We test cPDS on the problem of predicting hospitalizations due to heart diseases within a calendar year based on information in the patients Electronic Health Records prior to that year. cPDS converges faster than centralized methods at the cost of some communication between agents. It also converges faster and with less communication overhead compared to an alternative distributed algorithm. In both cases, it achieves similar prediction accuracy measured by the Area Under the Receiver Operating Characteristic Curve (AUC) of the classifier. We extract important features discovered by the algorithm that are predictive of future hospitalizations, thus providing a way to interpret the classification results and inform prevention efforts.

We consider the process of bidding by electricity suppliers in a dayahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in locationdependent prices.

This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental properties of the Wasserstein metric and the DRO formulation, we explore duality to arrive at tractable formulations and develop finite-sample, as well as asymptotic, performance guarantees. We consider a series of learning problems, including (i) distributionally robust linear regression; (ii) distributionally robust regression with group structure in the predictors; (iii) distributionally robust multi-output regression and multiclass classification, (iv) optimal decision making that combines distributionally robust regression with nearest-neighbor estimation; (v) distributionally robust semi-supervised learning, and (vi) distributionally robust reinforcement learning. A tractable DRO relaxation for each problem is being derived, establishing a connection between robustness and regularization, and obtaining bounds on the prediction and estimation errors of the solution. Beyond theory, we include numerical experiments and case studies using synthetic and real data. The real data experiments are all associated with various health informatics problems, an application area which provided the initial impetus for this work.

Folate is an essential nutrient for growth in early life. This study aimed to determine the levels and compositions of folate in Chinese breast milk samples. This study was part of the Maternal Nutrition and Infant Investigation (MUAI) study. A total of 205 healthy mothers were randomly recruited in Chengdu over 1–400 days postpartum. Five different species of folate, including tetrahydrofolate (THF), 5-methyl-THF, 5,10-methenyl-THF,5-formyl-THF and unmetabolized folic acid (UMFA), were measured for liquid chromatography–tandem mass spectrometry (LC-MS). The median levels of total folate ranged from 12.86 to 56.77 ng/mL in the breast milk of mothers at 1–400 days postpartum, gradually increasing throughout the lactating periods. The median levels of 5-methyl-THF, minor reduced folate (the sum of THF, 5,10-methenyl-THF and 5-formyl-THF) and UMFA were in the ranges of 8.52–40.65 ng/mL, 3.48–16.15 ng/mL and 0.00–1.24 ng/mL during 1–400 days postpartum, respectively. 5-Methyl-THF accounted for more than 65% of the total folate in all breast milk samples. The levels of UMFA in mature breast milk samples were higher in supplement users than nonusers, but not for colostrum and transitional milk samples (p < 0.05). In conclusion, the level of total folate in the breast milk changed along with the prolonged lactating periods, but 5-methyl-THF remains the dominant species of folate in the breast milk of Chinese populations across all entire lactating periods.

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