Missing data is common in datasets retrieved in various areas, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the logic behind the imputation is explainable, which is especially difficult for complex methods that are for example, based on deep learning. This motivates us to introduce a conditional Distribution based Imputation of Missing Values (DIMV) algorithm. This approach works based on finding the conditional distribution of a feature with missing entries based on the fully observed features. As will be illustrated in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods under comparison; (ii) is explainable; (iii) can provide an approximated confidence region for the missing values in a given sample; (iv) works for both small and large scale data; (v) in many scenarios, does not require a huge number of parameters as deep learning approaches and therefore can be used for mobile devices or web browsers; and (vi) is robust to the normally distributed assumption that its theoretical grounds rely on. In addition to DIMV, we also introduce the DPER* algorithm improving the speed of DPER for estimating the mean and covariance matrix from the data, and we confirm the speed-up via experiments.

翻译：数据缺失在医学、体育和金融等多个领域所获取的数据集中普遍存在。为对这些数据进行准确可靠的分析，通常需要对缺失值进行插补，且所采用的方法在插补值与真实值之间应具有较低的均方根误差（RMSE）。此外，在某些关键应用中，还常要求插补背后的逻辑具有可解释性，而基于深度学习等复杂方法尤其难以满足这一要求。这促使我们提出一种基于条件分布的缺失值插补（DIMV）算法。该方法基于完全观测到的特征，寻找含缺失条目的特征的条件分布。如本文所述，DIMV：（i）与对比的最先进方法相比，其插补值的RMSE较低；（ii）具有可解释性；（iii）能为给定样本中的缺失值提供近似的置信区间；（iv）适用于小规模和大规模数据；（v）在许多场景下无需像深度学习方法那样需要大量参数，因此可用于移动设备或网页浏览器；（vi）对其理论依据所依赖的正态分布假设具有鲁棒性。除DIMV外，我们还提出了DPER*算法，该算法改进了DPER从数据中估计均值和协方差矩阵的速度，并通过实验验证了其加速效果。