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依赖关系中的BELIEF：以二元数据的线性性质重思广义线性模型AI 解读

Two linearly uncorrelated binary variables must be also independent because nonlinear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they…

异质数据逐分辨率回归的非参数预测分布AI 解读

Modeling and inference for heterogeneous data have gained great interest recently due to rapid developments in personalized marketing. Most existing regression approaches are based on the conditional mean and may require additional cluster information to accommodate data heterogeneity. In this paper, we propose a novel nonparametric resolution-wise regression procedure to provide an estimated distribution of the response instead of one single value. We achieve this by…

BET：基于二进制展开的独立性检验AI 解读

Kai Zhang* Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NCCONTACT Kai Zhang zhangk@email.unc.edu Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599.* This article is dedicated to Professor Lawrence D. Brown with the author’s deepest appreciation for his teaching and mentoring.Color versions of one or more of the figures in the article can be found…

利用随机变分不等式技术构造 Lasso 置信区间与置信区域AI 解读

Summary Sparse regression techniques have been popular in recent years because of their ability in handling high dimensional data with built-in variable selection. The lasso is perhaps one of the most well-known examples. Despite intensive work in this direction, how to provide valid inference for sparse regularized methods remains a challenging statistical problem. We take a unique point of view of this problem and propose to make use of stochastic variational inequality…

有效的模型选择后推断AI 解读

It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori. We propose to produce valid “post-selection inference” by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence…