Gradient Descent using Duality Structures

Gradient descent is commonly used to solve optimization problems arising in machine learning, such as training neural networks. Although it seems to be effective for many different neural network training problems, it is unclear if the effectiveness of gradient descent can be explained using existing performance guarantees for the algorithm. We argue that existing analyses of gradient descent rely on assumptions that are too strong to be applicable in the case of multi-layer neural networks. To address this, we propose an algorithm, duality structure gradient descent (DSGD), that is amenable to a non-asymptotic performance analysis, under mild assumptions on the training set and network architecture. The algorithm can be viewed as a form of layer-wise coordinate descent, where at each iteration the algorithm chooses one layer of the network to update. The decision of what layer to update is done in a greedy fashion, based on a rigorous lower bound of the function decrease for each possible choice of layer. In the analysis, we bound the time required to reach approximate stationary points, in both the deterministic and stochastic settings. The convergence is measured in terms of a Finsler geometry that is derived from the network architecture and designed to confirm a Lipschitz-like property on the gradient of the training objective function. Numerical experiments in both the full batch and mini-batch settings suggest that the algorithm is a promising step towards methods for training neural networks that are both rigorous and efficient

Comparison of the Oxidation State of Fe in Comet 81P/Wild 2 and Chondritic-Porous Interplanetary Dust Particles

The fragile structure of chondritic-porous interplanetary dust particles (CP- IDPs) and their minimal parent-body alteration have led researchers to believe these particles originate in comets rather than asteroids where aqueous and thermal alteration have occurred. The solar elemental abundances and atmospheric entry speed of CP-IDPs also suggest a cometary origin. With the return of the Stardust samples from Jupiter-family comet 81P/Wild 2, this hypothesis can be tested. We have measured the Fe oxidation state of 15 CP-IDPs and 194 Stardust fragments using a synchrotron-based x-ray microprobe. We analyzed ~300 nanograms of Wild 2 material - three orders of magnitude more material than other analyses comparing Wild 2 and CP-IDPs. The Fe oxidation state of these two samples of material are >2{\sigma} different: the CP-IDPs are more oxidized than the Wild 2 grains. We conclude that comet Wild 2 contains material that formed at a lower oxygen fugacity than the parent body, or parent bodies, of CP-IDPs. If all Jupiter-family comets are similar, they do not appear to be consistent with the origin of CP-IDPs. However, comets that formed from a different mix of nebular material and are more oxidized than Wild 2 could be the source of CP-IDPs.Comment: Earth and Planetary Science Letters, in pres

Does the provision of a DVD-based audio-visual presentation improve recruitment in a clinical trial? A randomised trial of DVD trial invitations

Abstract Background Recruitment to clinical trials can be challenging. Methods that improve the efficiency of trial recruitment are needed to increase successful study completions. The aim of this study was to ascertain whether sending an audio-visual presentation on a digital versatile disc (DVD), along with usual study invitation materials, would improve recruitment to the Febuxostat versus Allopurinol Streamlined Trial (FAST), a clinical trial in patients with established gout. Methods Potential participants for the FAST study who were identified by searches of GP records in Scottish primary care practices between August 2013 and July 2014 were included in this study. Individuals were randomly allocated to receive either a standard invitation (letter and information leaflet) or a standard invitation and a DVD containing an audio-visual presentation explaining the background and operation of FAST. Data on invitation response rates, screening attendances and randomisations were collected by research nurses. Results One thousand fifty potential participants were invited to take part in FAST during this period. 509 individuals were randomised to receive the DVD presentation and the standard invitation and 541 received a standard invitation only. DVD recipients were less likely to respond to the initial invitation (adjusted OR 0.76, CI 0.58–0.99) and marginally less likely to return a positive response (OR 0.75, CI 0.59–0.96). There was no statistically significant difference between the groups in attendance for screening or randomisation. The DVD did not influence the age, gender, or socioeconomic deprivation scores of those responding positively to a letter of invitation. Conclusions The inclusion of a DVD presentation with FAST study invitations did not make any practical difference to the rate of positive response to invitation. Further innovation and evaluation will be required to improve recruitment to clinical trials. Trial registration EU Clinical Trials Register. EudraCT Number: 2011–001883-23. ISRCTN registry. ISRCTN72443278