Real-world machine learning applications may have requirements beyond accuracy, such as fast evaluation times and interpretability. In particular, guaranteed monotonicity of the learned function with respect to some of the inputs can be critical for user confidence. We propose meeting these goals for low-dimensional machine learning problems by learning flexible, monotonic functions using calibrated interpolated look-up tables. We extend the structural risk minimization framework of lattice regression to monotonic functions by adding linear inequality constraints. In addition, we propose jointly learning interpretable calibrations of each feature to normalize continuous features and handle categorical or missing data, at the cost of making the objective non-convex. We address large- scale learning through parallelization, mini-batching, and random sampling of additive regularizer terms. Case studies on real-world problems with up to sixteen features and up to hundreds of millions of training samples demonstrate the proposed monotonic functions can achieve state-of-the-art accuracy in practice while providing greater transparency to users.

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.

A key challenge in reducing the burden of cardiovascular disease is matching patients to treatments that are most appropriate for them. Different cardiac assessment tools have been developed to address this goal. Recent research has focused on heart rate motifs, i.e., short-term heart rate sequences that are over- or under-represented in long-term electrocardiogram (ECG) recordings of patients experiencing cardiovascular outcomes, which provide novel and valuable information for risk stratification. However, this approach can leverage only a small number of motifs for prediction and results in difficult to interpret models. We address these limitations by identifying latent structure in the large numbers of motifs found in long-term ECG recordings. In particular, we explore the application of topic models to heart rate time series to identify functional sets of heart rate sequences and to concisely describe patients using task-independent features for various cardiovascular outcomes. We evaluate the approach on a large collection of real-world ECG data, and investigate the performance of topic mixture features for the prediction of cardiovascular mortality. The topics provided an interpretable representation of the recordings and maintained valuable information for clinical assessment when compared with motif frequencies, even after accounting for commonly used clinical risk scores.