predict

Class: ClassificationLinear

Predict labels for linear classification models

Syntax

Label = predict(Mdl,X)

Label = predict(Mdl,X,'ObservationsIn',dimension)

[Label,Score] = predict(___)

Description

Label = predict(Mdl,X) returns predicted class labels for each observation in the predictor data X based on the trained, binary, linear classification model Mdl. Label contains class labels for each regularization strength in Mdl.

Label = predict(Mdl,X,'ObservationsIn',dimension) specifies the predictor data observation dimension, either 'rows' (default) or 'columns'. For example, specify 'ObservationsIn','columns' to indicate that columns in the predictor data correspond to observations.

[Label,Score] = predict(___) also returns classification scores for both classes using any of the input argument combinations in the previous syntaxes. Score contains classification scores for each regularization strength in Mdl.

Input Arguments

Mdl — Binary, linear classification model

ClassificationLinear model object

Binary, linear classification model, specified as a ClassificationLinear model object. You can create a ClassificationLinear model object using fitclinear.

X — Predictor data to be classified

full numeric matrix | sparse numeric matrix | table

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

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

• For a numeric matrix:

  • The variables in the columns of X must have the same order as the predictor variables that trained Mdl.

  • If you train Mdl using a table (for example, Tbl) and Tbl contains only numeric predictor variables, then X can be a numeric matrix. To treat numeric predictors in Tbl as categorical during training, identify categorical predictors by using the CategoricalPredictors name-value pair argument of fitclinear. 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 multicolumn variables or cell arrays other than cell arrays of character vectors.

  • If you train Mdl using a table (for example, Tbl), then all predictor variables in X must have the same variable names and data types as the variables that trained Mdl (stored in Mdl.PredictorNames). However, the column order of X does not need to correspond to the column order of Tbl. Also, Tbl and X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

  • If you train Mdl using a numeric matrix, then the predictor names in Mdl.PredictorNames must be the same as the corresponding predictor variable names in X. To specify predictor names during training, use the PredictorNames name-value pair argument of fitclinear. All predictor variables in X must be numeric vectors. X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

Note

If you orient your predictor matrix so that observations correspond to columns and specify 'ObservationsIn','columns', then you might experience a significant reduction in optimization execution time. You cannot specify 'ObservationsIn','columns' for predictor data in a table.

Data Types: table | double | single

dimension — Predictor data observation dimension

'rows' (default) | 'columns'

Predictor data observation dimension, specified as 'columns' or 'rows'.

Note

If you orient your predictor matrix so that observations correspond to columns and specify 'ObservationsIn','columns', then you might experience a significant reduction in optimization execution time. You cannot specify 'ObservationsIn','columns' for predictor data in a table.

Output Arguments

Label — Predicted class labels

categorical array | character array | logical matrix | numeric matrix | cell array of character vectors

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

The predict function classifies an observation into the class yielding the highest score. For an observation with NaN scores, the function classifies the observation into the majority class, which makes up the largest proportion of the training labels.

In most cases, Label is an n-by-L array of the same data type as the observed class labels (Y) used to train Mdl. (The software treats string arrays as cell arrays of character vectors.) n is the number of observations in X and L is the number of regularization strengths in Mdl.Lambda. That is, Label(i,j) is the predicted class label for observation i using the linear classification model that has regularization strength Mdl.Lambda(j).

If Y is a character array and L > 1, then Label is a cell array of class labels.

Score — Classification scores

numeric array

Classification scores, returned as a n-by-2-by-L numeric array. n is the number of observations in X and L is the number of regularization strengths in Mdl.Lambda. Score(i,k,j) is the score for classifying observation i into class k using the linear classification model that has regularization strength Mdl.Lambda(j). Mdl.ClassNames stores the order of the classes.

If Mdl.Learner is 'logistic', then classification scores are posterior probabilities.

Examples

Predict Training-Sample Labels

Load the NLP data set.

load nlpdata

X is a sparse matrix of predictor data, and Y is a categorical vector of class labels. There are more than two classes in the data.

The models should identify whether the word counts in a web page are from the Statistics and Machine Learning Toolbox™ documentation. So, identify the labels that correspond to the Statistics and Machine Learning Toolbox™ documentation web pages.

Ystats = Y == 'stats';

Train a binary, linear classification model using the entire data set, which can identify whether the word counts in a documentation web page are from the Statistics and Machine Learning Toolbox™ documentation.

rng(1); % For reproducibility 
Mdl = fitclinear(X,Ystats);

Mdl is a ClassificationLinear model.

Predict the training-sample, or resubstitution, labels.

label = predict(Mdl,X);

Because there is one regularization strength in Mdl, label is column vectors with lengths equal to the number of observations.

Construct a confusion matrix.

ConfusionTrain = confusionchart(Ystats,label);

The model misclassifies only one 'stats' documentation page as being outside of the Statistics and Machine Learning Toolbox documentation.

Predict Test-Sample Labels

Load the NLP data set and preprocess it as in Predict Training-Sample Labels. Transpose the predictor data matrix.

load nlpdata
Ystats = Y == 'stats';
X = X';

Train a binary, linear classification model that can identify whether the word counts in a documentation web page are from the Statistics and Machine Learning Toolbox™ documentation. Specify to hold out 30% of the observations. Optimize the objective function using SpaRSA.

rng(1) % For reproducibility 
CVMdl = fitclinear(X,Ystats,'Solver','sparsa','Holdout',0.30,...
    'ObservationsIn','columns');
Mdl = CVMdl.Trained{1};

CVMdl is a ClassificationPartitionedLinear model. It contains the property Trained, which is a 1-by-1 cell array holding a ClassificationLinear model that the software trained using the training set.

Extract the training and test data from the partition definition.

trainIdx = training(CVMdl.Partition);
testIdx = test(CVMdl.Partition);

Predict the training- and test-sample labels.

labelTrain = predict(Mdl,X(:,trainIdx),'ObservationsIn','columns');
labelTest = predict(Mdl,X(:,testIdx),'ObservationsIn','columns');

Because there is one regularization strength in Mdl, labelTrain and labelTest are column vectors with lengths equal to the number of training and test observations, respectively.

Construct a confusion matrix for the training data.

ConfusionTrain = confusionchart(Ystats(trainIdx),labelTrain);

The model misclassifies only three documentation pages as being outside of Statistics and Machine Learning Toolbox documentation.

Construct a confusion matrix for the test data.

ConfusionTest = confusionchart(Ystats(testIdx),labelTest);

The model misclassifies three documentation pages as being outside the Statistics and Machine Learning Toolbox, and two pages as being inside.

Estimate Posterior Class Probabilities

Estimate test-sample, posterior class probabilities, and determine the quality of the model by plotting a receiver operating characteristic (ROC) curve. Linear classification models return posterior probabilities for logistic regression learners only.

Load the NLP data set and preprocess it as in Predict Test-Sample Labels.

load nlpdata
Ystats = Y == 'stats';
X = X';

Randomly partition the data into training and test sets by specifying a 30% holdout sample. Identify the test-set indices.

cvp = cvpartition(Ystats,'Holdout',0.30);
idxTest = test(cvp);

Train a binary linear classification model. Fit logistic regression learners using SpaRSA. To hold out the test set, specify the partitioned model.

CVMdl = fitclinear(X,Ystats,'ObservationsIn','columns','CVPartition',cvp,...
    'Learner','logistic','Solver','sparsa');
Mdl = CVMdl.Trained{1};

Mdl is a ClassificationLinear model trained using the training set specified in the partition cvp only.

Predict the test-sample posterior class probabilities.

[~,posterior] = predict(Mdl,X(:,idxTest),'ObservationsIn','columns');

Because there is one regularization strength in Mdl, posterior is a matrix with 2 columns and rows equal to the number of test-set observations. Column i contains posterior probabilities of Mdl.ClassNames(i) given a particular observation.

Compute the performance metrics (true positive rates and false positive rates) for a ROC curve and find the area under the ROC curve (AUC) value by creating a rocmetrics object.

rocObj = rocmetrics(Ystats(idxTest),posterior,Mdl.ClassNames);

Plot the ROC curve for the second class by using the plot function of rocmetrics.

plot(rocObj,ClassNames=Mdl.ClassNames(2))

The ROC curve indicates that the model classifies the test-sample observations almost perfectly.

Find Good Lasso Penalty Using AUC

To determine a good lasso-penalty strength for a linear classification model that uses a logistic regression learner, compare test-sample values of the AUC.

Load the NLP data set. Preprocess the data as in Predict Test-Sample Labels.

load nlpdata
Ystats = Y == 'stats';
X = X';

Create a data partition that specifies to holdout 10% of the observations. Extract test-sample indices.

rng(10); % For reproducibility
Partition = cvpartition(Ystats,'Holdout',0.10);
testIdx = test(Partition);
XTest = X(:,testIdx);
n = sum(testIdx)

n = 
3157

YTest = Ystats(testIdx);

There are 3157 observations in the test sample.

Create a set of 11 logarithmically-spaced regularization strengths from $$10^{-6}$$ through $$10^{-0.5}$$.

Lambda = logspace(-6,-0.5,11);

Train binary, linear classification models that use each of the regularization strengths. Optimize the objective function using SpaRSA. Lower the tolerance on the gradient of the objective function to 1e-8.

CVMdl = fitclinear(X,Ystats,'ObservationsIn','columns',...
    'CVPartition',Partition,'Learner','logistic','Solver','sparsa',...
    'Regularization','lasso','Lambda',Lambda,'GradientTolerance',1e-8)

CVMdl = 
  ClassificationPartitionedLinear
    CrossValidatedModel: 'Linear'
           ResponseName: 'Y'
        NumObservations: 31572
                  KFold: 1
              Partition: [1x1 cvpartition]
             ClassNames: [0 1]
         ScoreTransform: 'none'

Extract the trained linear classification model.

Mdl1 = CVMdl.Trained{1}

Mdl1 = 
  ClassificationLinear
      ResponseName: 'Y'
        ClassNames: [0 1]
    ScoreTransform: 'logit'
              Beta: [34023x11 double]
              Bias: [-11.9079 -11.9079 -11.9079 -11.9079 -9.3362 -6.4290 -5.1424 -4.4991 -3.5732 -3.1742 -2.9839]
            Lambda: [1.0000e-06 3.5481e-06 1.2589e-05 4.4668e-05 1.5849e-04 5.6234e-04 0.0020 0.0071 0.0251 0.0891 0.3162]
           Learner: 'logistic'

Mdl is a ClassificationLinear model object. Because Lambda is a sequence of regularization strengths, you can think of Mdl as 11 models, one for each regularization strength in Lambda.

Estimate the test-sample predicted labels and posterior class probabilities.

[label,posterior] = predict(Mdl1,XTest,'ObservationsIn','columns');
Mdl1.ClassNames;
posterior(3,1,5)

ans = 
1.0000

label is a 3157-by-11 matrix of predicted labels. Each column corresponds to the predicted labels of the model trained using the corresponding regularization strength. posterior is a 3157-by-2-by-11 matrix of posterior class probabilities. Columns correspond to classes and pages correspond to regularization strengths. For example, posterior(3,1,5) indicates that the posterior probability that the first class (label 0) is assigned to observation 3 by the model that uses Lambda(5) as a regularization strength is 1.0000.

For each model, compute the AUC by using rocmetrics.

auc = 1:numel(Lambda);  % Preallocation
for j = 1:numel(Lambda)
    rocObj = rocmetrics(YTest,posterior(:,:,j),Mdl1.ClassNames);
    auc(j) = rocObj.AUC(1);
end

Higher values of Lambda lead to predictor variable sparsity, which is a good quality of a classifier. For each regularization strength, train a linear classification model using the entire data set and the same options as when you trained the model. Determine the number of nonzero coefficients per model.

Mdl = fitclinear(X,Ystats,'ObservationsIn','columns',...
    'Learner','logistic','Solver','sparsa','Regularization','lasso',...
    'Lambda',Lambda,'GradientTolerance',1e-8);
numNZCoeff = sum(Mdl.Beta~=0);

In the same figure, plot the test-sample error rates and frequency of nonzero coefficients for each regularization strength. Plot all variables on the log scale.

figure
yyaxis left
plot(log10(Lambda),log10(auc),'o-')
ylabel('log_{10} AUC')
yyaxis right
plot(log10(Lambda),log10(numNZCoeff + 1),'o-')
ylabel('log_{10} nonzero-coefficient frequency')
xlabel('log_{10} Lambda')
title('Test-Sample Statistics')
hold off

Choose the index of the regularization strength that balances predictor variable sparsity and high AUC. In this case, a value between $$10^{-2}$$ to $$10^{-1}$$ should suffice.

idxFinal = 9;

Select the model from Mdl with the chosen regularization strength.

MdlFinal = selectModels(Mdl,idxFinal);

MdlFinal is a ClassificationLinear model containing one regularization strength. To estimate labels for new observations, pass MdlFinal and the new data to predict.

More About

Classification Score

For linear classification models, the raw classification score for classifying the observation x, a row vector, into the positive class is defined by

$$f_j(x)=x{\beta }_j+b_j.$$

For the model with regularization strength j, $${\beta }_j$$ is the estimated column vector of coefficients (the model property Beta(:,j)) and $$b_j$$ is the estimated, scalar bias (the model property Bias(j)).

The raw classification score for classifying x into the negative class is –f(x). The software classifies observations into the class that yields the positive score.

If the linear classification model consists of logistic regression learners, then the software applies the 'logit' score transformation to the raw classification scores (see ScoreTransform).

Alternative Functionality

Simulink Block

To integrate the prediction of a linear classification model into Simulink^®, you can use the ClassificationLinear Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^® Function block with the predict function. For examples, see Predict Class Labels Using ClassificationLinear Predict Block and Predict Class Labels Using MATLAB Function Block.

When deciding which approach to use, consider the following:

• If you use the Statistics and Machine Learning Toolbox library block, you can use the Fixed-Point Tool (Fixed-Point Designer) to convert a floating-point model to fixed point.

• Support for variable-size arrays must be enabled for a MATLAB Function block with the predict function.

• If you use a MATLAB Function block, you can use MATLAB functions for preprocessing or post-processing before or after predictions in the same MATLAB Function block.

Extended Capabilities

Tall Arrays

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

The predict function supports tall arrays with the following usage notes and limitations:

• predict does not support tall table data.

For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• You can generate C/C++ code for both predict and update by using a coder configurer. Or, generate code only for predict by using saveLearnerForCoder, loadLearnerForCoder, and codegen.

  • Code generation for predict and update — Create a coder configurer by using learnerCoderConfigurer and then generate code by using generateCode. Then you can update model parameters in the generated code without having to regenerate the code.

  • Code generation for predict — 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 (MATLAB Coder) to generate code for the entry-point function.

• To generate single-precision C/C++ code for predict, specify the name-value argument "DataType","single" when you call the loadLearnerForCoder function.

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

  Argument	Notes and Limitations
  Mdl	For the usage notes and limitations of the model object, see Code Generation of the ClassificationLinear object.
  X	For general code generation, X must be a single-precision or double-precision matrix or a table containing numeric variables, categorical variables, or both. In the coder configurer workflow, X must be a single-precision or double-precision matrix. The number of observations in X can be a variable size, but the number of variables in X must be fixed. If you want to specify X as a table, then your model must be trained using a table, and your entry-point function for prediction must do the following: Accept data as arrays. Create a table from the data input arguments and specify the variable names in the table. Pass the table to predict. For an example of this table workflow, see Generate Code to Classify 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).
  Name-value pair arguments	Names in name-value arguments must be compile-time constants. The value for the 'ObservationsIn' name-value pair argument must be a compile-time constant. For example, to use the 'ObservationsIn','columns' name-value pair argument in the generated code, include {coder.Constant('ObservationsIn'),coder.Constant('columns')} in the -args value of codegen (MATLAB Coder).

For more information, see Introduction to Code Generation.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2016a

R2024a: Specify GPU arrays (requires Parallel Computing Toolbox)

predict fully supports GPU arrays.