期刊
JOURNAL OF MACHINE LEARNING RESEARCH
卷 24, 期 -, 页码 1-60出版社
MICROTOME PUBL
关键词
functional ANOVA; interaction discovery; kernel ridge regression; nonlinear; variable selection; sparse high-dimensional regression
This research solves the computational bottleneck in estimating effects and variable selection in scientific problems. The proposed method utilizes a kernel trick for variable selection and estimation, achieving accurate results in short runtime.
Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can lead to poor estimation and variable selection. Unfortunately, methods that simultaneously express sparsity, nonlinearity, and interactions are computationally intractable - with runtime at least quadratic in the number of covariates, and often worse. In the present work, we solve this computational bottleneck. We show that suitable interaction models have a kernel representation, namely there exists a kernel trick to perform variable selection and estimation in O(# covariates) time. Our resulting fit corresponds to a sparse orthogonal decomposition of the regression function in a Hilbert space (i.e., a functional ANOVA decomposition), where interaction effects represent all variation that cannot be explained by lower-order effects. On a variety of synthetic and real data sets, our approach outperforms existing methods used for large, high-dimensional data sets while remaining competitive (or being orders of magnitude faster) in runtime.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据