在高维中防范虚假的发现。

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2016-01-01
Jianqing Fan, Wen-Xin Zhou
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引用次数: 0

摘要

已经开发了许多数据挖掘和统计机器学习算法来选择协变量的子集与响应变量相关联。由于这种选择的巨大可能性,在高维数据分析中很容易出现虚假的发现。我们怎么能在统计上比偶然发现更了解我们的发现呢?在本文中,我们定义了伪拟合优度的度量,它显示了在零模型下,一个最优选择的协变量子集可以很好地拟合一个响应变量,并提出了一个简单有效的LAMM算法来计算它。它与线性模型的最大伪相关一致,可以看作是广义的最大伪相关。我们得到了广义线性模型和l1回归的伪拟合优度的渐近分布。这种渐近分布取决于样本大小、环境维度、拟合中使用的变量数量和协方差信息。它可以通过乘法器自举来一致地估计,并用作防止虚假发现的基准。它还可以应用于模型选择,即只考虑拟合优度优于伪拟合的候选模型。通过模拟实例和德国神经母细胞瘤试验二元结果的应用,令人信服地说明了该理论和方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Guarding against Spurious Discoveries in High Dimensions.

Guarding against Spurious Discoveries in High Dimensions.

Guarding against Spurious Discoveries in High Dimensions.

Many data-mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous possibilities of such selections. How can we know statistically our discoveries better than those by chance? In this paper, we define a measure of goodness of spurious fit, which shows how good a response variable can be fitted by an optimally selected subset of covariates under the null model, and propose a simple and effective LAMM algorithm to compute it. It coincides with the maximum spurious correlation for linear models and can be regarded as a generalized maximum spurious correlation. We derive the asymptotic distribution of such goodness of spurious fit for generalized linear models and L1-regression. Such an asymptotic distribution depends on the sample size, ambient dimension, the number of variables used in the fit, and the covariance information. It can be consistently estimated by multiplier bootstrapping and used as a benchmark to guard against spurious discoveries. It can also be applied to model selection, which considers only candidate models with goodness of fits better than those by spurious fits. The theory and method are convincingly illustrated by simulated examples and an application to the binary outcomes from German Neuroblastoma Trials.

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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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