# updateMetrics

Update performance metrics in naive Bayes incremental learning classification model given new data

## Description

Given streaming data, updateMetrics measures the performance of a configured naive Bayes classification model for incremental learning (incrementalClassificationNaiveBayes object). updateMetrics stores the performance metrics in the output model.

updateMetrics allows for flexible incremental learning. After you call the function to update model performance metrics on an incoming chunk of data, you can perform other actions before you train the model to the data. For example, you can decide whether you need to train the model based on its performance on a chunk of data. Alternatively, you can both update model performance metrics and train the model on the data as it arrives, in one call, by using the updateMetricsAndFit function.

To measure the model performance on a specified batch of data, call loss instead.

example

Mdl = updateMetrics(Mdl,X,Y) returns a naive Bayes classification model for incremental learning Mdl, which is the input naive Bayes classification model for incremental learning Mdl modified to contain the model performance metrics on the incoming predictor and response data, X and Y respectively.

When the input model is warm (Mdl.IsWarm is true), updateMetrics overwrites previously computed metrics, stored in the Metrics property, with the new values. Otherwise, updateMetrics stores NaN values in Metrics instead.

example

Mdl = updateMetrics(Mdl,X,Y,'Weights',Weights) also sets observation weights Weights.

## Examples

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Train a naive Bayes classification model by using fitcnb, convert it to an incremental learner, and then track its performance to streaming data.

Load the human activity data set. Randomly shuffle the data.

rng(1) % For reproducibility
n = numel(actid);
idx = randsample(n,n);
X = feat(idx,:);
Y = actid(idx);

For details on the data set, enter Description at the command line.

Train Naive Bayes Classification Model

Fit a naive Bayes classification model to a random sample of half the data.

idxtt = randsample([true false],n,true);
TTMdl = fitcnb(X(idxtt,:),Y(idxtt))
TTMdl =
ClassificationNaiveBayes
ResponseName: 'Y'
CategoricalPredictors: []
ClassNames: [1 2 3 4 5]
ScoreTransform: 'none'
NumObservations: 12053
DistributionNames: {1x60 cell}
DistributionParameters: {5x60 cell}

Properties, Methods

TTMdl is a ClassificationNaiveBayes model object representing a traditionally trained model.

Convert Trained Model

Convert the traditionally trained classification model to a naive Bayes classification model for incremental learning.

IncrementalMdl = incrementalLearner(TTMdl)
IncrementalMdl =
incrementalClassificationNaiveBayes

IsWarm: 1
Metrics: [1x2 table]
ClassNames: [1 2 3 4 5]
ScoreTransform: 'none'
DistributionNames: {1x60 cell}
DistributionParameters: {5x60 cell}

Properties, Methods

The incremental model is warm. Therefore, updateMetrics can track model performance metrics given data.

Track Performance Metrics

Track the model performance on the rest of the data by using the updateMetrics function. Simulate a data stream by processing 50 observations at a time. At each iteration:

1. Call updateMetrics to update the cumulative and window minimal cost of the model given the incoming chunk of observations. Overwrite the previous incremental model to update the losses in the Metrics property. Note that the function does not fit the model to the chunk of data—the chunk is "new" data for the model.

2. Store the minimal cost and mean of the first predictor in the first class ${\mu }_{11}$.

% Preallocation
idxil = ~idxtt;
nil = sum(idxil);
numObsPerChunk = 50;
nchunk = floor(nil/numObsPerChunk);
mc = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]);
mu11 = [IncrementalMdl.DistributionParameters{1,1}(1); zeros(nchunk,1)];
Xil = X(idxil,:);
Yil = Y(idxil);

% Incremental fitting
for j = 1:nchunk
ibegin = min(nil,numObsPerChunk*(j-1) + 1);
iend   = min(nil,numObsPerChunk*j);
idx = ibegin:iend;
IncrementalMdl = updateMetrics(IncrementalMdl,Xil(idx,:),Yil(idx));
mc{j,:} = IncrementalMdl.Metrics{"MinimalCost",:};
mu11(j + 1) = IncrementalMdl.DistributionParameters{1,1}(1);
end

IncrementalMdl is an incrementalClassificationNaiveBayes model object that has tracked the model performance to observations in the data stream.

Plot a trace plot of the performance metrics and ${\mu }_{11}$.

t = tiledlayout(2,1);
nexttile
h = plot(mc.Variables);
xlim([0 nchunk])
ylabel('Minimal Cost')
legend(h,mc.Properties.VariableNames)
nexttile
plot(mu11)
ylabel('\mu_{11}')
xlim([0 nchunk])
xlabel(t,'Iteration')

The cumulative loss is stable, whereas the window loss jumps throughout the training.

${\mu }_{11}$ does not change because updateMetrics does not fit the model to the data.

Create a naive Bayes classification model for incremental learning by calling incrementalClassificationNaiveBayes and specifying a maximum of 5 expected classes in the data. Specify tracking misclassification error rate in addition to minimal cost.

Mdl = incrementalClassificationNaiveBayes('MaxNumClasses',5,'Metrics',"classiferror");

Mdl is an incrementalClassificationNaiveBayes model. All its properties are read-only.

Determine whether the model is warm by querying the model property.

isWarm = Mdl.IsWarm
isWarm = logical
0

Mdl.IsWarm is 0; therefore, Mdl is not warm.

Determine the number of observations incremental fitting functions, such as fit, must process before measuring the performance of the model by displaying the size of the metrics warm-up period.

numObsBeforeMetrics = Mdl.MetricsWarmupPeriod
numObsBeforeMetrics = 1000

Load the human activity data set. Randomly shuffle the data.

n = numel(actid);
rng(1) % For reproducibility
idx = randsample(n,n);
X = feat(idx,:);
Y = actid(idx);

For details on the data set, enter Description at the command line.

Suppose that the data from a stationary subject (Y <= 2) has double the quality of the data from a moving subject. Create a weight variable that assigns a weight of 2 to observations from a stationary subject and 1 to a moving subject.

W = ones(n,1) + (Y <= 2);

Implement incremental learning by performing the following actions at each iteration:

• Simulate a data stream by processing a chunk of 50 observations.

• Measure model performance metrics on the incoming chunk using updateMetrics. Specify the corresponding observation weights and overwrite the input model.

• Fit the model to the incoming chunk. Specify the corresponding observation weights and overwrite the input model.

• Store ${\mu }_{11}$ and the misclassification error rate to see how they evolve during incremental learning.

% Preallocation
numObsPerChunk = 50;
nchunk = floor(n/numObsPerChunk);
ce = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]);
mu11 = zeros(nchunk,1);

% Incremental learning
for j = 1:nchunk
ibegin = min(n,numObsPerChunk*(j-1) + 1);
iend   = min(n,numObsPerChunk*j);
idx = ibegin:iend;
Mdl = updateMetrics(Mdl,X(idx,:),Y(idx),'Weights',W(idx));
ce{j,:} = Mdl.Metrics{"ClassificationError",:};
Mdl = fit(Mdl,X(idx,:),Y(idx),'Weights',W(idx));
mu11(j) = Mdl.DistributionParameters{1,1}(1);
end

Now, Mdl is an incrementalClassificationNaiveBayes model object trained on all the data in the stream.

To see how the parameters evolve during incremental learning, plot them on separate tiles.

t = tiledlayout(2,1);
nexttile
plot(mu11)
ylabel('\mu_{11}')
xlabel('Iteration')
axis tight
nexttile
plot(ce.Variables)
ylabel('ClassificationError')
xline(numObsBeforeMetrics/numObsPerChunk,'r-.')
xlim([0 nchunk])
legend(ce.Properties.VariableNames)
xlabel(t,'Iteration')

mdlIsWarm = numObsBeforeMetrics/numObsPerChunk
mdlIsWarm = 20

The plot suggests that fit always fits the model to the data, and updateMetrics does not track the classification error until after the metrics warm-up period (20 chunks).

Incrementally train a naive Bayes classification model only when its performance degrades.

Load the human activity data set. Randomly shuffle the data.

n = numel(actid);
rng(1) % For reproducibility
idx = randsample(n,n);
X = feat(idx,:);
Y = actid(idx);

For details on the data set, enter Description at the command line.

Configure a naive Bayes classification model for incremental learning so that the maximum number of expected classes is 5, the tracked performance metric includes the misclassification error rate, and the metrics window size is 1000. Fit the configured model to the first 1000 observations.

Mdl = incrementalClassificationNaiveBayes('MaxNumClasses',5,'MetricsWindowSize',1000, ...
'Metrics','classiferror');
initobs = 1000;
Mdl = fit(Mdl,X(1:initobs,:),Y(1:initobs));

Mdl is an incrementalClassificationNaiveBayes model object.

Perform incremental learning, with conditional fitting, by following this procedure for each iteration:

• Simulate a data stream by processing a chunk of 100 observations at a time.

• Update the model performance on the incoming chunk of data.

• Fit the model to the chunk of data only when the misclassification error rate is greater than 0.05.

• When tracking performance and fitting, overwrite the previous incremental model.

• Store the misclassification error rate and the mean of the first predictor in the second class ${\mu }_{21}$ to see how they evolve during training.

• Track when fit trains the model.

% Preallocation
numObsPerChunk = 100;
nchunk = floor((n - initobs)/numObsPerChunk);
mu21 = zeros(nchunk,1);
ce = array2table(nan(nchunk,2),'VariableNames',["Cumulative" "Window"]);
trained = false(nchunk,1);

% Incremental fitting
for j = 1:nchunk
ibegin = min(n,numObsPerChunk*(j-1) + 1 + initobs);
iend = min(n,numObsPerChunk*j + initobs);
idx = ibegin:iend;
Mdl = updateMetrics(Mdl,X(idx,:),Y(idx));
ce{j,:} = Mdl.Metrics{"ClassificationError",:};
if ce{j,2} > 0.05
Mdl = fit(Mdl,X(idx,:),Y(idx));
trained(j) = true;
end
mu21(j) = Mdl.DistributionParameters{2,1}(1);
end

Mdl is an incrementalClassificationNaiveBayes model object trained on all the data in the stream.

To see how the model performance and ${\mu }_{21}$ evolve during training, plot them on separate tiles.

t = tiledlayout(2,1);
nexttile
plot(mu21)
hold on
plot(find(trained),mu21(trained),'r.')
xlim([0 nchunk])
ylabel('\mu_{21}')
legend('\mu_{21}','Training occurs','Location','best')
hold off
nexttile
plot(ce.Variables)
xlim([0 nchunk])
ylabel('Misclassification Error Rate')
legend(ce.Properties.VariableNames,'Location','best')
xlabel(t,'Iteration')

The trace plot of ${\mu }_{21}$ shows periods of constant values, during which the loss within the previous observation window is at most 0.05.

## Input Arguments

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Naive Bayes classification model for incremental learning to measure the performance of, specified as an incrementalClassificationNaiveBayes model object. You can create Mdl directly or by converting a supported, traditionally trained machine learning model using the incrementalLearner function. For more details, see the corresponding reference page.

If Mdl.IsWarm is false, updateMetrics does not track the performance of the model. Before updateMetrics can track performance metrics, you must perform all the following actions:

• Fit the input model Mdl to all expected classes (see the MaxNumClasses and ClassNames arguments of incrementalClassificationNaiveBayes).

• Fit the input model Mdl to Mdl.MetricsWarmupPeriod observations by passing Mdl and the data to fit. For more details, see Performance Metrics.

Chunk of predictor data to measure the model performance, specified as an n-by-Mdl.NumPredictors floating-point matrix.

The length of the observation labels Y and the number of observations in X must be equal; Y(j) is the label of observation j (row) in X.

Note

If Mdl.NumPredictors = 0, updateMetrics infers the number of predictors from X, and sets the corresponding property of the output model. Otherwise, if the number of predictor variables in the streaming data changes from Mdl.NumPredictors, updateMetrics issues an error.

Data Types: single | double

Chunk of labels with which to measure the model performance, specified as a categorical, character, or string array; logical or floating-point vector; or cell array of character vectors.

The length of the observation labels Y and the number of observations in X must be equal; Y(j) is the label of observation j (row) in X.

updateMetrics issues an error when one or both of these conditions are met:

• Y contains a new label and the maximum number of classes has already been reached (see the MaxNumClasses and ClassNames arguments of incrementalClassificationNaiveBayes).

• The ClassNames property of the input model Mdl is nonempty, and the data types of Y and Mdl.ClassNames are different.

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

Chunk of observation weights, specified as a floating-point vector of positive values. updateMetrics weighs the observations in X with the corresponding values in Weights. The size of Weights must equal n, the number of observations in X.

By default, Weights is ones(n,1).

For more details, including normalization schemes, see Observation Weights.

Data Types: double | single

Note

If an observation (predictor or label) or weight contains at least one missing (NaN) value, updateMetrics ignores the observation. Consequently, updateMetrics uses fewer than n observations to compute the model performance, where n is the number of observations in X.

## Output Arguments

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Updated naive Bayes classification model for incremental learning, returned as an incremental learning model object of the same data type as the input model Mdl, an incrementalClassificationNaiveBayes object.

If the model is not warm, updateMetrics does not compute performance metrics. As a result, the Metrics property of Mdl remains completely composed of NaN values. If the model is warm, updateMetrics computes the cumulative and window performance metrics on the new data X and Y, and overwrites the corresponding elements of Mdl.Metrics. All other properties of the input model Mdl carry over to the output model Mdl. For more details, see Performance Metrics.

## Tips

• Unlike traditional training, incremental learning might not have a separate test (holdout) set. Therefore, to treat each incoming chunk of data as a test set, pass the incremental model and each incoming chunk to updateMetrics before training the model on the same data using fit.

## Algorithms

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### Performance Metrics

• updateMetrics tracks only model performance metrics, specified by the row labels of the table in Mdl.Metrics, from new data only when the incremental model is warm (IsWarm property is true).

• If you create an incremental model by using incrementalLearner and MetricsWarmupPeriod is 0 (default for incrementalLearner), the model is warm at creation.

• Otherwise, an incremental model becomes warm after the fit function performs both of these actions:

• Fit the incremental model to Mdl.MetricsWarmupPeriod observations, which is the metrics warm-up period.

• Fit the incremental model to all expected classes (see the MaxNumClasses and ClassNames arguments of incrementalClassificationNaiveBayes).

• Mdl.Metrics stores two forms of each performance metric as variables (columns) of a table, Cumulative and Window, with individual metrics in rows. When the incremental model is warm, updateMetrics updates the metrics at the following frequencies:

• Cumulative — The function computes cumulative metrics since the start of model performance tracking. The function updates metrics every time you call it and bases the calculation on the entire supplied data set.

• Window — The function computes metrics based on all observations within a window determined by the Mdl.MetricsWindowSize property. Mdl.MetricsWindowSize also determines the frequency at which the software updates Window metrics. For example, if Mdl.MetricsWindowSize is 20, the function computes metrics based on the last 20 observations in the supplied data (X((end – 20 + 1):end,:) and Y((end – 20 + 1):end)).

Incremental functions that track performance metrics within a window use the following process:

1. Store a buffer of length Mdl.MetricsWindowSize for each specified metric, and store a buffer of observation weights.

2. Populate elements of the metrics buffer with the model performance based on batches of incoming observations, and store corresponding observation weights in the weights buffer.

3. When the buffer is full, overwrite Mdl.Metrics.Window with the weighted average performance in the metrics window. If the buffer is overfills when the function processes a batch of observations, the latest incoming Mdl.MetricsWindowSize observations enter the buffer, and the earliest observations are removed from the buffer. For example, suppose Mdl.MetricsWindowSize is 20, the metrics buffer has 10 values from a previously processed batch, and 15 values are incoming. To compose the length 20 window, the function uses the measurements from the 15 incoming observations and the latest 5 measurements from the previous batch.

• The software omits an observation with a NaN score when computing the Cumulative and Window performance metric values.

### Observation Weights

For each conditional predictor distribution, updateMetrics computes the weighted average and standard deviation.

If the prior class probability distribution is known (in other words, the prior distribution is not empirical), updateMetrics normalizes observation weights to sum to the prior class probabilities in the respective classes. This action implies that the default observation weights are the respective prior class probabilities.

If the prior class probability distribution is empirical, the software normalizes the specified observation weights to sum to 1 each time you call updateMetrics.

## Version History

Introduced in R2021a