incrementalConceptDriftDetector
Syntax
Description
returns an incremental concept drift detector that utilizes the default method, Hoeffding's
Bounds Drift Detection Method with moving average test (HDDMA).IncCDDetector
= incrementalConceptDriftDetector()
returns an incremental concept drift detector that utilizes the method
IncCDDetector
= incrementalConceptDriftDetector(DetectionMethod
)DetectionMethod
.
specifies additional options using one or more IncCDDetector
= incrementalConceptDriftDetector(DetectionMethod
,Name=Value
)Name=Value
arguments.
Examples
Monitor Data Stream for Potential Drift
Initiate the concept drift detector using the Drift Detection Method (DDM).
incCDDetector = incrementalConceptDriftDetector("ddm");
Create a random stream such that for the first 1000 observations, failure rate is 0.1 and after 1000 observations, failure rate increases to 0.6.
rng(1234) % For reproducibility numObservations = 3000; switchPeriod = 1000; for i = 1:numObservations if i <= switchPeriod failurerate = 0.1; else failurerate = 0.6; end X(i) = rand()<failurerate; % Value 1 represents failure end
Preallocate variables for tracking drift status.
status = zeros(numObservations,1); statusname = strings(numObservations,1);
Continuously feed the data to the drift detector and perform incremental drift detection. At each iteration:
Update statistics of the drift detector and monitor for drift using the new data point with
detectdrift
. (Note:detectdrift
checks for drift after the warmup period.)Track and record the drift status for visualization purposes.
When a drift is detected, reset the incremental concept drift detector by using
reset
.
for i = 1:numObservations incCDDetector = detectdrift(incCDDetector,X(i)); statusname(i) = string(incCDDetector.DriftStatus); if incCDDetector.DriftDetected status(i) = 2; incCDDetector = reset(incCDDetector); % If drift detected, reset the detector sprintf("Drift detected at Observation #%d. Detector reset.",i) elseif incCDDetector.WarningDetected status(i) = 1; else status(i) = 0; end end
ans = "Drift detected at Observation #1078. Detector reset."
After the change in the failure rate at observation number 1000, detectdrift
detects the shift at observation number 1078.
Plot the drift status versus the observation number.
gscatter(1:numObservations,status,statusname,'gyr','*',4,'on',"Observation number","Drift status")
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 warmup 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 warmup 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.
Monitor Data Stream for Decrease in Failure Rate
Initiate the concept drift detector using the Drift Detection Method (DDM).
incCDDetector = incrementalConceptDriftDetector("ddm",Alternative="less",WarmupPeriod=100);
Create a random stream such that for the first 1000 observations, failure rate is 0.4 and after 1000 failure rate decreases to 0.1.
rng(1234) % For reproducibility numObservations = 3000; switchPeriod = 1000; for i = 1:numObservations if i <= switchPeriod failurerate = 0.4; else failurerate = 0.125; end X(i) = rand()<failurerate; % Value 1 represents failure end
Preallocate variables for tracking drift status and the optimal mean and optimal standard deviation value.
optmean = zeros(numObservations,1); optstddev = zeros(numObservations,1); status = zeros(numObservations,1); statusname = strings(numObservations,1);
Continuously feed the data to the drift detector and monitor for any potential change. Record the drift status for visualization purposes.
for i = 1:numObservations incCDDetector = detectdrift(incCDDetector,X(i)); statusname(i) = string(incCDDetector.DriftStatus); optmean(i) = incCDDetector.OptimalMean; optstddev(i) = incCDDetector.OptimalStandardDeviation; if incCDDetector.DriftDetected status(i) = 2; incCDDetector = reset(incCDDetector); % If drift detected, reset the detector sprintf("Drift detected at Observation #%d. Detector reset.",i) elseif incCDDetector.WarningDetected status(i) = 1; else status(i) = 0; end end
ans = "Drift detected at Observation #1107. Detector reset."
After the change in the failure rate at observation number 1000, detectdrift
detects the shift at observation number 1096.
Plot the change in the optimal mean and optimal standard deviation.
tiledlayout(2,1); ax1 = nexttile; plot(ax1,1:numObservations,optmean) ax2 = nexttile; plot(ax2,1:numObservations,optstddev)
Plot the drift status versus the observation number.
figure(); gscatter(1:numObservations,status,statusname,'gyr','*',4,'on',"Observation number","Drift status")
detectdrift
concludes on a warning status for multiple observations before it decides on a drift.
Input Arguments
DetectionMethod
— Incremental drift detection method
"ddm"
| "hddma"
| "hddmw"
Incremental drift detection method, specified as one of the following.
Detection Method | Definition |
---|---|
"ddm" | Drift Detection Method (DDM) |
"hddma" | Hoeffding's Bounds Drift Detection Method with moving average test (HDDMA) |
"hddmw" | Hoeffding's Bounds Drift Detection Method with exponentially weighted moving average (EWMA) test (HDDMW) |
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: Alternative="less",InputType="continuous",InputBounds=[-1,1],ForgettingFactor=0.075
specifies the alternative hypothesis as less, that is, left-sided, the input data type as
continuous data, lower and upper bounds of the input data as [-1,1] and the value of the
forgetting factor for the HDDMW method as 0.075.
Alternative
— Type of alternative hypothesis
"greater"
(default) | "less"
| "unequal"
(for HDDMA or HDDMW)
Type of alternative hypothesis for determining drift status, specified as one of
"unequal"
, "greater"
, or
"less"
. Given two test statistics and ,
"greater"
tests for a drift in the positive direction, that is, .In this case, the null hypothesis is .
"less"
tests for a drift in the negative direction, that is, .In this case, the null hypothesis is .
"unequal"
tests for a drift in the either direction, that is, .In this case, the null hypothesis is .
"unequal"
is for theHDDMA
andHDDMW
methods only.
For each type of test, detectdrift
updates the statistics and checks whether it can reject the null hypothesis in favor
of the alternative at the significance level of WarningThreshold
or DriftThreshold
. If it rejects the null hypothesis at the
significance level of WarningThreshold
, then it updates the
DriftStatus
to 'Warning'
. If it rejects the
null hypothesis at the DriftThreshold
, then it updates the
DriftStatus
to 'Drift'
.
Example: Alternative="less"
InputType
— Type of input to the drift detector
"binary"
(default) | "continuous"
Type of input to the drift detector, specified as either
"binary"
or "continuous"
.
Example: InputType="continuous"
WarmupPeriod
— Number of observations used for drift detector to warm up
30 (default) | nonnegative integer
Number of observations used for drift detector to warm up, specified as a
nonnegative integer. Until the end of the warmup period, detectdrift
trains the drift detector using the incoming data and updates the internal statistics,
but does not check for the drift status. After the software reaches the warmup period,
that is, once the drift detector is warm, it starts checking for any changes in the
drift status.
Example: WarmupPeriod=50
Data Types: double
| single
DriftThreshold
— Number of standard deviations for drift limit
3 (default) | nonnegative scalar value
Number of standard deviations for drift limit, specified as a nonnegative scalar value. This is the number of standard deviations the overall test statistic value can be away from the optimal test statistic value before the drift detector sets the drift status to drift. Default value of 3 corresponds to a 99.7% confidence level [1].
DriftThreshold
value must be strictly greater than the
WarningThreshold
value.
Example: DriftThreshold=2.5
Data Types: double
| single
WarningThreshold
— Number of standard deviations for warning limit
2 (default) | nonnegative scalar value
Number of standard deviations for warning limit, specified as a nonnegative scalar value. This is the number of standard deviations the overall test statistic value can be away from the optimal test statistic value before the drift detector sets the drift status to warning. Default value of 2 corresponds to a 95% confidence level [1].
WarningThreshold
value must be strictly smaller than the
DriftThreshold
value.
Example: WarningThreshold=1.75
Data Types: double
| single
DriftThreshold
— Threshold to determine if drift exists
0.001 (default) | nonnegative scalar value from 0 to 1
Threshold to determine if drift exists, specified as a nonnegative scalar value from 0 to 1. It is the significance level the drift detector uses for calculating the allowed error between a random variable and its expected value in Hoeffding's inequality and McDiarmid's inequality before it sets the drift status to drift [2].
DriftThreshold
value must be strictly smaller than the
WarningThreshold
value.
Example: DriftThreshold=0.003
Data Types: double
| single
EstimationPeriod
— Number of observations used to estimate the input bounds for continuous data
nonnegative integer
Number of observations used to estimate the input bounds for continuous data,
specified as a nonnegative integer. That is, when InputType
is
"continuous"
and you did not specify the
InputBounds
value, the software uses
EstimationPeriod
number of observations to estimate the input
bounds. After the estimation period, the software starts the warmup period.
If you specify the InputBounds
value or
InputType
is "binary"
, then the software
ignores EstimationPeriod
.
Default value is 100 when there is a need for estimating the input bounds. Otherwise, default value is 0.
Example: EstimationPeriod=150
Data Types: double
| single
InputBounds
— Lower and upper bounds of continuous input data
numeric vector of size 2
Lower and upper bounds of continuous input data, specified as a numeric vector of size 2.
If InputType
is "continuous"
and you do
not specify the InputBounds
value, then
detectdrift
estimates the bounds from the data during the
estimation period. Specify the number of observations to estimate the data input
bounds by using EstimationPeriod
.
If InputType
is "binary"
, then the drift
detector sets the InputBounds
value to [0,1] and the software
ignores the InputBounds
name-value argument.
HDDM uses Hoeffding's inequality and McDiarmid's inequality for drift detection and these inequalities assume bounded inputs [2].
Example: InputBounds=[-1 1]
Data Types: double
| single
ForgettingFactor
— Forgetting factor for HDDMW
method
0.05 (default) | scalar value from 0 to 1
Note
This option is only for the exponentially weighted moving average (EWMA) method
(corresponding to DetectionMethod
value set as
"hddmw"
).
Forgetting factor in the HDDMW method, specified as a scalar value from 0 to 1.
Forgetting factor is the λ
in the EWMA statistic [2]. Forgetting factor
determines how much the current prediction of mean is influenced by the past
observations. A higher value of ForgettingFactor
attains more
weight to the current observations and less value to the past observations.
Example: ForgettingFactor=0.075
Data Types: double
| single
WarningThreshold
— Threshold to determine warning versus drift
0.005 (default) | nonnegative scalar value from 0 to 1
Threshold to determine warning versus drift, specified as a nonnegative scalar value from 0 to 1. It is the significance level the drift detector uses for calculating the allowed error between a random variable and its expected value in Hoeffding's inequality and McDiarmid's inequality before it sets the drift status to warning [2].
WarningThreshold
value must be strictly greater than
DriftThreshold
value.
Example: WarningThreshold=0.007
Data Types: double
| single
Output Arguments
IncCDDetector
— Incremental concept drift detector
DriftDetectionMethod
| HoeffdingDriftDetectionMethod
Incremental concept drift detector, specified as either DriftDetectionMethod
or HoeffdingDriftDetectionMethod
object. For more information on these
objects and their properties, see the corresponding reference pages.
References
[1] Gama, Joao, Pedro Medas, Gladys Castillo, and Pedro P. Rodrigues. “Learning with drift detection.“ In Brazilian symposium on artificial intelligence, pp. 286-295. Berlin, Heidelberg: Springer. 2004, September.
[2] 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
See Also
DriftDetectionMethod
| HoeffdingDriftDetectionMethod
| reset
| detectdrift
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