Least Absolute Deviation

Least Absolute Deviation (LAD) methods focus on minimizing the sum of absolute errors, offering robustness to outliers compared to least squares approaches. Current research explores LAD's application in diverse areas, including privacy-preserving machine learning (using algorithms like FRAPPE), anomaly detection (leveraging deviation learning and large-margin losses), and robust parameter estimation in various models (e.g., sinusoidal models). This robustness makes LAD valuable for applications where data quality is uncertain or outliers are expected, impacting fields ranging from signal processing and remote sensing to machine learning and game theory.