Multiple Imputation Ensembles (MIE) for dealing with missing data

Missing data is a significant issue in many real-world datasets, yet there are no robust methods for dealing with it appropriately. In this paper, we propose a robust approach to dealing with missing data in classification problems: Multiple Imputation Ensembles (MIE). Our method integrates two approaches: multiple imputation and ensemble methods and compares two types of ensembles: bagging and stacking. We also propose a robust experimental set-up using 20 benchmark datasets from the UCI machine learning repository. For each dataset, we introduce increasing amounts of data Missing Completely at Random. Firstly, we use a number of single/multiple imputation methods to recover the missing values and then ensemble a number of different classifiers built on the imputed data. We assess the quality of the imputation by using dissimilarity measures. We also evaluate the MIE performance by comparing classification accuracy on the complete and imputed data. Furthermore, we use the accuracy of simple imputation as a benchmark for comparison. We find that our proposed approach combining multiple imputation with ensemble techniques outperform others, particularly as missing data increases

Robust Feature Selection by Mutual Information Distributions

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must consider sample-to-population inferential approaches. This paper deals with the distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean and an analytical approximation of the variance are reported. Asymptotic approximations of the distribution are proposed. The results are applied to the problem of selecting features for incremental learning and classification of the naive Bayes classifier. A fast, newly defined method is shown to outperform the traditional approach based on empirical mutual information on a number of real data sets. Finally, a theoretical development is reported that allows one to efficiently extend the above methods to incomplete samples in an easy and effective way.Comment: 8 two-column page