Question

What is the change detection theory? How would you easily and briefly explain it?

Answer 1

change detection theory or change point detection tries to identify times when the probability distribution of a stochastic process or time series changes. In general the problem concerns both detecting whether or not a change has occurred, or whether several changes might have occurred, and identifying the times of any such changes.

Specific applications, like step detection and edge detection, may be concerned with changes in the mean, variance, correlation, or spectral density of the process. More generally change detection also includes the detection of anomalous behavior: anomaly detection.

Online change detectionEdit

Using the sequential analysis ("online") approach, any change test must make a trade-off between these common metrics:

False alarm rateMisdetection rateDetection delay

In a Bayes change-detection problem, a prior distribution is available for the change time.

Online change detection is also done using streaming algorithms.

Minimax change detectionEdit

In minimax change detection, the objective is to minimize the expected detection delay for some worst-case change-time distribution, subject to a cost or constraint on false alarms.

A key technique for minimax change detection is the CUSUM procedure.

Offline change detectionEdit

Basseville discusses offline change-in-mean detection with hypothesis testing based on the works of Page[1] and Picard[2] and maximum-likelihood estimation of the change time, related to two-phase regression. Other approaches employ clustering based on maximum likelihood estimation.[citation needed

"Offline" approaches cannot be used on streaming data because they need to compare to statistics of the complete time series, and cannot react to changes in real time but often provide more accurate estimation of the change time and magnitude.

Applications of change detection:

Change detection tests are often used in manufacturing (quality control), intrusion detection, spam filtering, website tracking, and medical diagnostics.