Machine learning for problems with missing and uncertain data with applications to personalized medicine

Abstract

When we try to apply statistical learning in real-world applications, we frequently encounter data which include missing and uncertain values. This thesis explores the problem of learning from missing and uncertain data with a focus on applications in personalized medicine. In the first chapter, we present a framework for classification when data is uncertain that is based upon robust optimization. We show that adding robustness in both the features and labels results in tractable optimization problems for three widely used classification methods: support vector machines, logistic regression, and decision trees. Through experiments on 75 benchmark data sets, we characterize the learning tasks for which adding robustness provides the most value. In the second chapter, we develop a family of methods for missing data imputation based upon predictive methods and formal optimization.

We present formulations for models based on K-nearest neighbors, support vector machines, and decision trees, and we develop an algorithm OptImpute to find high quality solutions which scales to large data sets. In experiments on 84 benchmark data sets, we show that OptImpute outperforms state-of-the-art methods in both imputation accuracy and performance on downstream tasks. In the third chapter, we develop MedImpute, an extension of OptImpute specialized for imputing missing values in multivariate panel data. This method is tailored for data sets that have multiple observations of the same individual at different points in time. In experiments on the Framingham Heart Study and Dana Farber Cancer Institute electronic health record data, we demonstrate that MedImpute improves the accuracy of models predicting 10-year risk of stroke and 60-day risk of mortality for late-stage cancer patients.

In the fourth chapter, we develop a method for tensor completion which leverages noisy side information available on the rows and/or columns of the tensor. We apply this method to the task of predicting anti-cancer drug response at particular dosages. We demonstrate significant gains in out-of-sample accuracy filling in missing values on two large-scale anticancer drug screening data sets with genomic side information.