مقایسهٔ روش‌ها

	میانگین خطای مطلق (MAE)	میانگین مربعات خطا (MSE)
حوزه	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM
سال پیدایش	1799	1809
پدیدآور	Pierre-Simon Laplace	Carl Friedrich Gauss
نوع	Robust distance-based metric	Squared-error loss function
منبع بنیادین	Laplace, P. S. (1799). Traité de Mécanique Céleste. Paris: J.B.M. Duprat.	Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.
نام‌های دیگر	MAE, L1 error, mean absolute deviation	MSE, L2 error, quadratic error
مرتبط	3	4
خلاصه	Mean Absolute Error is a robust metric that measures the average absolute magnitude of prediction errors in regression models. Dating back to Pierre-Simon Laplace's work on observational errors (1799), MAE quantifies typical prediction deviation by averaging the absolute differences between observed and predicted values.	Mean Squared Error is the foundational loss function for regression models, measuring the average squared deviation between predictions and observations. Originating from Gauss and Legendre's method of least squares (1805-1809), MSE is the basis for ordinary least squares regression and remains central to modern machine learning optimization.