The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in recent years.A common feature of this work is that the adversarial robustification often corresponds exactly to regularization methods which appear as a loss function plus a penalty. In this paper we deepen and extend the understanding of the connection between robustification and regularization (as achieved by penalization) in regression problems. Specifically, (a) In the context of linear regression, we characterize precisely under which conditions on the model of uncertainty used and on the loss function penalties robustification and regularization are equivalent.(b) We extend the characterization of robustification and regularization to matrix regression problems (matrix completion and Principal Component Analysis).

IMPORTANCE Inpatient overcrowding is associated with delays in care, including the deferral of surgical care until beds are available to accommodate postoperative patients. Timely patient discharge is critical to address inpatient overcrowding and requires coordination among surgeons, nurses, case managers, and others. This is difficult to achieve without early identification and systemwide transparency of discharge candidates and their respective barriers to discharge. OBJECTIVE To validate the performance of a clinically interpretable feedforward neural network model that could improve the discharge process by predicting which patients would be discharged within 24 hours and their clinical and nonclinical barriers. DESIGN, SETTING, AND PARTICIPANTS This prognostic study included adult patients discharged from inpatient surgical care from May 1, 2016, to August 31, 2017, at a quaternary care teaching hospital. Model performance was assessed with standard cross-validation techniques. The model's performance was compared with a baseline model using historical procedure median length of stay to predict discharges. In prospective cohort analysis, the feedforward neural network model was used to make predictions on general surgical care floors with 63 beds. If patients were not discharged when predicted, the causes of delay were recorded. MAIN OUTCOMES AND MEASURES The primary outcome was the out-of-sample area under the receiver operating characteristic curve of the model. Secondary outcomes included the causes of discharge delay and the number of avoidable bed-days. RESULTS The model was trained on 15 201 patients (median [interquartile range] age, 60 [46-70] years; 7623 [50.1%] men) discharged from inpatient surgical care. The estimated out-of-sample area under the receiver operating characteristic curve of the model was 0.840 (SD, 0.008; 95% CI, 0.839-0.844). Compared with the baseline model, the neural network model had higher sensitivity (52.5% vs 56.6%) and specificity (51.7% vs 82.6%). The neural network model identified 65 barriers to discharge. In the prospective study of 605 patients, causes of delays included clinical barriers (41 patients [30.1%]), variation in clinical practice (30 patients [22.1%]), and nonclinical reasons (65 patients [47.8%]). Summing patients who were not discharged owing to variation in clinical practice and nonclinical reasons, 128 bed-days, or 1.2 beds per day, were classified as avoidable. CONCLUSIONS AND RELEVANCE This cohort study found that a neural network model could predict daily inpatient surgical care discharges and their barriers. The model identified systemic causes of discharge delays. Such models should be studied for their ability to increase the timeliness of discharges.

Abstract. We consider frames in a finite-dimensional Hilbert space H n where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R 2 was previously defined using polar coordinates and was used to characterize tight frames in R 2 in a geometric fashion. Reformulating the definition of a diagram vector in R 2 we provide a natural extension of this notion to R n and C n . Using the diagram vectors we give a characterization of tight frames in R n or C n . Further we provide a characterization of when a unit-norm frame in R n or C n can be scaled to a tight frame. This classification allows us to determine all scaling coefficients that make a unit-norm frame into a tight frame. Mathematics subject classification (2010): 42C15, 05B20, 15A03.

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing so show the following:1. Drawing parallels between robust statistics and robust optimization, we show that the trimmed-Lasso-regularized least squares problem can be viewed as a generalized form of total least squares under a specific model of uncertainty. In contrast, this same model of uncertainty, viewed instead through a robust optimization lens, leads to the convex SLOPE (or OWL) penalty.2. Further, in relating the trimmed Lasso to commonly used sparsity-inducing penalty functions, we provide a succinct characterization of the connection between trimmed-Lassolike approaches and penalty functions that are coordinate-wise separable, showing that the trimmed penalties subsume existing coordinate-wise separable penalties, with strict containment in general.3. Finally, we describe a variety of exact and heuristic algorithms, both existing and new, for trimmed Lasso regularized estimation problems. We include a comparison between the different approaches and an accompanying implementation of the algorithms.

In the hospital, fast and efficient communication among clinicians and other employees is paramount to ensure optimal patient care, workflow efficiency, patient safety and patient comfort. The implementation of the wireless Vocera® Badge, a hands-free wearable device distributed to perioperative team members, has increased communication efficiency across the perioperative environment at Massachusetts General Hospital (MGH). This quality improvement project, based upon identical pre- and post-implementation surveys, used qualitative and quantitative analysis to determine if and how the Vocera system affected the timeliness of information flow, ease of communication, and operating room noise levels throughout the perioperative environment. Overall, the system increased the speed of information flow and eased communication between coworkers yet was perceived to have raised the overall noise level in and around the operating rooms (ORs). The perceived increase in noise was outweighed by the closed-loop communication between clinicians. Further education of the system's features in regard to speech recognition and privacy along with expected conversation protocol are necessary to ensure hassle-free communication for all staff.