,1),X(:,2),Y,'k','dx*');
title 'Iris Petal Measurements and Posterior Probabilities';
xlabel 'Petal length (cm)';
ylabel 'Petal width (cm)';
axis tight
legend(gh,'Location','Best')
hold off

More About

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Misclassification Cost

A misclassification cost is the relative severity of a classifier labeling an observation into the wrong class.

There are two types of misclassification costs: true and expected. Let K be the number of classes.

True misclassification cost — A K-by-K matrix, where element (i,j) indicates the misclassification cost of predicting an observation into class j if its true class is i. The software stores the misclassification cost in the property Mdl.Cost, and used in computations. By default, Mdl.Cost(i,j) = 1 if i ≠ j, and Mdl.Cost(i,j) = 0 if i = j. In other words, the cost is 0 for correct classification, and 1 for any incorrect classification.
Expected misclassification cost — A K-dimensional vector, where element k is the weighted average misclassification cost of classifying an observation into class k, weighted by the class posterior probabilities. In other words,

$c_{k} = \sum_{j = 1}^{K} \hat{P} (Y = j | x_{1}, ..., x_{P}) C o s t_{j k} .$

the software classifies observations to the class corresponding with the lowest expected misclassification cost.

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,...,x_P) is

$\hat{P} (Y = k | x_{1}, .., x_{P}) = \frac{P (X_{1}, ..., X_{P} | y = k) π (Y = k)}{P (X_{1}, ..., X_{P})},$

where:

$P (X_{1}, ..., X_{P} | y = k)$ 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.
$P (X_{1}, .., X_{P})$ is the joint density of the predictors. The classes are discrete, so $P (X_{1}, ..., X_{P}) = \sum_{k = 1}^{K} P (X_{1}, ..., X_{P} | y = k) π (Y = k) .$

Prior Probability

The prior probability of a class is the believed relative frequency with which observations from that class occur in a population.

References

[1] Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning, Second Edition. NY: Springer, 2008.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. You can use models trained on either in-memory or tall data with this function.

For more information, see Tall Arrays (MATLAB).

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Use saveLearnerForCoder, loadLearnerForCoder, and codegen to generate code for the predict function. Save a trained model by using saveLearnerForCoder. Define an entry-point function that loads the saved model by using loadLearnerForCoder and calls the predict function. Then use codegen to generate code for the entry-point function.

This table contains notes about the arguments of predict. Arguments not included in this table are fully supported.

Argument Notes and Limitations

Argument	Notes and Limitations
`Mdl`	For the usage notes and limitations of the model object, see Code Generation of the `CompactClassificationNaiveBayes` object.
`X`	For general code generation, `X` must be a single-precision or double-precision matrix or a table containing `single` or `double` predictor variables. If you want to specify `X` as a table, then your model must be trained using a table, and you must ensure that your entry-point function for prediction: Accepts data as arrays Creates a table from the data input arguments and specifies the variable names in the table Passes the table to `predict` For an example of this table workflow, see Generate Code to Classify Numeric Data in Table. For more information on using tables in code generation, see Code Generation for Tables (MATLAB Coder) and Table Limitations for Code Generation (MATLAB Coder). The number of rows, or observations, in `X` can be a variable size, but the number of columns in `X` must be fixed.

Mdl

For the usage notes and limitations of the model object, see Code Generation of the CompactClassificationNaiveBayes object.

X

For general code generation, X must be a single-precision or double-precision matrix or a table containing single or double predictor variables.
If you want to specify X as a table, then your model must be trained using a table, and you must ensure that your entry-point function for prediction:
- Accepts data as arrays
- Creates a table from the data input arguments and specifies the variable names in the table
- Passes the table to predict
For an example of this table workflow, see Generate Code to Classify Numeric Data in Table. For more information on using tables in code generation, see Code Generation for Tables (MATLAB Coder) and Table Limitations for Code Generation (MATLAB Coder).
The number of rows, or observations, in X can be a variable size, but the number of columns in X must be fixed.

For more information, see Introduction to Code Generation.

Documentation

predict

Syntax

Description

Input Arguments

`Mdl` — Naive Bayes classifier
`ClassificationNaiveBayes` model | `CompactClassificationNaiveBayes` model

`X` — Predictor data to be classified
numeric matrix | table

Notes:

Output Arguments

`label` — Predicted class labels
categorical vector | character array | logical vector | numeric vector | cell array of character vectors

`Posterior` — Class posterior probabilities
numeric matrix

`Cost` — Expected misclassification costs
numeric matrix

Examples

Label Test Sample Observations of Naive Bayes Classifiers

Estimate Posterior Probabilities and Misclassification Costs

Plot Posterior Probability Regions for Naive Bayes Classifiers

More About

Misclassification Cost

Posterior Probability

Prior Probability

References

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Topics

Statistics and Machine Learning Toolbox Documentation

Support

Documentation

predict

Syntax

Description

Input Arguments

Mdl — Naive Bayes classifier ClassificationNaiveBayes model | CompactClassificationNaiveBayes model

X — Predictor data to be classified numeric matrix | table

Notes:

Output Arguments

label — Predicted class labels categorical vector | character array | logical vector | numeric vector | cell array of character vectors

Posterior — Class posterior probabilities numeric matrix

Cost — Expected misclassification costs numeric matrix

Examples

Label Test Sample Observations of Naive Bayes Classifiers

Estimate Posterior Probabilities and Misclassification Costs

Plot Posterior Probability Regions for Naive Bayes Classifiers

More About

Misclassification Cost

Posterior Probability

Prior Probability

References

Extended Capabilities

Tall Arrays Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Topics

Statistics and Machine Learning Toolbox Documentation

Support

`Mdl` — Naive Bayes classifier
`ClassificationNaiveBayes` model | `CompactClassificationNaiveBayes` model

`X` — Predictor data to be classified
numeric matrix | table

`label` — Predicted class labels
categorical vector | character array | logical vector | numeric vector | cell array of character vectors

`Posterior` — Class posterior probabilities
numeric matrix

`Cost` — Expected misclassification costs
numeric matrix

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.