2020/11/13 by Michaël Fanuel, Fanuel, Michaël, Joachim Schreurs +3
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Morphological variations and asymmetry #Point processes and geometric inequalities #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2011.06964
26 pages. Extended results. Typos corrected
openalex publication_date 2020/11/13 · arxiv created 2021/03/09 · arxiv updated 2021/03/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system includes a linear and non-linear component. We discuss here the use of a finite Determinantal Point Process (DPP) for approximating semi-parametric models. Recently, Barthelmé, Tremblay, Usevich, and Amblard introduced a novel representation of some finite DPPs. These authors formulated extended L-ensembles that can conveniently represent partial-projection DPPs and suggest their use for optimal interpolation. With the help of this formalism, we derive a key identity illustrating the implicit regularization effect of determinantal sampling for semi-parametric regression and interpolation. Also, a novel projected Nyström approximation is defined and used to derive a bound on the expected risk for the corresponding approximation of semi-parametric regression. This work naturally extends similar results obtained for kernel ridge regression.