Cusum

API reference for sovai.extensions.cusum

Module: sovai.extensions.cusum

Classes

CUSUM_Detector

class CUSUM_Detector

CUSUM Change Point Detector Class

Example:

detector = CUSUM_Detector(warmup_period=20, delta=15, threshold=30)
data = [12.3, 14.5, 15.6, 16.8, 17.9, 20.2, 25.7, 30.2, 32.5, 32.9, 33.0, 32.2, 31.8, 30.5, 30.1]
pos_changes, neg_changes, change_points = detector.detect_change_points(data)
detector.plot_change_points(data, change_points, pos_changes, neg_changes)

Attributes

• warmup_period

• delta

• threshold

Methods

__init__()

def __init__(self, warmup_period = 10, delta = 10, threshold = 20)

Initializes the Change Point Detector with the specified parameters.

Parameters

Parameter	Type	Description
warmup_period	int	The number of initial observations before starting to detect change points. Default is 10.
delta	float	Sensitivity parameter for detecting changes. Default is 10.
threshold	float	Threshold for detecting a change point. Default is 20.

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predict_next()

def predict_next(self, observation)

Predicts the next data point and detects change points.

Parameters

Parameter	Type	Description
observation	float	New data point.

Returns

• pos_change (numpy array): Cumulative sum for positive changes.

• neg_change (numpy array): Cumulative sum for negative changes.

• is_changepoint (bool): Indicates if a change point is detected.

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detect_change_points()

def detect_change_points(self, data)

Detects change points in the given data using the CUSUM detector.

Parameters

Parameter	Type	Description
data	numpy array	Data points to be analyzed.

Returns

• pos_changes (numpy array): Positive cumulative sum values.

• neg_changes (numpy array): Negative cumulative sum values.

• change_points (numpy array): Detected change points indices.

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plot_change_points()

def plot_change_points(self, data, change_points, pos_changes, neg_changes)

Plots data with detected change points and cumulative sums.

Parameters

Parameter	Type	Description
data	numpy array	Original data points.
change_points	list	List of detected change points.
pos_changes	list	List of positive cumulative sum values.
neg_changes	list	List of negative cumulative sum values.

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ProbCUSUM_Detector

class ProbCUSUM_Detector

A class to detect change points in sequential data using the Probabilistic Cumulative Sum (CUSUM) algorithm.

Example:

detector = ProbCUMSUM_Detector(warmup_period=10, threshold_probability=0.001)
data = [10.2, 11.5, 12.6, 12.8, 12.9, 13.2, 12.7, 12.5, 12.3, 12.9, 25.0, 12.2, 11.8, 10.5, 10.1]
probabilities, change_points = detector.detect_change_points(data)
detector.plot_change_points(data, change_points, probabilities)

Attributes

• warmup_period

• threshold_probability

• running_sum

Methods

__init__()

def __init__(self, warmup_period = 10, threshold_probability = 0.001)

Initializes the Probabilistic CUSUM Detector with the specified parameters.

Parameters

Parameter	Type	Description
warmup_period	int	The number of initial observations before starting to detect change points. Default is 10.
threshold_probability	float	The threshold probability below which a change point is detected. Default is 0.001.

---

predict_next()

def predict_next(self, observation)

Predicts the probability of a change point in the next observation.

Parameters

Parameter	Type	Description
observation	float	The next observation in the sequence.

Returns

• probability (float): The probability of a change point in the next observation.

• is_changepoint (bool): True if a change point is detected, False otherwise.

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detect_change_points()

def detect_change_points(self, data)

Detects change points in the given data using the CUSUM detector.

Parameters

Parameter	Type	Description
data	—	numpy array Data points to be analyzed.

Returns

• probabilities: numpy array Probability values for each data point.

• change_points: numpy array Detected change points indices.

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plot_change_points()

def plot_change_points(self, data, change_points, probabilities)

Plots data with detected change points and probabilities.

Parameters

Parameter	Type	Description
data	—	numpy array Original data points.
change_points	—	list List of detected change points.
probabilities	—	list List of probabilities associated with each data point.

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ChartCUSUM_Detector

class ChartCUSUM_Detector

Change Point Detector using CUSUM Control Chart.

Example:

detector = ChartCUSUM_Detector(warmup_period=20, level=2, deviation_type='sqr-dev')
np.random.seed(0)
data = np.concatenate([np.random.normal(0, 1, 30), np.random.normal(3, 1, 30)])
upper_limits, lower_limits, cusums, change_points = detector.detect_change_points(data)
detector.plot_change_points(data, change_points, cusums, upper_limits, lower_limits)

Attributes

• warmup_period

• level

• deviation_type

Methods

__init__()

def __init__(self, warmup_period = 10, level = 3, deviation_type = 'sqr-dev')

Initializes the Change Point Detector with the specified parameters.

Parameters

Parameter	Type	Description
warmup_period	int	The warmup period for the detector. Must be equal or greater than 10.
level	int	The level parameter for the CUSUM algorithm.
type	str	The type of deviation used in CUSUM algorithm. 'sqr-dev' for square deviation, else deviation.

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predict_next()

def predict_next(self, observation)

Predicts the next data point and detects change points.

Parameters

Parameter	Type	Description
observation	float	The next data point to predict.

Returns

• upper (float): The upper limit of the CUSUM.

• lower (float): The lower limit of the CUSUM.

• cusum (float): The current value of the CUSUM.

• is_changepoint (bool): Indicates if a change point is detected.

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detect_change_points()

def detect_change_points(self, data)

Detects change points in the given data using the CUSUM detector.

Parameters

Parameter	Type	Description
data	np.ndarray	The data to detect change points in.

Returns

• upper_limits (np.ndarray): Upper limits of the CUSUM for each observation.

• lower_limits (np.ndarray): Lower limits of the CUSUM for each observation.

• cusums (np.ndarray): Cumulative sums of deviations.

• change_points (np.ndarray): Indices of detected change points.

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plot_change_points()

def plot_change_points(self, data, change_points, cusums, upper_limits, lower_limits)

Plots data with detected change points and cumulative sums.

Parameters

Parameter	Type	Description
data	np.ndarray	The original data.
change_points	np.ndarray	Indices of detected change points.
cusums	np.ndarray	Cumulative sums of deviations.
upper_limits	np.ndarray	Upper limits of the CUSUM for each observation.
lower_limits	np.ndarray	Lower limits of the CUSUM for each observation.

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