FuSSO: Functional Shrinkage and Selection Operator
This provides a method for sparse functional regression, addressing variable selection in functional data analysis, but it appears incremental as an extension of LASSO to functional contexts.
The authors tackled the problem of selecting sparse functional input covariates for regression by introducing FuSSO, a functional analogue to LASSO, and demonstrated good results on synthetic and real-world data with asymptotic sparsistency proven under various conditions.
We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric assumptions about the nature of input functional covariates and assuming a linear form to the mapping of functional covariates to the response. We provide a statistical backing for use of the FuSSO via proof of asymptotic sparsistency under various conditions. Furthermore, we observe good results on both synthetic and real-world data.