The Implicit Bias of Gradient Descent on Separable Data

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The result also generalizes to other monotone decreasing loss functions with an infimum at infinity, to multi-class problems, and to training a weight layer in a deep network in a certain restricted setting. Furthermore, we show this convergence is very slow, and only logarithmic in the convergence of the loss itself. This can help explain the benefit of continuing to optimize the logistic or cross-entropy loss even after the training error is zero and the training loss is extremely small, and, as we show, even if the validation loss increases. Our methodology can also aid in understanding implicit regularization n more complex models and with other optimization methods.Comment: Final JMLR version, with improved discussions over v3. Main improvements in journal version over conference version (v2 appeared in ICLR): We proved the measure zero case for main theorem (with implications for the rates), and the multi-class cas

The association of preoperative cardiac stress testing with 30-day death and myocardial infarction among patients undergoing kidney transplantation

BACKGROUND:Although periodic cardiac stress testing is commonly used to screen patients on the waiting list for kidney transplantation for ischemic heart disease, there is little evidence to support this practice. We hypothesized that cardiac stress testing in the 18 months prior to kidney transplantation would not reduce postoperative death, total myocardial infarction (MI) or fatal MI. METHODS:Using the United States Renal Data System, we identified ESRD patients ≥40 years old with primary Medicare insurance who received their first kidney transplant between 7/1/2006 and 11/31/2013. Propensity matching created a 1:1 matched sample of patients with and without stress testing in the 18 months prior to kidney transplantation. The outcomes of interest were death, total (fatal and nonfatal) MI or fatal MI within 30 days of kidney transplantation. RESULTS:In the propensity-matched cohort of 17,304 patients, death within 30 days occurred in 72 of 8,652 (0.83%) patients who underwent stress testing and in 65 of 8,652 (0.75%) patients who did not (OR 1.07; 95% CI: 0.79-1.45; P = 0.66). MI within 30 days occurred in 339 (3.9%) patients who had a stress test and in 333 (3.8%) patients who did not (OR 1.03; 95% CI: 0.89-1.21; P = 0.68). Fatal MI occurred in 17 (0.20%) patients who underwent stress testing and 15 (0.17%) patients who did not (OR 0.97; 95% CI: 0.71-1.32; P = 0.84). CONCLUSION:Stress testing in the 18 months prior to kidney transplantation is not associated with a reduction in death, total MI or fatal MI within 30 days of kidney transplantation

ULVA: Tomorrow's "Wheat of the sea", a model for an innovative mariculture

A growing interest in the development of oceanic coastal shores has arisen over the past decade, seeking alternative sustainable food sources and other valuable products. Our initiative aims at exploiting the potential of marine seaweeds in Europe. Building on the successes of previous EU and pan-European projects on seaweeds, and due the unique characteristics of the genus Ulva (Linnaeus, 1753), we have identified these green algae as the most suitable candidate and model organism for a novel kind of European mariculture. Much of the knowledge on Ulva, generated in diverse scientific disciplines and different communities, is not easily comparable nor is it shared among scientists, stakeholders, end users and the public. This COST Action, "SeaWheat" (CA20106—TOMORROW'S 'WHEAT OF THE SEA': ULVA, A MODEL FOR AN INNOVATIVE MARICULTURE), proposes an innovative conceptual pathway to address these issues, significantly improving knowledge in the biology of the most promising Ulva spp., capitalising on their economic potential, and exploring commercial applications in the human food, animal feed, pharmaceutical industries and ecosystem service. The COST Action combines interdisciplinary approaches to the sustainable use of marine resources, encompassing all the facets of Ulva biology, ecology, aquaculture, engineering, economic and social sciences. This Action will lead to the development of advanced science, create business and job opportunities in the maritime and coastal economies, and have a significant impact on societal welfare. This COST Action fulfils the current ‘Societal Challenges Priorities’ of European Horizon 2020 strategy for food security, and its application will contribute to the UN Sustainable Development Goals 14 (UNSDG) to conserve and sustainably exploit natural resources