Saturating Splines and Feature Selection.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2018-04-01
Nicholas Boyd, Trevor Hastie, Stephen Boyd, Benjamin Recht, Michael I Jordan
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引用次数: 0

Abstract

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data via a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method. Unlike many existing approaches, our algorithm solves the original infinite-dimensional (for splines of degree at least two) optimization problem without pre-specified knot locations. We then adapt our algorithm to fit generalized additive models with saturating splines as coordinate functions and show that the saturation requirement allows our model to simultaneously perform feature selection and nonlinear function fitting. Finally, we briefly sketch how the method can be extended to higher order splines and to different requirements on the extension outside the data range.

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饱和样条和特征选择
我们扩展了自适应回归样条曲线模型,将饱和度(即函数在一定范围外扩展为常数的自然要求)纳入其中。我们通过一个度量空间上的凸优化问题将饱和样条曲线拟合到数据中,并使用基于条件梯度法的高效算法解决该问题。与许多现有方法不同的是,我们的算法无需预先指定节点位置,即可解决原始的无限维(对于阶数至少为 2 的样条曲线)优化问题。然后,我们将算法调整为拟合以饱和样条为坐标函数的广义加法模型,并证明饱和度要求允许我们的模型同时执行特征选择和非线性函数拟合。最后,我们简要介绍了如何将该方法扩展到更高阶的样条线,以及数据范围外扩展的不同要求。
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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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