Learning smooth models of nonsmooth functions via convex optimization

F. Lauer, V.L. Le, G. Bloch
2012 2012 IEEE International Workshop on Machine Learning for Signal Processing  
This paper proposes a learning framework and a set of algorithms for nonsmooth regression, i.e., for learning piecewise smooth target functions with discontinuities in the function itself or the derivatives at unknown locations. In the proposed approach, the model belongs to a class of smooth functions. Though constrained to be globally smooth, the trained model can have very large derivatives at particular locations to approximate the nonsmoothness of the target function. This is obtained
more » ... gh the definition of new regularization terms which penalize the derivatives in a location-dependent manner and training algorithms in the form of convex optimization problems. Examples of application to hybrid dynamical system identification and image reconstruction are provided.
doi:10.1109/mlsp.2012.6349755 dblp:conf/mlsp/LauerLB12 fatcat:ibet2qkkqbae7mhexvaccifip4