updateMetricsAndFit

Update performance metrics in incremental drift-aware learning model given new data and train model

Since R2022b

Syntax

Mdl = updateMetricsAndFit(Mdl,X,Y)

Mdl = updateMetricsAndFit(Mdl,X,Y,Name=Value)

Description

Mdl = updateMetricsAndFit(Mdl,X,Y) returns an incremental drift-aware learning model Mdl, which is the input incremental drift-aware learning model 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 performing incremental drift-aware learning.

The input and output models have the same data type.

Mdl = updateMetricsAndFit(Mdl,X,Y,Name=Value) uses additional options specified by one or more name-value arguments. For example, you can specify that the columns of the predictor data matrix correspond to observations, and set observation weights.

Examples

Compute Performance Metrics and Monitor Concept Drift

Create the random concept data and concept drift generator using the helper functions, HelperSineGenerator and HelperConceptDriftGenerator, respectively.

concept1 = HelperSineGenerator(ClassificationFunction=1,IrrelevantFeatures=true,TableOutput=false);
concept2 = HelperSineGenerator(ClassificationFunction=3,IrrelevantFeatures=true,TableOutput=false);
driftGenerator = HelperConceptDriftGenerator(concept1,concept2,15000,1000);

When ClassificationFunction is 1, HelperSineGenerator labels all points that satisfy x1 < sin(x2) as 1, otherwise the function labels them as 0. When ClassificationFunction is 3, this is reversed. That is, HelperSineGenerator labels all points that satisfy x1 >= sin(x2) as 1, otherwise the function labels them as 0 [2]. The software returns the data in matrices for using in incremental learners.

HelperConceptDriftGenerator establishes the concept drift. The object uses a sigmoid function 1./(1+exp(-4*(numobservations-position)./width)) to decide the probability of choosing the first stream when generating data [3]. In this case, the position argument is 15000 and the width argument is 1000. As the number of observations exceeds the position value minus half of the width, the probability of sampling from the first stream when generating data decreases. The sigmoid function allows a smooth transition from one stream to the other. Larger width values indicate a larger transition period where both streams are approximately equally likely to be selected.

Initiate an incremental drift-aware model for classification as follows:

1. Create an incremental Naive Bayes classification model for binary classification.

2. Initiate an incremental concept drift detector that uses the Hoeffding's Bounds Drift Detection Method with moving average (HDDMA).

3. Using the incremental linear model and the concept drift detector, initiate an incremental drift-aware model. Specify the training period as 5000 observations.

BaseLearner = incrementalClassificationNaiveBayes(MaxNumClasses=2,Metrics="classiferror");
dd = incrementalConceptDriftDetector("hddma");
idal = incrementalDriftAwareLearner(BaseLearner,DriftDetector=dd,TrainingPeriod=5000);

Preallocate the number of variables in each chunk and number of iterations for creating a stream of data.

numObsPerChunk = 10;
numIterations = 4000;

Preallocate the variables for tracking the drift status and drift time, and storing the classification error.

dstatus = zeros(numIterations,1);
statusname = strings(numIterations,1);
driftTimes = [];
ce = array2table(zeros(numIterations,2),VariableNames=["Cumulative" "Window"]);

Simulate a data stream with incoming chunks of 10 observations each and perform incremental drift-aware learning. At each iteration:

1. Simulate predictor data and labels, and update driftGenerator using the helper function hgenerate.

2. Call updateMetricsAndFit to update the performance metrics and fit the incremental drift-aware model to the incoming data.

3. Track and record the drift status and the classification error for visualization purposes.

rng(12); % For reproducibility

for j = 1:numIterations
 
 % Generate data
 [driftGenerator,X,Y] = hgenerate(driftGenerator,numObsPerChunk); 

 % Update performance metrics and fit
 idal = updateMetricsAndFit(idal,X,Y); 

 % Record drift status and classification error
 statusname(j) = string(idal.DriftStatus); 
 ce{j,:} = idal.Metrics{"ClassificationError",:};
 if idal.DriftDetected
       dstatus(j) = 2;  
    elseif idal.WarningDetected
       dstatus(j) = 1;
    else 
       dstatus(j) = 0;
    end   
 if idal.DriftDetected
    driftTimes(end+1) = j; 
 end
 
end

Plot the cumulative and per window classification error. Mark the warmup and training periods, and where the drift was introduced.

h = plot(ce.Variables);

xlim([0 numIterations])
ylim([0 0.22])
ylabel("Classification Error")
xlabel("Iteration")

xline(idal.MetricsWarmupPeriod/numObsPerChunk,"g-.","Warmup Period",LineWidth=1.5)
xline(idal.MetricsWarmupPeriod/numObsPerChunk+driftTimes,"g-.","Warmup Period",LineWidth=1.5)
xline(idal.TrainingPeriod/numObsPerChunk,"b-.","Training Period",LabelVerticalAlignment="middle",LineWidth=1.5)
xline(driftTimes,"m--","Drift",LabelVerticalAlignment="middle",LineWidth=1.5)

legend(h,ce.Properties.VariableNames)
legend(h,Location="best")

The updateMetricsAndFit function first evaluates the performance of the model by calling updateMetrics on incoming data, and then fits the model to data by calling fit:

The updateMetrics function evaluates the performance of the model as it processes incoming observations. The function writes specified metrics, measured cumulatively and within a specified window of processed observations, to the Metrics model property.

The fit function fits the model by updating the base learner and monitoring for drift given an incoming batch of data. When you call fit, the software performs the following procedure:

• Trains the model up to NumTrainingObservations observations.

• After training, the software starts tracking the model loss to see if any concept drift has occurred and updates drift status accordingly.

• When the drift status is Warning, the software trains a temporary model to replace theBaseLearner in preparation for an imminent drift.

• When the drift status is Drift, temporary model replaces the BaseLearner.

• When the drift status is Stable, the software discards the temporary model.

For more information, see the Algorithms section.

Plot the drift status versus the iteration number.

gscatter(1:numIterations,dstatus,statusname,"gmr","o",5,"on","Iteration","Drift Status","filled")

Input Arguments

Mdl — Incremental drift-aware learning model

incrementalDriftAwareLearner model object

Incremental drift-aware learning model fit to streaming data, specified as an incrementalDriftAwareLearner model object. You can create Mdl using the incrementalDriftAwareLearner function. For more details, see the object reference page.

X — Chunk of predictor data

floating-point matrix

Chunk of predictor data to which the model is fit, specified as a floating-point matrix of n observations and Mdl.BaseLearner.NumPredictors predictor variables.

When Mdl.BaseLearner accepts the ObservationsIn name-value argument, the value of ObservationsIn determines the orientation of the variables and observations. The default ObservationsIn value is "rows", which indicates that observations in the predictor data are oriented along the rows of X.

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

Note

• If Mdl.BaseLearner.NumPredictors = 0, updateMetricsAndFit 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.BaseLearner.NumPredictors, updateMetricsAndFit issues an error.

• updateMetricsAndFit supports only floating-point input predictor data. If your input data includes categorical data, you must prepare an encoded version of the categorical data. Use dummyvar to convert each categorical variable to a numeric matrix of dummy variables. Then, concatenate all dummy variable matrices and any other numeric predictors. For more details, see Dummy Variables.

Data Types: single | double

Y — Chunk of observed responses (or labels)

floating-point vector | categorical array | character array | string array | logical vector | cell array of character vectors

Chunk of responses (or labels) to which the model is fit, specified as one of the following:

• Floating-point vector of n elements for regression models, where n is the number of rows in X.

• Categorical, character, or string array, logical vector, or cell array of character vectors for classification models. If Y is a character array, it must have one class label per row. Otherwise, Y must be a vector with n elements.

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

For classification problems:

• When Mdl.BaseLearner.ClassNames is nonempty, the following conditions apply:

  • If Y contains a label that is not a member of Mdl.BaseLearner.ClassNames, updateMetricsAndFit issues an error.

  • The data type of Y and Mdl.BaseLearner.ClassNames must be the same.

• When Mdl.BaseLearner.ClassNames is empty, updateMetricsAndFit infers Mdl.BaseLearner.ClassNames from data.

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

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: ObservationsIn="columns",Weights=W specifies that the columns of the predictor matrix correspond to observations, and the vector W contains observation weights to apply during incremental learning.

ObservationsIn — Orientation of data in X

"rows" (default) | "columns"

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

updateMetricsAndFit supports ObservationsIn only if Mdl.BaseLearner supports the ObservationsIn name-value argument.

Example: ObservationsIn="columns"

Data Types: char | string

Weights — Chunk of observation weights

floating-point vector of positive values

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).

Example: Weights=w

Data Types: double | single

Output Arguments

Mdl — Updated incremental drift-aware learning model

incrementalDriftAwareLearner model object

Updated incremental drift-aware learning model, returned as an incremental learning model object of the same data type as the input model Mdl, incrementalDriftAwareLearner.

Algorithms

Incremental Drift-Aware Learning

Incremental learning, or online learning, is a branch of machine learning concerned with processing incoming data from a data stream, possibly given little to no knowledge of the distribution of the predictor variables, aspects of the prediction or objective function (including tuning parameter values), or whether the observations are labeled. Incremental learning differs from traditional machine learning, where enough labeled data is available to fit to a model, perform cross-validation to tune hyperparameters, and infer the predictor distribution. For more details, see Incremental Learning Overview.

Unlike other incremental learning functionality offered by Statistics and Machine Learning Toolbox™, updateMetricsAndFit model object combines incremental learning and concept drift detection.

After creating an incrementalDriftAwareLearner object, use updateMetrics to update model performance metrics and fit to fit the base model to incoming chunk of data, check for potential drift in the model performance (concept drift), and update or reset the incremental drift-aware learner, if necessary. You can also use updateMetricsAndFit. The fit function implements the Reactive Drift Detection Method (RDDM) [1] as follows:

• After Mdl.BaseLearner.EstimationPeriod (if necessary) and MetricsWarmupPeriod, the function trains the incremental drift-aware model up to NumTrainingObservations observations until it reaches TrainingPeriod. (If the TrainingPeriod value is smaller than the Mdl.BaseLearner.MetricsWarmupPeriod value, then incrementalDriftAwareLearner sets the TrainingPeriod value as Mdl.BaseLearner.MetricsWarmupPeriod.)

• When NumTrainingObservations > TrainingPeriod, the software starts tracking the model loss. The software computes the per observation loss using the perObservationLoss function. While computing the per observation loss, the software uses the "classiferror" loss metric for classification models and "squarederror" for regression models. The function then appends the loss values computed using the last chunk of data to the existing buffer loss values.

• Next, the software checks to see if any concept drift occurred by using the detectdrift function and updates DriftStatus accordingly.

Based on the drift status, fit performs the following procedure:

• DriftStatus is 'Warning' – The software first increases the consecutive 'Warning' status count by 1.

  • If the consecutive 'Warning' status count is less than the WarningCountLimit value and the PreviousDriftStatus value is Stable, then the software trains a temporary incremental learner (if one does not exist) and sets it (or the existing one) to BaseLearner.

    Then the software resets the temporary incremental learner using the learner's reset function.

  • If the consecutive 'Warning' status count is less than the WarningCountLimit value and the PreviousDriftStatus value is 'Warning', then the software trains the existing temporary incremental model using the latest chunk of data.

  • If the consecutive 'Warning' status count is more than the WarningCountLimit value, then the software sets the DriftStatus value to 'Drift'.

• DriftStatus is 'Drift' – The software performs the following steps.

  • Sets the consecutive 'Warning' status count to 0.

  • Resets DriftDetector using the reset function.

  • Empties the buffer loss values and appends the loss values for the latest chunk of data to buffer loss values.

  • If the temporary incremental model is not empty, then the software sets the current BaseLearner value to the temporary incremental model and empties the temporary incremental model.

  • If the temporary incremental model is empty, then the software resets the BaseLearner value by using the learner's reset function.

• DriftStatus is 'Stable' – The software first increases the consecutive 'Stable' status count by 1.

  • If the consecutive 'Stable' status count is less than the StableCountLimit and the PreviousDriftStatus value is 'Warning', then the software sets the number of warnings to zero and empties the temporary model.

  • If the consecutive 'Stable' status count is more than the StableCountLimit value, then the software resets the DriftDetector using the reset function. Then the software tests all of the saved loss values in the buffer for concept drift by using the detectdrift function.

Once DriftStatus is set to 'Drift', and the BaseLearner and DriftDetector are reset, the software waits until Mdl.BaseLearner.EstimationPeriod + Mdl.BaseLearner.MetricsWarmupPeriod before it starts computing the performance metrics.

Performance Metrics

• The updateMetrics and updateMetricsAndFit functions track model performance metrics (Metrics) from new data when the incremental model is warm (Mdl.BaseLearner.IsWarm property). An incremental model becomes warm after fit or updateMetricsAndFit fits the incremental model to MetricsWarmupPeriod observations, which is the metrics warm-up period.

  If Mdl.BaseLearner.EstimationPeriod > 0, the functions estimate hyperparameters before fitting the model to data. Therefore, the functions must process an additional EstimationPeriod observations before the model starts the metrics warm-up period.

• The Metrics property of the incremental model 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 and updateMetricsAndFit update the metrics at the following frequencies:

  • Cumulative — The functions compute cumulative metrics since the start of model performance tracking. The functions update metrics every time you call the functions, and base the calculation on the entire supplied data set until a model reset.

  • Window — The functions compute metrics based on all observations within a window determined by the MetricsWindowSize name-value argument. MetricsWindowSize also determines the frequency at which the software updates Window metrics. For example, if MetricsWindowSize is 20, the functions compute 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 MetricsWindowSize amount of values for each specified metric, and store the same amount of observation weights.

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

    3. When the window of observations is filled, overwrite Mdl.Metrics.Window with the weighted average performance in the metrics window. If the window is overfilled when the function processes a batch of observations, the latest incoming MetricsWindowSize observations are stored, and the earliest observations are removed from the window. For example, suppose MetricsWindowSize is 20, there are 10 stored values from a previously processed batch, and 15 values are incoming. To compose the length 20 window, the functions use 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.

References

[1] Barros, Roberto S.M. , et al. "RDDM: Reactive drift detection method." Expert Systems with Applications. vol. 90, Dec. 2017, pp. 344-55. https://doi.org/10.1016/j.eswa.2017.08.023.

[2] Bifet, Albert, et al. "New Ensemble Methods for Evolving Data Streams." Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM Press, 2009, p. 139. https://doi.org/10.1145/1557019.1557041.

[3] Gama, João, et al. "Learning with drift detection". Advances in Artificial Intelligence – SBIA 2004, edited by Ana L. C. Bazzan and Sofiane Labidi, vol. 3171, Springer Berlin Heidelberg, 2004, pp. 286–95. https://doi.org/10.1007/978-3-540-28645-5_29.

Version History

Introduced in R2022b