incrementalDriftAwareLearner

Construct drift-aware model for incremental learning

Since R2022b

Description

incrementalDriftAwareLearner creates an incrementalDriftAwareLearner model object, which incorporates an incremental classification or regression learner and an incremental concept drift detector to provide a self-adjusting incremental machine learning model. incrementalDriftAwareLearner supports all classification and regression models for incremental learning and all concept drift detection methods supported by Statistics and Machine Learning Toolbox™.

Unlike most Statistics and Machine Learning Toolbox model objects, incrementalDriftAwareLearner can be called directly. After you create an incrementalDriftAwareLearner object, it is prepared for incremental drift-aware learning.

incrementalDriftAwareLearner is best suited for incremental learning that adapts for concept drift. For a traditional approach to batch drift detection, see detectdrift.

Creation

You can create an incrementalDriftAwareLearner model object in the following ways:

• Initiate an incremental classification or regression learner using any incremental learner. Pass the incremental learning model as an input in the call to incrementalDriftAwareLearner. For example,

  BaseLearner = incrementalClassificationLinear();
  Mdl = incrementalDriftAwareLearner(BaseLearner);

• Initiate an incremental classification or regression learner using any incremental learner. Initiate an incremental concept drift detector using incrementalConceptDriftDetector. Pass both the incremental learning model and concept drift detector as inputs in the call to incrementalDriftAwareLearner. For example,

  BaseLearner = incrementalRegressionKernel();
  DDM = incrementalConceptDriftDetector("ddm");
  Mdl = incrementalDriftAwareLearner(BaseLearner,DriftDetector=DDM);

Syntax

Mdl = incrementalDriftAwareLearner(BaseLearner)

Mdl = incrementalDriftAwareLearner(BaseLearner,Name=Value)

Description

Mdl = incrementalDriftAwareLearner(BaseLearner) returns a drift-aware model Mdl for incremental learning with default model parameters and default drift detector.

Mdl = incrementalDriftAwareLearner(BaseLearner,Name=Value) sets additional options using name-value arguments. For example, incrementalDriftAwareLearner(BaseLearner,DriftDetector=CDDetector,TrainingPeriod=1000) specifies the concept drift detector as a predefined CDDetector and sets the training period to 1000 observations.

Input Arguments

BaseLearner — Underlying incremental classification or regression model

incrementalClassificationKernel object | incrementalClassificationLinear object | incrementalClassificationECOC object | incrementalClassificationNaiveBayes object | incrementalRegressionKernel object | incrementalRegressionLinear object

Underlying incremental classification or regression model, specified as one of the following.

Classification	Regression
incrementalClassificationKernel	incrementalRegressionKernel
incrementalClassificationLinear	incrementalRegressionLinear
incrementalClassificationECOC
incrementalClassificationNaiveBayes

To learn how to create these learners, refer to the corresponding reference page.

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: BufferSize=5000,TrainingPeriod=8000,StableCountLimit=6000 specifies the buffer size as 5000, the training period as 8000, and the limit of consecutive stable states before a reset as 6000 observations.

BufferSize — Size of buffer to store loss values

7000 (default) | scalar integer

Size of the buffer to store the loss values of BaseLearner for each training observation, specified as a scalar integer.

Example: BufferSize=5000

Data Types: single | double

DriftDetector — Incremental concept drift detector

HoeffdingDriftDetectionMethod object | DriftDetectionMethod object

Incremental concept drift detector used for monitoring and detecting drift, specified as a HoeffdingDriftDetectionMethod or DriftDetectionMethod object.

• If BaseLearner is an incremental classification object, then the default detector is HoeffdingDriftDetectionMethod that uses the moving average method. That is, incrementalDriftAwareLearner creates the drift detector using incrementalConceptDriftDetector("hddma").

• If BaseLearner is an incremental regression object, then the default is HoeffdingDriftDetectionMethod that uses the moving average method for continuous variables. That is, incrementalDriftAwareLearner creates the drift detector using incrementalConceptDriftDetector("hddma",InputType="continuous").

To specify an incremental concept drift detector that uses a different method, see the incrementalConceptDriftDetector reference page.

Example: DriftDetector=dd

TrainingPeriod — Number of observations used for training

10000 (default) | scalar integer

Number of observations used for training, specified as a scalar integer.

If you specify the TrainingPeriod value as Inf, then the software always trains with incoming data.

If the TrainingPeriod value is smaller than the BaseLearner.MetricsWarmupPeriod value, then incrementalDriftAwareLearner sets the TrainingPeriod value as BaseLearner.MetricsWarmupPeriod.

Example: TrainingPeriod=7000

Data Types: single | double

StableCountLimit — Maximum number of consecutive 'Stable' observations before soft reset

40000 (default) | scalar integer

Maximum number of consecutive 'Stable' observations before a soft reset, specified as a scalar integer.

Example: StableCountLimit=35000

Data Types: single | double

WarningCountLimit — Maximum number of consecutive 'Warning' observations before reset

1400 (default) | scalar integer

Maximum number of consecutive 'Warning' observations before a reset, specified as a scalar integer.

Example: WarningCountLimit=1000

Data Types: single | double

Properties

BaseLearner — Underlying incremental classification or regression model

incrementalClassificationKernel object | incrementalClassificationLinear object | incrementalClassificationECOC object | incrementalClassificationNaiveBayes object | incrementalRegressionKernel object | incrementalRegressionLinear object

This property is read-only.

Underlying incremental classification or regression model, specified as one of the following model objects.

Classification	Regression
incrementalClassificationKernel	incrementalRegressionKernel
incrementalClassificationLinear	incrementalRegressionLinear
incrementalClassificationECOC
incrementalClassificationNaiveBayes

This property is set by the BaseLearner input argument.

Access the properties of BaseLearner using the dot operator, for example, Mdl.BaseLearner.Solver.

DriftDetector — Underlying incremental concept drift detector

HoeffdingDriftDetectionMethod object | DriftDetectionMethod object

This property is read-only.

Underlying incremental concept drift detector, specified as either a HoeffdingDriftDetectionMethod or DriftDetectionMethod object.

This property is set by the DriftDetector name-value argument.

Access the properties of DriftDetector using the dot operator, for example, Mdl.DriftDetector.WarningThreshold.

TrainingPeriod — Number of observations used for training

scalar integer

This property is read-only.

Number of observations used for training before the software starts monitoring for potential drift, specified as a scalar integer.

This property is set by the TrainingPeriod name-value argument.

Data Types: double

StableCountLimit — Maximum number of consecutive 'Stable' observations before a soft reset

scalar integer

This property is read-only.

Maximum number of consecutive 'Stable' observations before a soft reset, specified as a scalar integer.

This property is set by the StableCountLimit name-value argument.

Data Types: double

PreviousDriftStatus — Status of DriftDetector prior to training most recent data

'Stable' | 'Warning' | 'Drift'

This property is read-only.

Status of DriftDetector prior to training most recent data, specified as 'Stable', 'Warning', or 'Drift'.

Data Types: char

DriftStatus — Current status of DriftDetector

'Stable' | 'Warning' | 'Drift'

This property is read-only.

Current status of DriftDetector after training with the most recent data, specified as 'Stable', 'Warning', or 'Drift'.

Data Types: char

DriftDetected — Flag indicating whether DriftStatus is 'Drift'

false or 0 | true or 1

This property is read-only.

Flag indicating whether DriftStatus is 'Drift', specified as logical 0 (false) or 1 (true).

Data Types: logical

WarningCountLimit — Maximum number of consecutive 'Warning' observations before a reset

scalar integer

This property is read-only.

Maximum number of consecutive 'Warning' observations before a reset, specified as a scalar integer.

Data Types: double

WarningDetected — Flag indicating whether DriftStatus is 'Warning'

false or 0 | true or 1

This property is read-only.

Flag indicating whether DriftStatus is 'Warning', specified as logical 0 (false) or 1 (true).

Data Types: logical

IsTraining — Flag indicating whether BaseLearner continues training with incoming data

false or 0 | true or 1

This property is read-only.

Flag indicating whether BaseLearner continues training with incoming data, specified as logical 0 (false) or 1 (true).

Data Types: logical

IsWarm — Flag indicating whether model tracks performance metrics

false or 0 | true or 1

This property is read-only.

Flag indicating whether the incremental model tracks performance metrics, specified as logical 0 (false) or 1 (true).

incrementalDriftAwareLearner takes this property from Mdl.BaseLearner.

The incremental model Mdl is warm (IsWarm becomes true) after incremental fitting functions fit (Mdl.BaseLearner.EstimationPeriod + MetricsWarmupPeriod) observations to the incremental model.

Value	Description
true or 1	The incremental model Mdl is warm. Consequently, updateMetrics and updateMetricsAndFit track performance metrics in the Metrics property of Mdl.
false or 0	The incremental model Mdl is not warm. updateMetrics and updateMetricsAndFit do not track performance metrics, and all metrics values are NaN.

Data Types: logical

NumPredictors — Number of predictor variables

nonnegative numeric scalar

This property is read-only.

Number of predictor variables, specified as a nonnegative numeric scalar.

incrementalDriftAwareLearner takes this property from Mdl.BaseLearner. You can specify the number of predictor variables during the initiation of BaseLearner.

Data Types: double

NumTrainingObservations — Number of observations fit to incremental model

0 (default) | nonnegative numeric scalar

This property is read-only.

Number of observations fit to the incremental model Mdl, specified as a nonnegative numeric scalar.

incrementalDriftAwareLearner pulls this property from Mdl.BaseLearner.

NumTrainingObservations increases when you pass Mdl and training data to fit or updateMetricsAndFit.

Note

If you convert a traditionally trained model to create Mdl.BaseLearner, incrementalDriftAwareLearner does not add the number of observations fit to the traditionally trained model to NumTrainingObservations.

Data Types: double

Metrics — Model performance metrics

table

This property is read-only.

Model performance metrics updated during incremental learning by updateMetrics or updateMetricsAndFit, specified as a table with two columns and m rows, where m is the number of metrics specified by the Metrics name-value argument during the initiation of BaseLearner.

incrementalDriftAwareLearner takes this property from Mdl.BaseLearner.

The columns of Metrics are labeled Cumulative and Window.

• Cumulative – Element j is the model performance, as measured by metric j, from the time the model becomes warm (IsWarm is 1).

• Window – Element j is the model performance, as measured by metric j, evaluated over all observations within the window specified by the MetricsWindowSize property. The software updates Window after it processes MetricsWindowSize observations.

Rows are labeled by the specified metrics.

Data Types: table

MetricsWarmupPeriod — Number of observations fit before tracking performance metrics

nonnegative integer

This property is read-only.

Number of observations to which the incremental model must be fit before it tracks performance metrics in its Metrics property, specified as a nonnegative integer.

incrementalDriftAwareLearner takes this property from Mdl.BaseLearner. You can specify the metrics warm up period during the initiation of BaseLearner.

Data Types: double

MetricsWindowSize — Number of observations to use to compute window performance metrics

positive integer

This property is read-only.

Number of observations to use to compute window performance metrics, specified as a positive integer.

incrementalDriftAwareLearner pulls this property from Mdl.BaseLearner. You can specify the metrics window size during the initiation of the BaseLearner.

Data Types: double

Object Functions

fit	Train drift-aware learner for incremental learning with new data
loss	Regression or classification error of incremental drift-aware learner
perObservationLoss	Per observation regression or classification error of incremental drift-aware learner
predict	Predict responses for new observations from incremental drift-aware learning model
reset	Reset incremental drift-aware learner
updateMetrics	Update performance metrics in incremental drift-aware learning model given new data
updateMetricsAndFit	Update performance metrics in incremental drift-aware learning model given new data and train model

Examples

Create Incremental Drift-Aware Learner Without Any Prior Information

Load the human activity dataset. Randomly shuffle the data.

load humanactivity;
n = numel(actid);
rng(1) % For reproducibility
idx = randsample(n,n);

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

Define the predictor and response variables.

X = feat(idx,:);
Y = actid(idx);

Responses can be one of five classes: Sitting, Standing, Walking, Running, or Dancing. Dichotomize the response by identifying whether the subject is moving (actid > 2).

Y = Y > 2;

Flip labels for the second half of the dataset to simulate drift.

Y(floor(numel(Y)/2):end,:) = ~Y(floor(numel(Y)/2):end,:);

Initiate a default incremental drift-aware model for classification as follows:

1. Create a default incremental linear SVM model for binary classification.

2. Initiate a default incremental drift-aware model using the incremental linear SVM model.

incMdl = incrementalClassificationLinear();
idaMdl = incrementalDriftAwareLearner(incMdl);

idaMdl is an incrementalDriftAwareLearner model. All its properties are read-only.

Preallocate the number of variables in each chunk for creating a stream of data and the variable to store the classification error.

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

Preallocate variables for tracking drift status.

status = zeros(nchunk,1);
statusname = strings(nchunk,1);

Simulate a data stream with incoming chunks of 50 observations each. At each iteration:

1. Call updateMetricsAndFit to update the performance metrics and fit the drift-aware model to the incoming data. Overwrite the previous incremental model with the new one.

2. Store the cumulative and per iteration classification error in ce. The Metrics property of idaMdl stores the cumulative and window classification error, which is updated at each iteration.

for j = 1:nchunk
 ibegin = min(n,numObsPerChunk*(j-1)+1);
 iend   = min(n,numObsPerChunk*j);
 idx = ibegin:iend;    

 idaMdl = updateMetricsAndFit(idaMdl,X(idx,:),Y(idx));

 statusname(j) = string(idaMdl.DriftStatus);
 if idaMdl.DriftDetected
       status(j) = 2;  
    elseif idaMdl.WarningDetected
       status(j) = 1;
    else 
       status(j) = 0;
    end   
 ce{j,:} = idaMdl.Metrics{"ClassificationError",:};
end

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

h = plot(ce.Variables);

xlim([0 nchunk])
ylabel("Classification Error")
xlabel("Iteration")

xline(idaMdl.MetricsWarmupPeriod/numObsPerChunk,"g-.","Warmup Period",LineWidth= 1.5)
xline(idaMdl.TrainingPeriod/numObsPerChunk,"b-.","Training Period",LabelVerticalAlignment="middle",LineWidth= 1.5)
xline(floor(numel(Y)/2)/numObsPerChunk,"m--","Drift",LabelVerticalAlignment="middle",LineWidth= 1.5)

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

Plot the drift status versus the iteration number.

figure()
gscatter(1:nchunk,status,statusname,'gmr','*ox',[4 5 5],'on',"Iteration","Drift Status","filled")

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")

Monitor Concept Drift in Regression Model

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

concept1 = HelperRegrGenerator(NumFeatures=100,NonZeroFeatures=[1,20,40,50,55], ...
    FeatureCoefficients=[4,5,10,-2,-6],NoiseStd=1.1,TableOutput=false);
concept2 = HelperRegrGenerator(NumFeatures=100,NonZeroFeatures=[10,20,45,56,80], ...
    FeatureCoefficients=[4,5,10,-2,-6],NoiseStd=1.1,TableOutput=false);
driftGenerator = HelperConceptDriftGenerator(concept1,concept2,15000,1000);

HelperRegrGenerator generates streaming data using features and feature coefficients for regression specified in the call to the function. At each step, the function samples the predictors from a normal distribution. Then, the function computes the response using the feature coefficients and predictor values and adding a random noise from a normal distribution with mean zero and specified noise standard deviation. 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 regression as follows:

1. Create an incremental linear model for regression. Specify the linear regression model type and solver type.

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, instantiate an incremental drift-aware model. Specify the training period as 6000 observations.

baseMdl = incrementalRegressionLinear(Learner="leastsquares",Solver="sgd",EstimationPeriod=1000,Standardize=false);
dd = incrementalConceptDriftDetector("hddma",Alternative="greater",InputType="continuous",WarmupPeriod=1000);
idal = incrementalDriftAwareLearner(baseMdl,DriftDetector=dd,TrainingPeriod=6000);

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 regression 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 the drift generator 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 regression 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 regression error
 statusname(j) = string(idal.DriftStatus); 
 ce{j,:} = idal.Metrics{"MeanSquaredError",:};
 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 regression error. Mark the warmup and training periods, and where the drift was introduced.

h = plot(ce.Variables);

xlim([0 numIterations])
ylabel("Mean Squared Error")
xlabel("Iteration")

xline((idal.MetricsWarmupPeriod+idal.BaseLearner.EstimationPeriod)/numObsPerChunk,"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")

Plot the drift status versus the iteration number.

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

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, incrementalDriftAwareLearner 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