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Patient-Reported Outcomes (PRO) are collected directly from the patients using symptom questionnaires. In the case of head and neck cancer patients, PRO surveys are recorded every week during treatment with each patient’s visit to the clinic and at different follow-up times after the treatment has concluded. PRO surveys can be very informative regarding the patient’s status and the effect of treatment on the patient’s quality of life (QoL). Processing PRO data is challenging for several reasons. First, missing data is frequent as patients might skip a question or a questionnaire altogether. Second, PROs are patient-dependent, a rating of 5 for one patient might be a rating of 10 for another patient. Finally, most patients experience severe symptoms during treatment which usually subside over time. However, for some patients, late toxicities persist negatively affecting the patient’s QoL. These long-term severe symptoms are hard to predict and are the focus of this study. In this work, we model PRO data collected from head and neck cancer patients treated at the MD Anderson Cancer Center using the MD Anderson Symptom Inventory (MDASI) questionnaire as time series. We impute missing values with a combination of K nearest neighbor (KNN) and Long Short-Term Memory (LSTM) neural networks, and finally, apply LSTM to predict late symptom severity 12 months after treatment. We compare performance against clinical and ARIMA models. We show that the LSTM model combined with KNN imputation is effective in predicting late-stage symptom ratings for occurrence and severity under the AUC and F1 score metrics. 

Structured prediction of tree-shaped objects is heavily studied under the name of syntactic dependency parsing. Current practice based on maximum likelihood or margin is either agnostic to or inconsistent with the evaluation loss. Risk minimization alleviates the discrepancy between training and test objectives but typically induces a non-convex problem. These approaches adopt explicit regularization to combat overfitting without probabilistic interpretation. We propose a momentbased distributionally robust optimization approach for tree structured prediction, where the worst-case expected loss over a set of distributions within bounded moment divergence from the empirical distribution is minimized. We develop efficient algorithms for arborescences and other variants of trees. We derive Fisher consistency, convergence rates and generalization bounds for our proposed method. We evaluate its empirical effectiveness on dependency parsing benchmarks. 

Plasma jets are widely investigated both in the laboratory and in nature. Astrophysical objects such as black holes, active galactic nuclei and young stellar objects commonly emit plasma jets in various forms. With the availability of data from plasma jet experiments resembling astrophysical plasma jets, classification of such data would potentially aid in not only investigating the underlying physics of the experiments but also the study of astrophysical jets. In this work we use deep learning to process all of the laboratory plasma images from the Caltech Spheromak Experiment spanning two decades. We found that cosine similarity can aid in feature selection, classify images through comparison of feature vector direction and be used as a loss function for the training of AlexNet for plasma image classification. We also develop a simple vector direction comparison algorithm for binary and multi-class classification. Using our algorithm we demonstrate 93 % accurate binary classification to distinguish unstable columns from stable columns and 92 % accurate five-way classification of a small, labelled data set which includes three classes corresponding to varying levels of kink instability. 

We consider the problem of learning the underlying structure of a general discrete pairwise Markov network. Existing approaches that rely on empirical risk minimization may perform poorly in settings with noisy or scarce data. To overcome these limitations, we propose a computationally efficient and robust learning method for this problem with near-optimal sample complexities. Our approach builds upon distributionally robust optimization (DRO) and maximum conditional log-likelihood. The proposed DRO estimator minimizes the worst-case risk over an ambiguity set of adversarial distributions within bounded transport cost or f-divergence of the empirical data distribution. We show that the primal minimax learning problem can be efficiently solved by leveraging sufficient statistics and greedy maximization in the ostensibly intractable dual formulation. Based on DRO’s approximation to Lipschitz and variance regularization, we derive near-optimal sample complexities matching existing results. Extensive empirical evidence with different corruption models corroborates the effectiveness of the proposed methods.