While discriminative classifiers often yield strong predictive performance, missing feature values at prediction time can still be a challenge. Classifiers may not behave as expected under certain ways of substituting the missing values, since they inherently make assumptions about the data distribution they were trained on. In this paper, we propose a novel framework that classifies examples with missing features by computing the expected prediction with respect to a feature distribution. Moreover, we use geometric programming to learn a naive Bayes distribution that embeds a given logistic regression classifier and can efficiently take its expected predictions. Empirical evaluations show that our model achieves the same performance as the logistic regression with all features observed, and outperforms standard imputation techniques when features go missing during prediction time. Furthermore, we demonstrate that our method can be used to generate "sufficient explanations" of logistic regression classifications, by removing features that do not affect the classification.
The second one investigates how to impute the missing values. In essence, imputation is a form of reasoning about missing values from observed ones @cite_0 @cite_20 @cite_27 . An iterative process is commonly used during this reasoning process @cite_24 . Some recent works also adapt auto-encoders and GANs for the task @cite_10 @cite_19 . Some of these works can be incorporated into a framework called multiple imputations to reflect and better bound one's uncertainty @cite_26 @cite_9 . These existing methods focus on substituting missing values with those closer to the ground truth, but do not model how the imputed values interact with the trained classifier. On the other hand, our proposed method explicitly reasons about what the classifier is expected to return.
@cite_26 @cite_9 @cite_0 @cite_24 @cite_27 @cite_19 @cite_10 @cite_20
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We propose a novel method for imputing missing data by adapting the well-known Generative Adversarial Nets (GAN) framework. Accordingly, we call our method Generative Adversarial Imputation Nets (GAIN). The generator (G) observes some components of a real data vector, imputes the missing components conditioned on what is actually observed, and outputs a completed vector. The discriminator (D) then takes a completed vector and attempts to determine which components were actually observed and which were imputed. To ensure that D forces G to learn the desired distribution, we provide D with some additional information in the form of a hint vector. The hint reveals to D partial information about the missingness of the original sample, which is used by D to focus its attention on the imputation quality of particular components. This hint ensures that G does in fact learn to generate according to the true data distribution. We tested our method on various datasets and found that GAIN significantly outperforms state-of-the-art imputation methods. Missing numerical values are prevalent, e.g., owing to unreliable sensor reading, collection and transmission among heterogeneous sources. Unlike categorized data imputation over a limited domain, the numerical values suffer from two issues: (1) sparsity problem, the incomplete tuple may not have sufficient complete neighbors sharing the same similar values for imputation, owing to the (almost) infinite domain; (2) heterogeneity problem, different tuples may not fit the same (regression) model. In this study, enlightened by the conditional dependencies that hold conditionally over certain tuples rather than the whole relation, we propose to learn a regression model individually for each complete tuple together with its neighbors. Our IIM, Imputation via Individual Models, thus no longer relies on sharing similar values among the k complete neighbors for imputation, but utilizes their regression results by the aforesaid learned individual (not necessary the same) models. Remarkably, we show that some existing methods are indeed special cases of our IIM, under the extreme settings of the number l of learning neighbors considered in individual learning. In this sense, a proper number l of neighbors is essential to learn the individual models (avoid over-fitting or under-fitting). We propose to adaptively learn individual models over various number l of neighbors for different complete tuples. By devising efficient incremental computation, the time complexity of learning a model reduces from linear to constant. Experiments on real data demonstrate that our IIM with adaptive learning achieves higher imputation accuracy than the existing approaches. This paper proposes to utilize information within incomplete instances (instances with missing values) when estimating missing values. Accordingly, a simple and efficient nonparametric iterative imputation algorithm, called the NIIA method, is designed for iteratively imputing missing target values. The NIIA method imputes each missing value several times until the algorithm converges. In the first iteration, all the complete instances are used to estimate missing values. The information within incomplete instances is utilized since the second imputation iteration. We conduct some experiments for evaluating the efficiency, and demonstrate: (1) the utilization of information within incomplete instances is of benefit to easily capture the distribution of a dataset; and (2) the NIIA method outperforms the existing methods in accuracy, and this advantage is clearly highlighted when datasets have a high missing ratio. Missing values are a common problem when applying classification algorithms to real-world medical data. This is especially true for trauma patients, where the emergent nature of the cases makes it difficult to collect all of the relevant data for each patient. Standard methods for handling missingness first learn a model to estimate missing data values, and subsequently train and evaluate a classifier using data imputed with this model. Recently, several proposed methods have demonstrated the benefits of jointly estimating the imputation model and classifier parameters. However, these methods make assumptions that limit their utility with many real-world medical datasets. For example, the assumption that data elements are missing at random is often invalid.We address this situation by exploring a novel approach for jointly learning the imputation model and classifier. Unlike previous algorithms, our approach makes no assumptions about the missingness of the data, can be used with arbitrary probabilistic data models and classification loss functions, and can be used when both the training and testing data have missing values. We investigate the utility of this approach on the prediction of several patient outcomes in a large national registry of trauma patients, and find that it significantly outperforms standard sequential methods.