(Weighted) least squares fits

A classic. Surprisingly deep.

A few non-comprehensive notes to approximating by the arbitrary-but-convenient expedient of minimising the sum of the squares of the deviances.

As used in many many problems. e.g. lasso regression.

  • Nonlinear least squares with ceres-solver:

    Ceres Solve is an open source C++ library for modeling and solving large, complicated optimization problems. It can be used to solve Non-linear Least Squares problems with bounds constraints and general unconstrained optimization problems. It is a mature, feature rich, and performant library that has been used in production at Google since 2010.

  • Boyd and Vandenberghe’s Julia Companion to their Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares is a solid introduction to both linear algebra and Julia, focussing especially on least-squares problems.

in mechanism design

TBD. See quadratic voting and public goods provision (Buterin, Hitzig, and Weyl 2019).


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