Linear approximation is a method used to estimate the value of a function near a given point using the tangent line at that point. This technique simplifies complex functions into a linear form ...

In previous work we introduced principal surfaces as hyperridges of probability distributions in a differential geometrical sense. Specifically, given an n-dimensional probability distribution over ...

Piecewise Local Linear Model In this project, we provide a method to construct piecewise local linear approximations of a black box model. The main idea behind building piecewise approximations is to ...

Journal of Applied Probability, Vol. 43, No. 1 (Mar., 2006), pp. 185-194 (10 pages) Local linear approximations have been the main component in the construction of a class of effective numerical ...