datadriftR (version 1.0.0)

PageHinkley: Page-Hinkley Test for Change Detection

Description

Implements the Page-Hinkley test, a sequential analysis technique used to detect changes in the average value of a continuous signal or process. It is effective in detecting small but persistent changes over time, making it suitable for real-time monitoring applications.

Public fields

min_instances

Minimum number of instances required to start detection.

delta

Minimal change considered significant for detection.

threshold

Decision threshold for signaling a change.

alpha

Forgetting factor for the cumulative sum calculation.

x_mean

Running mean of the observed values.

sample_count

Counter for the number of samples seen.

sum

Cumulative sum used in the change detection.

change_detected

Boolean indicating if a drift has been detected.

Methods

Public methods

• PageHinkley$new()

• PageHinkley$reset()

• PageHinkley$add_element()

• PageHinkley$detected_change()

• PageHinkley$clone()

---

Method new()

Initializes the Page-Hinkley test with specific parameters.

Usage

PageHinkley$new(
  min_instances = 30,
  delta = 0.005,
  threshold = 50,
  alpha = 1 - 1e-04
)

Arguments

min_instances

Minimum number of samples before detection starts.

delta

Change magnitude to trigger detection.

threshold

Cumulative sum threshold for change detection.

alpha

Weight for older data in cumulative sum.

---

Method reset()

Resets all the internal states of the detector to initial values.

Usage

PageHinkley$reset()

---

Method add_element()

Adds a new element to the data stream and updates the detection status based on the Page-Hinkley test.

Usage

PageHinkley$add_element(x)

Arguments

x

New data value to add and evaluate.

---

Method detected_change()

Checks if a change has been detected based on the last update.

Usage

PageHinkley$detected_change()

Returns

Boolean indicating whether a change was detected.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

PageHinkley$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

The Page-Hinkley test is a type of cumulative sum (CUSUM) test that accumulates differences between data points and a reference value (running mean). It triggers a change detection signal when the cumulative sum exceeds a predefined threshold. This test is especially useful for early detection of subtle shifts in the behavior of the monitored process.

References

E. S. Page. 1954. Continuous Inspection Schemes. Biometrika 41, 1/2 (1954), 100–115.

Montiel, Jacob, et al. "Scikit-Multiflow: A Multi-output Streaming Framework." Journal of Machine Learning Research, 2018. This framework provides tools for multi-output and stream data mining and was an inspiration for some of the implementations in this class.

Implementation: https://github.com/scikit-multiflow/scikit-multiflow/blob/a7e316d1cc79988a6df40da35312e00f6c4eabb2/src/skmultiflow/drift_detection/page_hinkley.py

Examples

set.seed(123)  # Setting a seed for reproducibility
data_part1 <- sample(c(0, 1), size = 100, replace = TRUE, prob = c(0.7, 0.3))

# Introduce a change in data distribution
data_part2 <- sample(c(0, 5), size = 100, replace = TRUE, prob = c(0.3, 0.7))

# Combine the two parts
data_stream <- c(data_part1, data_part2)
ph <- PageHinkley$new()
for (i in seq_along(data_stream)) {
  ph$add_element(data_stream[i])
  if (ph$detected_change()) {
    cat(sprintf("Change has been detected in data: %s - at index: %d\n", data_stream[i], i))
  }
}