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Streaming Anomaly Detection
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Streaming Anomaly Detection

HardPython

Problem

Implement a function to process a stream of data and detect anomalies.

The function receives numeric observations, a rolling window size, and a z-score threshold. For each observation after the window is full, compare it with the preceding window and return the indices whose absolute z-score exceeds the threshold. If the preceding window has zero variance, any different value is anomalous; the first window_size observations cannot be flagged.

Input/output: detect_anomalies(stream, window_size, threshold) receives a list of numbers, a positive integer, and a positive number. It returns a list of anomalous zero-based indices.

Constraints

  • 1 <= len(stream) <= 100000
  • 1 <= window_size <= len(stream)
  • threshold > 0
  • -10^9 <= stream[i] <= 10^9
  • Use the population standard deviation of the preceding window
  • Anomaly detection uses a strict comparison: z-score > threshold

Function Signature

def detect_anomalies(stream, window_size, threshold):
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