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A sign based loss approach to model selection in nonparametric regression

机译：非参数回归中基于符号的损失模型选择方法

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摘要

In parametric regression models the sign of a coefficient often plays an important role in its interpretation. One possible approach to model selection in these situations is to consider a loss function that formulates prediction of the sign of a coefficient as a decision problem. Taking a Bayesian approach, we extend this idea of a sign based loss for selection to more complex situations. In generalized additive models we consider prediction of the sign of the derivative of an additive term at a set of predictors. Being able to predict the sign of the derivative at some point (that is, whether a term is increasing or decreasing) is one approach to selection of terms in additive modelling when interpretation is the main goal. For models with interactions, prediction of the sign of a higher order derivative can be used similarly. There are many advantages to our sign-based strategy for selection: one can work in a full or encompassing model without the need to specify priors on a model space and without needing to specify priors on parameters in submodels. Also, avoiding a search over a large model space can simplify computation. We consider shrinkage prior specifications on smoothing parameters that allow for good predictive performance in models with large numbers of terms without the need for selection, and a frequentist calibration of the parameter in our sign-based loss function when it is desired to control a false selection rate for interpretation.
机译：在参数回归模型中，系数的符号通常在其解释中起重要作用。在这些情况下进行模型选择的一种可能方法是考虑将公式的系数符号预测作为决策问题的损失函数。采用贝叶斯方法，我们将基于符号损失的思想扩展到更复杂的情况。在广义加性模型中，我们考虑在一组预测变量上预测加项的导数的符号。当解释是主要目标时，能够在某个点预测导数的符号（即项是增加还是减少）是在加性模型中选择项的一种方法。对于具有相互作用的模型，可以类似地使用高阶导数符号的预测。我们基于符号的选择策略有很多优点：可以在完整或包含模型中工作，而无需在模型空间上指定先验，也无需在子模型中指定参数的先验。另外，避免在较大的模型空间上进行搜索可以简化计算。我们考虑对平滑参数进行收缩的先前规范，以便在具有大量项的模型中无需选择就可以提供良好的预测性能，并且在需要控制错误选择时在基于符号的损失函数中对参数进行频繁校准解释率。

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