Questions
Hi,
I wonder if there is an efficient algorithm of multivariate piecewise linear regression.
I've seen a post about the construction of multivariate piecewise linear approximator, but the construction seems computationally inefficient.
Here, "efficient" means, for example, it is well-known that convex optimisation is "efficient".
Thoughts
A multivariate piecewise linear approximator may be expressed as $$ \hat{f}(x) = \max_{i=1, 2, \ldots N} a_i^T x + b_i. $$ And if the regression problem is solved as the minimisation of "function distance", for example, $\min_{a_i, b_i} \lVert \hat{f} - f \rVert$, it seems not straightforward to be expressed as a known "easy" problem such as convex optimisation. Anyone has a good idea?