Nouvelles méthodes pour la détermination des orbites des comètes (Method of Least Squares)

First published formulation of the method of least squares for solving overdetermined systems of linear equations.

Underpins all ordinary least squares regression, Kalman filtering, and convex quadratic loss optimization in production ML.

Assumptions

• Linear relationship between observations and target parameters
• Residual sum of squares minimization yields optimal parameter estimate

Limitations

• Highly sensitive to gross outlier measurements
• Does not provide a probabilistic framework for confidence intervals without Gaussian error assumptions