HoeffdingDriftDetectionMethod

Incremental concept drift detector that utilizes Hoeffding's Bounds Drift Detection Method (HDDM)

Since R2022a

Description

HoeffdingDriftDetectionMethod model object represents an incremental concept drift detector that uses the Hoeffding's Bounds nonparametric drift detection methods based on moving averages (A-test) or exponentially weighted moving averages (W-test) [1]. After creating the object, you can use the detectdrift object function to update the statistics and check for any drift in the concept data (for example, failure rate, regression loss, and so on).

HoeffdingDriftDetectionMethod is suitable for incremental concept drift detection. For drift detection on raw data, see detectdrift for batch drift detection.

Creation

You can create HoeffdingDriftDetectionMethod by specifying the DetectionMethod argument as "hddma" or "hddmw" in the call to incrementalConceptDriftDetector.

Properties

Object Input Parameters

Alternative — Type of alternative hypothesis

Read-only: 'greater' (default) | 'less' | 'unequal'

This property is read-only.

Type of alternative hypothesis for determining the drift status, specified as 'greater', 'less', or 'unequal'.

Data Types: char

DriftThreshold — Threshold to determine if drift exists

Read-only: 0.001 (default) | nonnegative scalar value from 0 to 1

This property is read-only.

Threshold to determine if drift exists, specified as a nonnegative scalar value from 0 to 1. It is the significance level the software uses for calculating the allowed error between a random variable and its expected value in Hoeffding's inequality or McDiarmid's inequality before it sets DriftStatus to 'Drift'.

Data Types: double

EstimationPeriod — Number of observations used for estimating the input bound

Read-only: nonnegative integer

This property is read-only.

Number of observations used for estimating the input bound for continuous variables, specified as a nonnegative integer.

Data Types: double

ForgettingFactor — Forgetting factor for HDDMW method

Read-only: 0.05 (default) | scalar value from 0 to 1

This property is read-only.

Note

This option is for the exponentially weighted moving average method (ewma) only.

Forgetting factor for the exponentially weighted moving average (EWMA) method (HDDMW), specified as a scalar value from 0 to 1.

Data Types: double

InputBounds — Bounds of input data

Read-only: numeric vector of size 2

This property is read-only.

Bounds of input data, specified as a numeric vector of size 2.

Data Types: double

InputType — Type of input data

Read-only: 'binary' (default) | 'continuous'

This property is read-only.

Type of input data, specified as either 'binary' or 'continuous'.

Data Types: char

TestMethod — Test method used for drift detection

Read-only: 'ewma' | 'average'

This property is read-only.

Test method used for drift detection, specified as either 'ewma' or 'average' corresponding to the "hddmw" and "hddma" detection methods, respectively, in the call to incrementalConceptDriftDetector.

Data Types: char

WarningThreshold — Threshold to determine warning versus drift

Read-only: 0.005 (default) | nonnegative scalar value from 0 to 1

This property is read-only.

Threshold to determine warning versus drift, specified as a nonnegative scalar value from 0 to 1. It is the significance level the software uses for calculating the allowed error between a random variable and its expected value in Hoeffding's inequality or McDiarmid's inequality before it sets DriftStatus to 'Warning'.

Data Types: double

WarmupPeriod — Number of observations for drift detector warm-up

Read-only: nonnegative integer value

This property is read-only.

Number of observations for drift detector warm-up, specified as a nonnegative integer.

Data Types: double

Drift Detection Parameters

CutHoeffdingBound — Hoeffding's bound for input data observed up to the cut point

Read-only: numeric value

This property is read-only.

Hoeffding's bound for input data observed up to the cut point, specified as a numeric value.

detectdrift updates CutMean and CutHoeffdingBound and resets PostCutMean and PostCutHoeffdingBound when any one of these conditions is satisfied:

• Alternative is "greater" and Mean + HoeffdingBound is less than or equal to CutMean + CutHoeffdingBound.

• Alternative is "less" and Mean - HoeffdingBound is greater than or equal to CutMean - CutHoeffdingBound.

• Alternative is "unequal" and Mean + HoeffdingBound is less than or equal to CutMean - CutHoeffdingBound or Mean - HoeffdingBound is greater than or equal to CutMean + CutHoeffdingBound.

Data Types: double

CutMean — Weighted average

Read-only: numeric value

This property is read-only.

Weighted average of data observed up to the cut point, specified as a numeric value.

detectdrift updates CutMean and CutHoeffdingBound and resets PostCutMean and PostCutHoeffdingBound when any one of these conditions is satisfied:

• Alternative is "greater" and Mean + HoeffdingBound is less than or equal to CutMean + CutHoeffdingBound.

• Alternative is "less" and Mean - HoeffdingBound is greater than or equal to CutMean - CutHoeffdingBound.

• Alternative is "unequal" and Mean + HoeffdingBound is less than or equal to CutMean - CutHoeffdingBound or Mean - HoeffdingBound is greater than or equal to CutMean + CutHoeffdingBound.

Data Types: double

HoeffdingBound — Hoeffding's bound for all input data

Read-only: numeric value

This property is read-only.

Hoeffding's bound for all input data used for training the drift detector, specified as a numeric value.

Data Types: double

Mean — Weighted average of all input data

Read-only: numeric value

This property is read-only.

Weighted average of all input data used for training the drift detector, specified as a numeric value.

Data Types: double

NumTrainingObservations — Number of observations used for training

Read-only: nonnegative integer value

This property is read-only.

Number of observations used for training the drift detector, specified as a nonnegative integer value.

Data Types: double

PostCutMean — Weighted average of data observed after the cut point

Read-only: numeric value

This property is read-only.

Weighted average of data observed after the cut point, specified as a numeric value.

detectdrift updates CutMean and CutHoeffdingBound and resets PostCutMean and PostCutHoeffdingBound when any one of these conditions is satisfied:

• Alternative is "greater" and Mean + HoeffdingBound is less than or equal to CutMean + CutHoeffdingBound.

• Alternative is "less" and Mean - HoeffdingBound is greater than or equal to CutMean - CutHoeffdingBound.

• Alternative is "unequal" and Mean + HoeffdingBound is less than or equal to CutMean - CutHoeffdingBound or Mean - HoeffdingBound is greater than or equal to CutMean + CutHoeffdingBound.

Data Types: double

PostCutHoeffdingBound — Hoeffding's bound for data observed after the cut point

Read-only: numeric value

This property is read-only.

Hoeffding's bound for data observed after the cut point, specified as a numeric value.

detectdrift updates CutMean and CutHoeffdingBound and resets PostCutMean and PostCutHoeffdingBound when any one of these conditions is satisfied:

• Alternative is "greater" and Mean + HoeffdingBound is less than or equal to CutMean + CutHoeffdingBound.

• Alternative is "less" and Mean - HoeffdingBound is greater than or equal to CutMean - CutHoeffdingBound.

• Alternative is "unequal" and Mean + HoeffdingBound is less than or equal to CutMean - CutHoeffdingBound or Mean - HoeffdingBound is greater than or equal to CutMean + CutHoeffdingBound.

Data Types: double

Drift Status Parameters

DriftDetected — Flag indicating whether software detects drift

Read-only: 1 | 0

This property is read-only.

Flag indicating whether software detects drift or not, specified as either 1 or 0. Value of 1 means DriftStatus is 'Drift'.

Data Types: logical

DriftStatus — Current drift status

Read-only: 'Stable' | 'Warning' | 'Drift'

This property is read-only.

Current drift status, specified as 'Stable', 'Warning', or 'Drift'. You can see the transition in the drift status by comparing DriftStatus and PreviousDriftStaus.

Data Types: char

IsWarm — Flag indicating whether warm-up period is over

Read-only: 1 | 0

This property is read-only.

Flag indicating whether the warm-up period is over or not, specified as 1 (true) or 0(false).

Data Types: logical

PreviousDriftStatus — Drift status prior to the latest training

Read-only: 'Stable' | 'Warning' | 'Drift'

This property is read-only.

Drift status prior to the latest training using the most recent batch of data, specified as 'Stable', 'Warning', or 'Drift'. You can see the transition in the drift status by comparing DriftStatus and PreviousDriftStaus.

Data Types: char

WarningDetected — Flag indicating whether there is warning

Read-only: 1 | 0

This property is read-only.

Flag indicating whether there is warning or not, specified as either 1 or 0. Value of 1 means DriftStatus is 'Warning'.

Data Types: logical

Object Functions

detectdrift	Update drift detector states and drift status with new data
reset	Reset incremental concept drift detector

Examples

Monitor Continuous Data for Drift

Create a random stream such that the observations come from a normal distribution with standard deviation 0.75, but the mean changes over time. First 1000 observations come from a distribution with mean 2, the next 1000 come from a distribution with mean 4, and the following 1000 come from a distribution with mean 7.

rng(1234) % For reproducibility
numObservations = 3000;
switchPeriod1 = 1000;
switchPeriod2 = 2000;
X = zeros([numObservations 1]);

% Generate the data
for i = 1:numObservations
   if i <= switchPeriod1
      X(i) = normrnd(2,0.75);
   elseif i <= switchPeriod2
      X(i) = normrnd(4,0.75);
   else
      X(i) = normrnd(7,0.75);
   end
end

In an incremental drift detection application, access to data stream and model update would happen consecutively. One would not collect the data first and then feed into the model. However, for the purpose of clarification, this example demonstrates the simulation of data separately.

Specify the drift warm-up period as 50 observations and estimation period for the data input bounds as 100.

driftWarmupPeriod = 50;
estimationPeriod = 100;

Initiate the incremental concept drift detector. Utilize the Hoeffding's bounds method with exponentially weighted moving average method (EWMA). Specify the input type and warm-up period.

incCDDetector = incrementalConceptDriftDetector("hddmw",InputType="continuous", ...
                WarmupPeriod=driftWarmupPeriod,EstimationPeriod=estimationPeriod)

incCDDetector = 
  HoeffdingDriftDetectionMethod

        PreviousDriftStatus: 'Stable'
                DriftStatus: 'Stable'
                     IsWarm: 0
    NumTrainingObservations: 0
                Alternative: 'greater'
                  InputType: 'continuous'
                 TestMethod: 'ewma'


  Properties, Methods

incDDetector is a HoeffdingDriftDetectionMethod object. When you first create the object, properties such as DriftStatus, IsWarm, CutMean, and NumTrainingObservations are at their initial state. detectdrift updates them as you feed the data incrementally and monitor for drift.

Preallocate the batch size and the variables to record drift status and the mean the drift detector computes with each income of data.

status = zeros([numObservations 1]);
statusname = strings([numObservations 1]);
M = zeros([numObservations 1]);

Simulate the data stream of one observation at a time and perform incremental drift detection. At each iteration:

• Monitor for drift using the new data with detectdrift.

• Track and record the drift status and the statistics for visualization purposes.

• When a drift is detected, reset the incremental concept drift detector by using the function reset.

for i = 1:numObservations
    
    incCDDetector = detectdrift(incCDDetector,X(i));
    
    M(i) = incCDDetector.Mean;
        
    if incCDDetector.DriftDetected
        status(i) = 2;
        statusname(i) = string(incCDDetector.DriftStatus);
        incCDDetector = reset(incCDDetector); % If drift detected, reset the detector
        sprintf("Drift detected at observation #%d. Detector reset.",i)
    elseif incCDDetector.WarningDetected
        status(i) = 1;
        statusname(i) = string(incCDDetector.DriftStatus);
        sprintf("Warning detected at observation #%d.",i)
    else 
        status(i) = 0;
        statusname(i) = string(incCDDetector.DriftStatus);
    end      
end

ans = 
"Warning detected at observation #1024."

ans = 
"Warning detected at observation #1025."

ans = 
"Warning detected at observation #1026."

ans = 
"Warning detected at observation #1027."

ans = 
"Warning detected at observation #1028."

ans = 
"Warning detected at observation #1029."

ans = 
"Drift detected at observation #1030. Detector reset."

ans = 
"Warning detected at observation #2012."

ans = 
"Warning detected at observation #2013."

ans = 
"Warning detected at observation #2014."

ans = 
"Drift detected at observation #2015. Detector reset."

Plot the drift status versus the observation number.

gscatter(1:numObservations,status,statusname,'gyr','*',5,'on',"Number of observations","Drift status")

Plot the mean values versus the number of observations.

scatter(1:numObservations,M)

You can see the increase in the sample mean from the plot. The mean value becomes larger and the software eventually detects the drift in the data. Once a drift is detected, reset the incremental drift detector. This also resets the mean value. In the plot, the observations where the sample mean is zero correspond to the estimation periods. There is an estimation period at the beginning and then twice after the drift detector is reset following the detection of a drift.

References

[1] Frias-Blanco, Isvani, Jose del Campo-Ávila, Ramos-Jimenez Gonzalo, Rafael Morales-Bueno, Augustin Ortiz-Diaz, and Yaile Caballero-Mota. “Online and non-parametric drift detection methods based on Hoeffding's bounds.“ IEEE Transactions on Knowledge and Data Engineering, Vol. 27, No. 3, pp.810-823. 2014.

Version History

Introduced in R2022a