Optimization and Machine Learning Methods for Medical and Healthcare Applications
The increasing amounts of data being gathered in healthcare and medical systems and the convergence of different domains are leading medical and healthcare research to a new direction of precision and personalized medicine. The trends bring a unique opportunity and good promise to solving various critical tasks in medical and healthcare research. However, such promise heavily relies on whether we could find useful patterns to characterize the target problems, discover informative mechanisms underlying the noisy and fragmented factual information, as well as transform these knowledge into intelligent decision making. Previously many efforts have been made via various approaches such as machine learning, optimization, statistical analysis, mathematical modeling, biomedical informatics, etc. This thesis will extend along the lines of machine learning and optimization methods, and to build novel models for solving the medical or healthcare challenges. Particularly, the thesis focus on the following topic domains, including medical image or recording based disease differentiation and diagnosis, image guided precision surgery, disease progression modeling, and personalized health behavior recommendation. To summarize, the thesis mainly includes five models that are fit for a wide varieties of healthcare and medical applications. The first model is an integrated feature ranking and selection framework that is capable of selecting a sparse model while preserving the most informative features. The framework combines information theoretic criteria and the least absolute shrinkage and selection operator (lasso) method into a two-step feature selection process. It can be applied to biomarker selection problems when the number of subjects is small comparing with number of candidate biomarkers. The second is a structure learning model capable of achieving personalized identification of surgery insertion location. I introduce a method to craft novel patient-specific features from their medical images. In addition, I propose a supervised structure learning and prediction model with special inter-dimensional and response structure regularization terms to capture spatial relations of features and responses. The third is a systematic framework that unifies dynamic modeling, sparse learning, dictionary learning, and matrix completion to translate users’ behavioral data into deeply personalized health planning. The framework is fit for longitudinal user behavior data, and can potentially be a backend algorithm for mobile health (mHealth) technologies. The fourth model is an optimal expert knowledge elicitation strategy for identifying pairwise Bayesian network structure from observational data. It combines observational data and expert knowledge and iteratively elicit new expert knowledge that is optimally matched to the observational data to maximally reduce the uncertainty in the structure identification. The strategy can be applied to leverage expert knowledge in learning causal relation from data when the observational data is limited. In the thesis we use it to learn the underlying progression mechanism of Alzheimer’s disease. Last, the thesis also presents a decomposed version of the k nearest neighbor (DKNN) method for the classification of an unseen object based on the distances to the centroids of the k nearest neighbors. The DKNN has a training process to learn the local-optima-free distance metric by solving a convex optimization problem. The optimization problem not only learns a metric that minimizes classification errors and maximizes the margin between intra-class and inter-class distance. In addition, it also selects important features and removes irrelevant features when L1 regularization is incorporated in the optimization model. The DKNN algorithm is designed as a general method, but could be used in identifying discriminating features for a particular disease (binary cases) or different patient cohorts (multi-class cases). To demonstrate the utility of the proposed machine learning and optimization models, numerical studies are performed using simulation, public and/or real data. Real data including magnetic resonance imaging (MRI) data, electroencephalogram (EEG) recordings, positron emission tomography (PET) data, data from wearable devices, computed tomography (CT) scan, etc. Through extensive experiments and analysis, the proposed approaches outperform baseline methods, and demonstrate their utility and efficacy in medical and healthcare applications.