This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when a (natural) recently proposed method, based on convex optimization, succeeds in exact recovery. Our result allows for the simultaneous presence of random and deterministic components in both the error and erasure patterns. On the one hand, corollaries obtained by specializing this one single result in different ways recovers (upto poly-log factors) all the existing works in matrix completion, and sparse and low-rank matrix recovery. On the other hand, our results also provide the first guarantees for (a) deterministic matrix completion, and (b) recovery when we observe a vanishing fraction of entries of a corrupted matrix.

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when the natural convex relaxation of minimizing rank plus support succeeds in exact recovery. Our result allows for the simultaneous presence of random and deterministic components in both the error and erasure patterns. On the one hand, corollaries obtained by specializing this one single result in different ways recover (up to poly-log factors) all the existing works in matrix completion, and sparse and low-rank matrix recovery. On the other hand, our results also provide the first guarantees for (a) recovery when we observe a vanishing fraction of entries of a corrupted matrix, and (b) deterministic matrix completion.

Today, billions of display ad impressions are purchased on a daily basis through a public auction hosted by real time bidding (RTB) exchanges. A decision has to be made for advertisers to submit a bid for each selected RTB ad request in milliseconds. Restricted by the budget, the goal is to buy a set of ad impressions to reach as many targeted users as possible. A desired action (conversion), advertiser specific, includes purchasing a product, filling out a form, signing up for emails, etc. In addition, advertisers typically prefer to spend their budget smoothly over the time in order to reach a wider range of audience accessible throughout a day and have a sustainable impact. However, since the conversions occur rarely and the occurrence feedback is normally delayed, it is very challenging to achieve both budget and performance goals at the same time. In this paper, we present an online approach to the smooth budget delivery while optimizing for the conversion performance. Our algorithm tries to select high quality impressions and adjust the bid price based on the prior performance distribution in an adaptive manner by distributing the budget optimally across time. Our experimental results from real advertising campaigns demonstrate the effectiveness of our proposed approach.

Sparse linear regression -finding an unknown vector from linear measurements -is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where several related vectors -with partially shared support sets -have to be recovered. A natural question in this setting is whether one can use the sharing to further decrease the overall number of samples required. A line of recent research has studied the use of ℓ1/ℓq norm block-regularizations with q > 1 for such problems; however these could actually perform worse in sample complexity -vis a vis solving each problem separately ignoring sharingdepending on the level of sharing.We present a new method for multiple sparse linear regression that can leverage support and parameter overlap when it exists, but not pay a penalty when it does not. a very simple idea: we decompose the parameters into two components and regularize these differently. We show both theoretically and empirically, our method strictly and noticeably outperforms both ℓ1 or ℓ1/ℓq methods, over the entire range of possible overlaps (except at boundary cases, where we match the best method). We also provide theoretical guarantees that the method performs well under high-dimensional scaling.

The Norwood surgical procedure restores functional systemic circulation in neonatal patients with single ventricle congenital heart defects, but this complex procedure carries a high mortality rate. In this study we address the need to provide an accurate patient specific risk prediction for one-year postoperative mortality or cardiac transplantation and prolonged length of hospital stay with the purpose of assisting clinicians and patients' families in the preoperative decision making process. Currently available risk prediction models either do not provide patient specific risk factors or only predict in-hospital mortality rates. We apply machine learning models to predict and calculate individual patient risk for mortality and prolonged length of stay using the Pediatric Heart Network Single Ventricle Reconstruction trial dataset. We applied a Markov Chain Monte-Carlo simulation method to impute missing data and then fed the selected variables to multiple machine learning models. The individual risk of mortality or cardiac transplantation calculation produced by our deep neural network model demonstrated 89 ± 4% accuracy and 0.95 ± 0.02 area under the receiver operating characteristic curve (AUROC). The C-statistics results for prediction of prolonged length of stay were 85 ± 3% accuracy and AUROC 0.94 ± 0.04. These predictive models and calculator may help to inform clinical and organizational decision making.

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Periventricular leukomalacia (PVL) is brain injury that develops commonly in neonates after cardiac surgery. Earlier identification of patients who are at higher risk for PVL may improve clinicians' ability to optimize care for these challenging patients. The aim of this study was to apply machine learning algorithms and wavelet analysis to vital sign and laboratory data obtained from neonates immediately after cardiac surgery to predict PVL occurrence. We analyzed physiological data of patients with and without hypoplastic left heart syndrome (HLHS) during the first 12 h after cardiac surgery. Wavelet transform was applied to extract time-frequency information from the data. We ranked the extracted features to select the most discriminative features, and the support vector machine with radial basis function as a kernel was selected as the classifier. The classifier was optimized via three methods: (1) mutual information, (2) modified mutual information considering the reliability of features, and (3) modified mutual information with reliability index and maximizing set's mutual information. We assessed the accuracy of the classifier at each time point. A total of 71 neonates met the study criteria. The rates of PVL occurrence were 33% for all patients, with 41% in the HLHS group and 25% in the non-HLHS group. The F-score results for HLHS patients and non-HLHS patients were 0.88 and 1.00, respectively. Using maximizing set's mutual information improved the classifier performance in the all patient groups from 0.69 to 0.81. The novel application of a modified mutual information ranking system with the reliability index in a PVL prediction model provided highly accurate identification. This tool is a promising step for improving the care of neonates who are at higher risk for developing PVL following cardiac surgery.

Background: Craniosynostosis is the premature fusion of ≥1 cranial sutures and often requires surgical intervention. Surgery may involve extensive osteotomies, which can lead to substantial blood loss. Currently, there are no consensus recommendations for guiding blood conservation or transfusion in this patient population. The aim of this study is to develop a machine-learning model to predict blood product transfusion requirements for individual pediatric patients undergoing craniofacial surgery. METHODS: Using data from 2143 patients in the Pediatric Craniofacial Surgery Perioperative Registry, we assessed 6 machine-learning classification and regression models based on random forest, adaptive boosting (AdaBoost), neural network, gradient boosting machine (GBM), support vector machine, and elastic net methods with inputs from 22 demographic and preoperative features. We developed classification models to predict an individual’s overall need for transfusion and regression models to predict the number of blood product units to be ordered preoperatively. The study is reported according to the Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis (TRIPOD) checklist for prediction model development. RESULTS: The GBM performed best in both domains, with an area under receiver operating characteristic curve of 0.87 ± 0.03 (95% confidence interval) and F-score of 0.91 ± 0.04 for classification, and a mean squared error of 1.15 ± 0.12, R-squared (R 2) of 0.73 ± 0.02, and root mean squared error of 1.05 ± 0.06 for regression. GBM feature ranking determined that the following variables held the most information for prediction: platelet count, weight, preoperative hematocrit, surgical volume per institution, age, and preoperative hemoglobin. We then produced a calculator to show the number of units of blood that should be ordered preoperatively for an individual patient. CONCLUSIONS: Anesthesiologists and surgeons can use this continually evolving predictive model to improve clinical care of patients presenting for craniosynostosis surgery.