Main Content

updateMetricsAndFit

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

Description

Given streaming data, updateMetricsAndFit first evaluates the performance of a configured naive Bayes classification model for incremental learning (incrementalClassificationNaiveBayes object) by calling updateMetrics on incoming data. Then updateMetricsAndFit fits the model to that data by calling fit. In other words, updateMetricsAndFit performs prequential evaluation because it treats each incoming chunk of data as a test set, and tracks performance metrics measured cumulatively and over a specified window [1].

updateMetricsAndFit provides a simple way to update model performance metrics and train the model on each chunk of data. Alternatively, you can perform the operations separately by calling updateMetrics and then fit, which allows for more flexibility (for example, you can decide whether you need to train the model based on its performance on a chunk of data).

example

Mdl = updateMetricsAndFit(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 with the following modifications:

  1. updateMetricsAndFit measures the model performance on the incoming predictor and response data, X and Y respectively. When the input model is warm (Mdl.IsWarm is true), updateMetricsAndFit overwrites previously computed metrics, stored in the Metrics property, with the new values. Otherwise, updateMetricsAndFit stores NaN values in Metrics instead.

  2. updateMetricsAndFit fits the modified model to the incoming data by updating the conditional posterior mean and standard deviation of each predictor variable, given the class, and stores the new estimates, among other configurations, in the output model Mdl.

The input and output models have the same data type.

example

Mdl = updateMetricsAndFit(Mdl,X,Y,'Weights',Weights) specifies observation weights Weights.

Examples

collapse all

Create a naive Bayes classification model for incremental learning by calling incrementalClassificationNaiveBayes and specifying a maximum of 5 expected classes in the data.

Mdl = incrementalClassificationNaiveBayes('MaxNumClasses',5)
Mdl = 
  incrementalClassificationNaiveBayes

                    IsWarm: 0
                   Metrics: [1×2 table]
                ClassNames: [1×0 double]
            ScoreTransform: 'none'
         DistributionNames: 'normal'
    DistributionParameters: {}


  Properties, Methods

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

Mdl must be fit to data before you can use it to perform any other operations.

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

load humanactivity
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.

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

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

  • Overwrite the previous incremental model with a new one fitted to the incoming observation.

  • Store the conditional mean of the first predictor in the first class μ11, the cumulative metrics, and the window metrics to see how they evolve during incremental learning.

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

% Incremental fitting
for j = 1:nchunk
    ibegin = min(n,numObsPerChunk*(j-1) + 1);
    iend   = min(n,numObsPerChunk*j);
    idx = ibegin:iend;    
    Mdl = updateMetricsAndFit(Mdl,X(idx,:),Y(idx));
    mc{j,:} = Mdl.Metrics{"MinimalCost",:};
    mu11(j + 1) = Mdl.DistributionParameters{1,1}(1);
end

Mdl is an incrementalClassificationNaiveBayes model object trained on all the data in the stream. During incremental learning and after the model is warmed up, updateMetricsAndFit checks the performance of the model on the incoming observation, and then fits the model to that observation.

To see how the performance metrics and μ11 evolved during training, plot them on separate subplots.

figure;
subplot(2,1,1)
plot(mu11)
ylabel('\beta_1')
xlim([0 nchunk]);
subplot(2,1,2)
h = plot(mc.Variables);
xlim([0 nchunk]);
ylabel('Minimal Cost')
xline(Mdl.MetricsWarmupPeriod/numObsPerChunk,'r-.');
legend(h,mc.Properties.VariableNames)
xlabel('Iteration')

The plot suggests that updateMetricsAndFit does the following:

  • Fits μ11 during all incremental learning iterations.

  • Compute performance metrics after the metrics warm-up period only.

  • Compute the cumulative metrics during each iteration.

  • Compute the window metrics after processing 500 observations.

Train a naive Bayes classification model by using fitcnb, convert it to an incremental learner, track its performance on streaming data and fit it to the data in one call. Specify observation weights.

Load and Preprocess Data

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

load humanactivity
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.

Suppose that the data collected when the subject was not moving (Y <= 2) has double the quality than when the subject was moving. Create a weight variable that attributes 2 to observations collected from a still subject, and 1 to a moving subject.

W = ones(n,1) + ~Y;

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),'Weights',W(idxtt))
TTMdl = 
  ClassificationNaiveBayes
              ResponseName: 'Y'
     CategoricalPredictors: []
                ClassNames: [1 2 3 4 5]
            ScoreTransform: 'none'
           NumObservations: 12053
         DistributionNames: {1×60 cell}
    DistributionParameters: {5×60 cell}


  Properties, Methods

TTMdl is a ClassificationNaiveBayes model object representing a traditionally trained naive Bayes classification model.

Convert Trained Model

Convert the traditionally trained model to a naive Bayes classification for incremental learning. Specify tracking the misclassification error rate during incremental learning.

IncrementalMdl = incrementalLearner(TTMdl,'Metrics',"classiferror")
IncrementalMdl = 
  incrementalClassificationNaiveBayes

                    IsWarm: 1
                   Metrics: [2×2 table]
                ClassNames: [1 2 3 4 5]
            ScoreTransform: 'none'
         DistributionNames: {1×60 cell}
    DistributionParameters: {5×60 cell}


  Properties, Methods

IncrementalMdl is an incrementalClassificationNaiveBayes model. Because class names are specified in Mdl.ClassNames, labels encountered during incremental learning must be in Mdl.ClassNames.

Separately Track Performance Metrics and Fit Model

Perform incremental learning on the rest of the data by using the updateMetricsAndfit function. At each iteration:

  1. Simulate a data stream by processing 50 observations at a time.

  2. Call updateMetricsAndFit to update the cumulative and window performance metrics of the model given the incoming chunk of observations, and then fit the model to the data. Overwrite the previous incremental model to update the losses in the Metrics property. Specify the observation weights.

  3. Store the misclassification error rate.

% Preallocation
idxil = ~idxtt;
nil = sum(idxil);
numObsPerChunk = 50;
nchunk = floor(nil/numObsPerChunk);
mc = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]);
Xil = X(idxil,:);
Yil = Y(idxil);
Wil = W(idxil);

% Incremental fitting
for j = 1:nchunk
    ibegin = min(nil,numObsPerChunk*(j-1) + 1);
    iend   = min(nil,numObsPerChunk*j);
    idx = ibegin:iend;
    IncrementalMdl = updateMetricsAndFit(IncrementalMdl,Xil(idx,:),Yil(idx),...
        'Weights',Wil(idx));
    mc{j,:} = IncrementalMdl.Metrics{"ClassificationError",:};
end

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

Plot a trace plot of the misclassification error rate.

h = plot(mc.Variables);
xlim([0 nchunk]);
ylabel('Classification Error')
legend(h,mc.Properties.VariableNames)
xlabel('Iteration')

The cumulative loss initially jump, but stabilizes around 0.05, whereas the window loss jumps.

Input Arguments

collapse all

Naive Bayes classification model for incremental learning whose performance is measured and then the model is fit to data, 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, updateMetricsAndFit does not track the performance of the model. For more details, see Performance Metrics.

Chunk of predictor data with which to measure the model performance and then to fit the model to, 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 or column) in X.

Note

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

Data Types: single | double

Chunk of labels with which to measure the model performance and then fit the model to, 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 or column) in X. updateMetricsAndFit issues an error when at least one of the conditions is met:

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

  • 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. updateMetricsAndFit weighs the observations in X with the corresponding values in Weights. The size of Weights must equal n, which is 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 Weight contains at least one missing (NaN) value, updateMetricsAndFit ignores the observation. Consequently, updateMetricsAndFit uses fewer than n observations to compute the model performance.

Output Arguments

collapse all

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, incrementalClassificationNaiveBayes.

If the model is not warm, updateMetricsAndFit does not compute performance metrics. As a result, the Metrics property of Mdl remains completely composed of NaN values. If the model is warm, updateMetricsAndFit 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.

In addition to updating distribution model parameters, updateMetricsAndFit performs the following actions when Y contains expected, but unprocessed, classes:

  • If you do not specify all expected classes by using the ClassNames name-value argument when you create the input model Mdl using incrementalClassificationNaiveBayes, updateMetricsAndFit:

    1. Appends any newly encountered labels in Y to the tail of Mdl.ClassNames.

    2. Expands Mdl.Cost to a c-by-c matrix, where c is the number of classes Mdl.ClassNames. The resulting misclassification cost matrix is balanced.

    3. Expands Mdl.Prior to a length c vector of an updated empirical class distribution.

  • If you specify all expected classes when you create the input model Mdl or convert a traditionally trained naive Bayes model using incrementalLearner, but you do not specify a misclassification cost matrix (Mdl.Cost), updateMetricsAndFit sets misclassification costs of processed classes to 1 and unprocessed classes to NaN. For example, if updateMetricsAndFit processes the first two classes of a possible three classes, Mdl.Cost is [0 1 NaN; 1 0 NaN; 1 1 0].

More About

collapse all

Bag-of-Tokens Model

In the bag-of-tokens model, the value of predictor j is the nonnegative number of occurrences of token j in the observation. The number of categories (bins) in the multinomial model is the number of distinct tokens (number of predictors).

Algorithms

collapse all

Normal Distribution Estimators

If predictor variable j has a conditional normal distribution (see the DistributionNames property), the software fits the distribution to the data by computing the class-specific weighted mean and the biased (maximum likelihood) estimate of the weighted standard deviation. For each class k:

  • The weighted mean of predictor j is

    x¯j|k={i:yi=k}wixij{i:yi=k}wi,

    where wi is the weight for observation i. The software normalizes weights within a class such that they sum to the prior probability for that class.

  • The unbiased estimator of the weighted standard deviation of predictor j is

    sj|k=[{i:yi=k}wi(xijx¯j|k)2{i:yi=k}wi]1/2.

Estimated Probability for Multinomial Distribution

If all predictor variables compose a conditional multinomial distribution (see the DistributionNames property), the software fits the distribution using the Bag-of-Tokens Model. The software stores the probability that token j appears in class k in the property DistributionParameters{k,j}. With additive smoothing [2], the estimated probability is

P(token j|class k)=1+cj|kP+ck,

where:

  • cj|k=nk{i:yi=k}xijwi{i:yi=k}wi, which is the weighted number of occurrences of token j in class k.

  • nk is the number of observations in class k.

  • wi is the weight for observation i. The software normalizes weights within a class so that they sum to the prior probability for that class.

  • ck=j=1Pcj|k, which is the total weighted number of occurrences of all tokens in class k.

Estimated Probability for Multivariate Multinomial Distribution

If predictor variable j has a conditional multivariate multinomial distribution (see the DistributionNames property), the software follows this procedure:

  1. The software collects a list of the unique levels, stores the sorted list in CategoricalLevels, and considers each level a bin. Each combination of predictor and class is a separate, independent multinomial random variable.

  2. For each class k, the software counts instances of each categorical level using the list stored in CategoricalLevels{j}.

  3. The software stores the probability that predictor j in class k has level L in the property DistributionParameters{k,j}, for all levels in CategoricalLevels{j}. With additive smoothing [2], the estimated probability is

    P(predictor j=L|class k)=1+mj|k(L)mj+mk,

    where:

    • mj|k(L)=nk{i:yi=k}I{xij=L}wi{i:yi=k}wi, which is the weighted number of observations for which predictor j equals L in class k.

    • nk is the number of observations in class k.

    • I{xij=L}=1 if xij = L, and 0 otherwise.

    • wi is the weight for observation i. The software normalizes weights within a class so that they sum to the prior probability for that class.

    • mj is the number of distinct levels in predictor j.

    • mk is the weighted number of observations in class k.

Performance Metrics

  • updateMetricsAndFit tracks model performance metrics, specified by the row labels of the table in Mdl.Metrics, from new data when the incremental model is warm (IsWarm property is true). An incremental model is warm when an incremental fitting, like updateMetricsAndFit performs both of the following 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 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, updateMetricsAndFit 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 the function 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. For each specified metric, store a buffer of length Mdl.MetricsWindowSize and 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 observations weights in the weights buffer.

      3. When the buffer is filled, overwrite Mdl.Metrics.Window with the weighted average performance in the metrics window. If the buffer is overfilled 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.

Observation Weights

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

If the prior class probability distribution is known (in other words, the prior distribution is not empirical), updateMetricsAndFit 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 updateMetricsAndFit.

Compatibility Considerations

expand all

Behavior changed in R2021b

References

[1] Bifet, Albert, Ricard Gavaldá, Geoffrey Holmes, and Bernhard Pfahringer. Machine Learning for Data Streams with Practical Example in MOA. Cambridge, MA: The MIT Press, 2007.

[2] Manning, Christopher D., Prabhakar Raghavan, and Hinrich Schütze. Introduction to Information Retrieval, NY: Cambridge University Press, 2008.

Introduced in R2021a