We construct @math kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a conditional probability density function. This allows to embed incomplete data into the function space and to define a kernel between two missing data points based on scalar product in @math . Experiments show that introduced kernel applied to SVM classifier gives better results than other state-of-the-art methods, especially in the case when large number of features is missing. Moreover, it is easy to implement and can be used together with any kernel approaches with no additional modifications.
The most common approach to learning from incomplete data is known as deterministic imputation @cite_11 . In this two-step procedure, the missing features are filled first, and only then a standard classifier is applied to the complete data @cite_18 . Although the imputation-based techniques are easy to use for practitioners, they lead to the loss of information which features were missing and do not take into account the reasons of missingness. To preserve the information of missing attributes, one can use an additional vector of binary flags, indicating which coordinates were missing.
@cite_18 @cite_11
2803403013 1916256034 2951397438 2282784388
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 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. Missing data is a significant problem impacting all domains. State-of-the-art framework for minimizing missing data bias is multiple imputation, for which the choice of an imputation model remains nontrivial. We propose a multiple imputation model based on overcomplete deep denoising autoencoders. Our proposed model is capable of handling different data types, missingness patterns, missingness proportions and distributions. Evaluation on several real life datasets show our proposed model significantly outperforms current state-of-the-art methods under varying conditions while simultaneously improving end of the line analytics. Incomplete information often occur along with many database applications, e.g., in data integration, data cleaning or data exchange. The idea of data imputation is to fill the missing data with the values of its neighbors who share the same information. Such neighbors could either be identified certainly by editing rules or statistically by relational dependency networks. Unfortunately, owing to data sparsity, the number of neighbors (identified w.r.t. value equality) is rather limited, especially in the presence of data values with variances. In this paper, we argue to extensively enrich similarity neighbors by similarity rules with tolerance to small variations. More fillings can thus be acquired that the aforesaid equality neighbors fail to reveal. To fill the missing values more, we study the problem of maximizing the missing data imputation. Our major contributions include (1) the np-hardness analysis on solving and approximating the problem, (2) exact algorithms for tackling the problem, and (3) efficient approximation with performance guarantees. Experiments on real and synthetic data sets demonstrate that the filling accuracy can be improved.