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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.

Outline

- Motivation
- Background
- Proposed contribution
- Future work and Conclusion

Motivation

- 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

- 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)

Dataset

shift

(Torres et al.

2012),

Non-stationary

environments

(M Krauledat 2008),

(Sugiyama 2012).

- Dataset shift-detection

Supervised learning

(Mitchell, 1997)

(Sugiyama et al. 2009)

Proposed

Work

Shift-Detection

- Proposed Work

- 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

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

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

XY: Predictive model (e.g., spam filtering)

YX: Generative model (e.g., Fault detection )

Types of Dataset Shift

- Covariate Shift
- Prior Probability Shift
- Concept Shift

Prior probability shift appears only in YX problems

Concept shifts appears

- Covariate shift appears only in XYproblems

Dataset Shift-Detection

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

- 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)

(1)

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

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

(2)

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

(3)

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

UCL

LCL

Datasets

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): 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: 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.

(a)

(b)

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 :SD-EWMA shift detection in time-series data

Table : Simulation results on different tests

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

Table 4: SD-EWMA shift detection in BCI data

Conclusion and Future Work

- 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.

Thank You !

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