When data is partially missing at random, imputation and importance weighting are often used to estimate moments of the unobserved population. In this paper, we study 1-nearest neighbor (1NN) importance weighting, which estimates moments by replacing missing data with the complete data that is the nearest neighbor in the non-missing covariate space. We define an empirical measure, the 1NN measure, and show that it is weakly consistent for the measure of the missing data. The main idea behind this result is that the 1NN measure is performing inverse probability weighting in the limit. We study applications to missing data and mitigating the impact of covariate shift in prediction tasks.
@cite_21 outlines many of the common methods for dealing with missing data, including imputation, importance weighting, and likelihood based methods (such as the EM algorithm). Importance weighting, or propensity scoring, is commonly used for correcting sampling selection bias @cite_13 , which arises in survey sampling and causal inference. Tree-based methods and SVMs have been used to obtain estimates of the ideal importance weights in @cite_0 @cite_15 . Hot-deck imputation has been studied empirically in @cite_2 @cite_26 @cite_17 but is not a commonly used as model-based approaches.
@cite_26 @cite_21 @cite_0 @cite_2 @cite_15 @cite_13 @cite_17
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Covariate data which are missing or measured with error form the subject of a growing body of statistical literature. Parametric methods have not been widely adopted, quite possibly due to the necessity of specifying the form of a 'nuisance function' not required for complete data analysis, and the non-robustness of the methods to mis-specification. A non-parametric counterpart of multiple imputation, known as 'hot deck', was proposed by Rubin (1987) and has been used by the Census Bureau to complete public-use databases. However, inference using this method has not been possible due to the distribution theory not being available. Recently, it has been shown that the hot deck estimator has the same asymptotic distribution as the 'mean score' estimator, so that inference using hot deck is now possible. The method is intuitively appealing and easily implemented. Furthermore, it accommodates missingness which depends on outcome, which is an important generalization of many currently available methods. In this paper, the hot deck multiple imputation method is explained, its asymptotic distribution presented and its application to data analysis demonstrated by an example. The predictive analysis of longitudinal social surveys is highly sensitive to the effects of missing data in temporal observations. Such high sensitivity to missing values raises the need for accurate data imputation, because without it a large fraction of collected data could not be used properly. Previous studies focused on the treatment of missing data in longitudinal social networks due to non-respondents and dealt with the problem largely by imputing missing links in isolation or analyzing the imputation effects on network statistics. We propose to account for changing network topology and interdependence between actors' links and attributes to construct a unified approach for imputation of links and attributes in longitudinal social surveys. The new method, based on an exponential random graph model, is evaluated experimentally for five scenarios of missing data models utilizing synthetic and real life datasets with 20 ---60 of nodes missing. The obtained results outperformed all alternatives, four of which were link imputation methods and two node attribute imputation methods. We further discuss the applicability and scalability of our approach to real life problems and compare our model with the latest advancements in the field. Our findings suggest that the proposed method can be used as a viable imputation tool in longitudinal studies. The simplest approach to dealing with missing data is to restrict the analysis to complete cases, i.e. individuals with no missing values. This can induce bias, however. Inverse probability weighting (IPW) is a commonly used method to correct this bias. It is also used to adjust for unequal sampling fractions in sample surveys. This article is a review of the use of IPW in epidemiological research. We describe how the bias in the complete-case analysis arises and how IPW can remove it. IPW is compared with multiple imputation (MI) and we explain why, despite MI generally being more efficient, IPW may sometimes be preferred. We discuss the choice of missingness model and methods such as weight truncation, weight stabilisation and augmented IPW. The use of IPW is illustrated on data from the 1958 British Birth Cohort. A novel algorithm based on random forests with surrogate splits is proposed to address the classification problem of incomplete data without imputation.The algorithm allows each tree to cast a vote even the voting process is interrupted by missing attributes.Experimental results on various acknowledged datasets show that the proposed method is robust and efficient. Random forests (RF) is known as an efficient algorithm in classification, however it depends on the integrity of datasets. Conventional methods in dealing with missing values usually employ estimation and imputation approaches whose efficiency is tied to the assumptions of data features. Recently, algorithm of surrogate decisions in RF was developed and this paper proposes a random forests algorithm with modified surrogate splits (Adjusted Weight Voting Random Forest, AWVRF) which is able to address the incomplete data without imputation.Differing from the present surrogate method, in AWVRF algorithm, when the primary splitting attribute and the surrogate attributes of an internal node are all missing, the undergoing instance is allowed to exit at the current node with a vote. Then the weight of the vote is adjusted by the strength of the involved attributes and the final decision is made by weighted voting. AWVRF does not comprise imputation step, thus it is independent of data features.AWVRF is compared with the methods of mean imputation, LeoFill, knnimpute, BPCAfill and conventional RF with surrogate decisions (surrRF) using 50 times repeated 5-fold cross validation on 10 acknowledged datasets. In a total of 22 experiment settings, the method of AWVRF harvests the highest accuracy in 14 settings and the largest AUC in 7 settings, exhibiting its superiority over other methods. Compared with surrRF, AWVRF is significantly more efficient and remain good discrimination of prediction. Experimental results show that the present AWVRF algorithm can successfully handle the classification task for incomplete data.