Adaptive Weighted Total Variation Penalty for Precise Change Point Detection

Total variation (TV)‐based methods, such as the fused lasso, are standard for change point detection but are impaired by issues like local monotonicity. To address these limitations, this study comparatively analyses the fused lasso with two alternative methodologies. These methodologies are the Penalised Regression Spline (PRS) and a novel Adaptive Penalised Regression Spline (APRS) that incorporates data‐adaptive weights. Using an efficient coordinate descent algorithm, we evaluated the three methods on both simulated and real‐world data. The comparative analysis, conducted under various Signal‐to‐Noise Ratio (SNR) conditions, revealed that APRS demonstrated superior performance, particularly in minimising false positives.