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The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each missing entry, and then train a prediction model with the new dataset. A drawback of this naive approach is that the uncertainty in the missing entries is not properly incorporated in the prediction. In order to evaluate prediction uncertainty, the multiple imputation (MI) approach has been studied, but the performance of MI is sensitive to the choice of the probabilistic model of the true values in the missing entries, and the computational cost of MI is high because multiple models must be trained. In this paper, we propose an alternative approach called the Interval-based Prediction Uncertainty Bounding (IPUB) method. The IPUB method represents the uncertainties due to missing entries as intervals, and efficiently computes the lower and upper bounds of the prediction results when all possible training sets constructed by imputing arbitrary values in the intervals are considered. The IPUB method can be applied to a wide class of convex learning algorithms including penalized least-squares regression, support vector machine (SVM), and logistic regression. We demonstrate the advantages of the IPUB method by comparing it with an existing method in numerical experiment with benchmark datasets.
In many application settings, the data have missing entries which make analysis challenging. An abundant literature addresses missing values in an inferential framework: estimating parameters and their variance from incomplete tables. Here, we consid
How to learn a good predictor on data with missing values? Most efforts focus on first imputing as well as possible and second learning on the completed data to predict the outcome. Yet, this widespread practice has no theoretical grounding. Here we
Missing data are a concern in many real world data sets and imputation methods are often needed to estimate the values of missing data, but data sets with excessive missingness and high dimensionality challenge most approaches to imputation. Here we
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to approximate a map
In a variety of settings, limitations of sensing technologies or other sampling mechanisms result in missing labels, where the likelihood of a missing label in the training set is an unknown function of the data. For example, satellites used to detec