论文标题
通过半监督的学习方法,协变量中高率数据的归因
Imputations for High Missing Rate Data in Covariates via Semi-supervised Learning Approach
论文作者
论文摘要
数据收集技术的进步和数据资源的异质性可以产生对变量(例如块丢失数据)的高比例。在缺失数据方案下,传统方法,例如简单的平均值,$ k $ - 最近的邻居,多重和回归归档可能会导致结果不稳定或无法计算的结果。由半监督学习的概念的促进(参见,例如,Zhu和Goldberg,2009和Chapelle等人,2010年),我们提出了一种新颖的方法来填补较高率较高率的协变量中缺失值。具体而言,我们将任何协变量中的丢失和未错过的受试者视为未标记和标记的目标输出,并将其相应的响应视为未标记和标记的输入。这种创新的设置使我们能够在不施加任何模型假设的情况下重新数量丢失的数据。此外,由此产生的插补具有连续协变量的封闭形式,并且可以有效地计算出来。类似程序适用于离散协变量。我们进一步采用非参数技术来显示估算协变量的理论特性。提出了模拟研究和在线消费者财务示例,以说明该方法的有用性。
Advancements in data collection techniques and the heterogeneity of data resources can yield high percentages of missing observations on variables, such as block-wise missing data. Under missing-data scenarios, traditional methods such as the simple average, $k$-nearest neighbor, multiple, and regression imputations may lead to results that are unstable or unable be computed. Motivated by the concept of semi-supervised learning (see, e.g., Zhu and Goldberg, 2009 and Chapelle et al., 2010), we propose a novel approach with which to fill in missing values in covariates that have high missing rates. Specifically, we consider the missing and non-missing subjects in any covariate as the unlabelled and labelled target outputs, respectively, and treat their corresponding responses as the unlabelled and labelled inputs. This innovative setting allows us to impute a large number of missing data without imposing any model assumptions. In addition, the resulting imputation has a closed form for continuous covariates, and it can be calculated efficiently. An analogous procedure is applicable for discrete covariates. We further employ the nonparametric techniques to show the theoretical properties of imputed covariates. Simulation studies and an online consumer finance example are presented to illustrate the usefulness of the proposed method.