The Bernstein Basis

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Fitting a function to data while obeying shape constraints is a useful modeling ability. The Bernstein Basis enables this by relying on a special property.

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Sources

I first learned of the idea from my managed at Lyft, Sean Taylor (twitter : @seanjtaylor). We used this technique for modeling demand- something we have data on, but also can make fairly strong/safe assumptions about (e.g. it's downward sloping).

[1] was useful for understanding the history and properties of the Bernstein Basis (which was not originally designed for regression problems). [2] was useful for understanding its use in regression problems. [3] was where I discovered the generalization to the multivariate case.

[1] Rida T. Farouki, (2012), The Bernstein polynomial basis: a centennial retrospective, Department of Mechanical and Aerospace Engineering,
University of California, Davis, CA

[2] S. M. Curtis, S. K. Ghosh, (2009), A Variable Selection Approach to Bayesian Monotonic Regression with Bernstein Polynomials, Journal of Applied Statistics

[3] https://www.iue.tuwien.ac.at/phd/heit...