Change Point Detection

1. Introduction

Change Point Detection (CPD) refers to identifying points in a data sequence where the statistical properties change. This technique is crucial in various fields such as finance, manufacturing, and environmental monitoring, as it helps in understanding anomalies in time series data.

2. Key Concepts

• **Change Point**: A point in time where the properties of the data change.
• **Time Series Data**: Data points collected or recorded at specific time intervals.
• **Anomaly Detection**: The identification of rare items, events, or observations that raise suspicions by differing significantly from the majority of the data.

3. Methodologies

Different methodologies for Change Point Detection include:

1. Statistical Tests: Methods such as the CUSUM (Cumulative Sum Control Chart) test.
2. Machine Learning Approaches: Utilizing models like Hidden Markov Models (HMM).
3. Bayesian Methods: Leveraging Bayesian inference for identifying change points.

4. Implementation

The following Python example demonstrates how to implement Change Point Detection using the ruptures library:

import numpy as np
import matplotlib.pyplot as plt
import ruptures as rpt

# Generate synthetic data
n = 500
signal = np.random.randn(n)  # Random noise
signal[200:300] += 5  # Change point

# Detect change points
model = "l2"  # model type
algo = rpt.Pelt(model=model).fit(signal)
result = algo.predict(pen=10)  # Penalty parameter

# Display results
rpt.display(signal, result)
plt.title("Change Point Detection")
plt.show()

5. Best Practices

• Use multiple methods for validation.
• Adjust parameters based on domain knowledge.
• Visualize results to confirm detected change points.

6. FAQ