مقایسهٔ روش‌ها

	میانگین مربعات خطا (MSE)	میانگین خطای مطلق (MAE)
حوزه	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM
سال پیدایش	1809	1799
پدیدآور	Carl Friedrich Gauss	Pierre-Simon Laplace
نوع	Squared-error loss function	Robust distance-based metric
منبع بنیادین	Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.	Laplace, P. S. (1799). Traité de Mécanique Céleste. Paris: J.B.M. Duprat.
نام‌های دیگر	MSE, L2 error, quadratic error	MAE, L1 error, mean absolute deviation
مرتبط	4	3
خلاصه	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.	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.