Documentation

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

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 `NaN`s 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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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`)

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`

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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```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' } ```

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 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 5526 classreg.learning.classif.CompactClassificationNaiveBayes Mdl 1x1 12851 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 array {'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`.

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```

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## References

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