Finite-Sum Smooth Optimization with SARAH

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n} \sum_{i=1}^n f_i(w)$ has been proven to be at least $\Omega(\sqrt{n}/\epsilon)$ for $n \leq \mathcal{O}(\epsilon^{-2})$ where $\epsilon$ denotes the attained accuracy $\mathbb{E}[ \|\nabla F(\tilde{w})\|^2] \leq \epsilon$ for the outputted approximation $\tilde{w}$ (Fang et al., 2018). In this paper, we provide a convergence analysis for a slightly modified version of the SARAH algorithm (Nguyen et al., 2017a;b) and achieve total complexity that matches the lower-bound worst case complexity in (Fang et al., 2018) up to a constant factor when $n \leq \mathcal{O}(\epsilon^{-2})$ for nonconvex problems. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance

Prognosis of neonatal tetanus in the modern management era: an observational study in 107 Vietnamese infants.

OBJECTIVES: Most data regarding the prognosis in neonatal tetanus originate from regions where limited resources have historically impeded management. It is not known whether recent improvements in critical care facilities in many low- and middle-income countries have affected indicators of a poor prognosis in neonatal tetanus. We aimed to determine the factors associated with worse outcomes in a Vietnamese hospital with neonatal intensive care facilities. METHODS: Data were collected from 107 cases of neonatal tetanus. Clinical features on admission were analyzed against mortality and a combined endpoint of 'death or prolonged hospital stay'. RESULTS: Multivariable analysis showed that only younger age (odds ratio (OR) for mortality 0.69, 95% confidence interval (CI) 0.48-0.98) and lower weight (OR for mortality 0.06, 95% CI 0.01-0.54) were significantly associated with both the combined endpoint and death. A shorter period of onset (OR 0.94, 95% CI 0.88-0.99), raised white cell count (OR 1.17, 95% CI 1.02-1.35), and time between first symptom and admission (OR 3.77, 95% CI 1.14-12.51) were also indicators of mortality. CONCLUSIONS: Risk factors for a poor outcome in neonatal tetanus in a setting with critical care facilities include younger age, lower weight, delay in admission, and leukocytosis