论文标题
确定点过程隐含地正规化半参数回归问题
Determinantal Point Processes Implicitly Regularize Semi-parametric Regression Problems
论文作者
论文摘要
半参数回归模型用于几种需要无理性的应用，而无需牺牲准确性。典型的例子是地球物理学或非线性时间序列问题中的样条插值，其中系统包含线性和非线性分量。我们在这里讨论有限的确定点过程（DPP）用于近似半参数模型。最近，Barthelmé，Tremblay，Usevich和Amblard引入了一些有限的DPP的新颖代表。这些作者制定了可以方便地表示部分预测DPP的扩展L-依赖组，并建议其用于最佳插值。在这种形式主义的帮助下，我们得出了一个关键的身份，说明了确定性采样对半参数回归和插值的隐式正则化作用。此外，定义了一种新型的投影NyStröm近似，并用于导致与半参数回归相应近似的预期风险结合。这项工作自然扩展了内核脊回归的相似结果。
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.
