Determinantal Point Processes Implicitly Regularize Semi-parametric Regression Problems

• URL: http://arxiv.org/abs/2011.06964v2
• Date: Tue, 9 Mar 2021 13:47:11 GMT
• Title: Determinantal Point Processes Implicitly Regularize Semi-parametric Regression Problems
• Authors: Micha\"el Fanuel, Joachim Schreurs, Johan A.K. Suykens
• Abstract summary: We discuss the use of a finite Determinantal Point Process (DPP) for approximating semi-parametric models. With the help of this formalism, we derive a key identity illustrating the implicit regularization effect of determinantal sampling. Also, a novel projected Nystr"om approximation is defined and used to derive a bound on the expected risk for the corresponding approximation.
• Score: 13.136143245702915
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, Barthelm\'e, 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 Nystr\"om 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.

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