Dataset shift detection in non stationary environments using ewma charts
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Dataset Shift Detection in Non-Stationary Environments using EWMA Charts. Prof. Girijesh Prasad Co-authors: Haider Raza, Yuhua Li School of Computing & Intelligent Systems @ Magee , Faculty of Computing & Engineering, Derry~Londonderry . [email protected] Outline. Motivation

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Dataset shift detection in non stationary environments using ewma charts

Dataset Shift Detection in Non-Stationary Environments using EWMA Charts

Prof.Girijesh Prasad

Co-authors: Haider Raza, Yuhua Li

School of Computing & Intelligent Systems @ Magee,

Faculty of Computing & Engineering, Derry~Londonderry.

[email protected]

Outline EWMA Charts

  • Motivation

  • Background

  • Proposed contribution

  • Future work and Conclusion

Motivation EWMA Charts

  • Classical learning systems are built upon the assumption that the input data distribution for the trainingand testing are same.

  • Real-world environments are often non-stationary(e.g., EEG-based BCI)

  • So, learning in real-time environments is difficult due to the non-stationarity effects and the performance of system degrades with time.

  • So, predictors need to adapt online. However, online adaptation particularly for classifiers is difficult to perform and should be avoided as far as possible and this requires performing in real-time:

    • Non-stationary shift-detection test.

Background EWMA Charts

  • Supervised learning

  • Non-stationary environments

  • Dataset shift

Dataset shift-detection(Shewhart 1939),

(Page 1954),

(Roberts 1959),

(Alippi et al. 2011b),

(Alippi & Roveri 2008a;

Alippi & Roveri 2008b)



(Torres et al.




(M Krauledat 2008),

(Sugiyama 2012).

  • Dataset shift-detection

Supervised learning

(Mitchell, 1997)

(Sugiyama et al. 2009)




  • Proposed Work

Supervised Learning EWMA Charts

  • Training samples: Input and output (

  • Learn input-output rule:

  • Assumption: “Trainingand test samples are drawn from same probability distribution” i.e.,

    Is this assumption really true?

Reason :- Non-StationaryEnvironments !

No….!!! Not always true 

Non-Stationarity EWMA Charts

For examples:

  • Learning from past only is of limited use 

  • Brain-computer interface

  • Robot control

  • Remote sensing application

  • Network intrusion detection

    What is the challenge?

Dataset shift
Dataset Shift EWMA Charts

Dataset Shift appears when training and testjoint distributions are different. That is, when (Torres, 2012)

*Note : Relationship between covariates (x) and class label (y)

XY: Predictive model (e.g., spam filtering)

YX: Generative model (e.g., Fault detection )

Types of Dataset Shift

  • Covariate Shift

  • Prior Probability Shift

  • Concept Shift

Prior probability shift appears only in YX problems

Concept shifts appears

  • Covariate shift appears only in XYproblems

Dataset shift detection
Dataset Shift-Detection EWMA Charts

Detecting abrupt and gradual shifts in time-series data is called the data shift-detection.

Types of Shift-Detection

  • Retrospective/offline-detection: (i.e., Shift-point analysis)

  • Real-time/online-detection: (i.e., Control charts)

    Types of Control Charts

  • Shewart Chart (Shewart, 1939)

  • Cumulative Sum(CUSUM) (E S Page, 1954)

  • Exponentially Weighted Moving Average (EWMA) (S W Roberts, 1959)

  • Computational Intelligence CUSUM (CI-CUSUM) (Alippi et al., 2008)

  • Intersection of Confidence Interval (ICI) (Alippi et al., 2011 )

Proposed contribution
Proposed EWMA ChartsContribution

  • We have proposed dataset shift-detection test.

    • Shift-Detection based on Exponentially Weight Moving Average (SD-EWMA) model

Shift detection based on exponentially weight moving average sd ewma
Shift-Detection based on EWMA ChartsExponentially Weight Moving Average (SD-EWMA)


where λ is the smoothing constant (0<λ≤1).

It is a first-order integrated moving average (ARIMA) model.


Where is a sequence of i.i.d random signal with zero mean and constant variance.

Equation (1) with , is the optimal 1-step-ahead prediction for this process

The 1-step-aheaderror are calculated as


IF the 1-step-ahead erroris normally distributed, then



Datasets EWMA Charts

Synthetic Data

Dataset 1-Jumping Mean (D1):

where is a noise with mean and standard deviation 1.5. The initial values are set as.

A change point is inserted at every 100 time steps by setting the noise mean at time as

where is a natural number such that.

Dataset 2-Scaling Variance (D2): The change point is inserted at every 100 time steps by setting the noise

standard deviation at time as

where is a natural number such that

Dataset 3-Positive-Auto-correlated (D3): The dataset is consisting of 2000 data-points, the non stationarity

occurs in the middle of the data stream, shifting from to, where denotes the

normal distribution with mean and standard deviation respectively.

Dataset 4-Auto-correlated (D4) EWMA Charts: The dataset is a time-series consisting of 2000 data-points using 1-D digital filter from matlab. The filter function creates a direct form II transposed implementation of a standard difference equation. In the filter, the denominator coefficient is changed from 2 to 0.5 after producing 1000 number of points.

Real-world Dataset: EEG Based Brain Signals

The real-world data used here are from BCI competition-III dataset (IV-b). This dataset, contains 2 classes,

118 EEG channels (0.05-200Hz), 1000Hz sampling rate which is down-sampled to 100Hz, 210 training trials,

and 420 test trials.

Figure : pdf plot of 3 different sessions’ data taken from the training dataset. It is clear from the plot that, in each session the distribution is changed by shifting the mean from session-to-session transfer.

Figure EWMA Charts: Shift detection based on SD-EWMA: Dataset 1 (jumping mean): (a) the shift point is detected at every 100th point. (b) Zoomed view of figure a: shift is detected at 401st sample by crossing the upper control limit.



Figure : Shift detection based on SD-EWMA: (a) Dataset 2 (scaling variance): the shift is detected at 3 points.

(b) Dataset 3 (positive auto-correlated): detects the shift after producing 1000 observations.

(c) Dataset 4 (Auto-correlated): detects the shift after producing 1000 observations.

Table EWMA Charts:SD-EWMA shift detection in time-series data

Table : Simulation results on different tests

Figure 4 EWMA Charts: A window of 2000 samples obtained from real-world dataset.

Table 4: SD-EWMA shift detection in BCI data

Conclusion and future work
Conclusion and Future Work EWMA Charts

  • The drawback of classical supervised learning techniques in non-stationary environments and the motivation behind the dataset shift-detection were discussed.

  • The background of non-stationary environments and dataset shift-detection were presented.

  • A proposed SD-EWMA method is presented and the results are discussed.

  • In future, the SD-EWMAwill be combined into an adaptive learning framework for non-stationary learning.

Questions EWMA Charts

Thank You !