The work of Peter Aaby and Christine Stabell Benn has long been controversial. Until Robert F. Kennedy Jr. became US health policy chief, most vaccine scientists tended to ignore it. In 1996, Guinea-Bissau seemed like an ideal research post for budding pediatrician Lone Graff Stensballe. Her supervisor, a fellow Dane named Peter Aaby, had spent nearly two decades collecting data on 100,000 people living in the mud brick homes of the West African country's capital. Aaby and his partner, Christine Stabell Benn, believed that the years of research in the impoverished country had yielded a major discovery about vaccines--and what they described as "non-specific effects": The measles and tuberculosis vaccines, which were derived from live, weakened viruses and bacteria, they said, boosted child survival beyond protecting against those particular pathogens. But, the scientists said, shots made from deactivated whole germs, or pieces of them, such as the diphtheria-tetanus-pertussis (DTP) shot, caused more deaths--especially in little girls--than getting no vaccine at all.

We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the targets of estimation. This unified framework is achieved by a specially structured neural network -- the Belted and Ensembled Neural Network (BENN) -- that consists of a narrow latent layer, which we call the belt, and a family of transformations of the response, which we call the ensemble. By strategically placing the belt at different layers of the neural network, we can achieve linear or nonlinear sufficient dimension reduction, and by choosing the appropriate transformation families, we can achieve dimension reduction for the conditional distribution or the conditional mean. Moreover, thanks to the advantage of the neural network, the method is very fast to compute, overcoming a computation bottleneck of the traditional sufficient dimension reduction estimators, which involves the inversion of a matrix of dimension either p or n. We develop the algorithm and convergence rate of our method, compare it with existing sufficient dimension reduction methods, and apply it to two data examples.

Some people love buying Christmas presents. Polly Arrowsmith starts making a note of what her friends and family like, then hunts for bargains, slowly and carefully. Vie Portland begins her shopping in January and has a theme each year, from heart mirrors to inspirational books. And Betsy Benn spent so much time thinking about presents, she ended up opening her own online gift business. How would these gift-giving experts react to a trend that is either a timesaving brainwave or an appalling corruption of the Christmas spirit: asking ChatGPT to do it for them?

Binary neural networks (BNN) have been studied extensively since they run dramatically faster at lower memory and power consumption than floating-point networks, thanks to the efficiency of bit operations. However, contemporary BNNs whose weights and activations are both single bits suffer from severe accuracy degradation. To understand why, we investigate the representation ability, speed and bias/variance of BNNs through extensive experiments. We conclude that the error of BNNs are predominantly caused by the intrinsic instability (training time) and non-robustness (train & test time). Inspired by this investigation, we propose the Binary Ensemble Neural Network (BENN) which leverages ensemble methods to improve the performance of BNNs with limited efficiency cost. While ensemble techniques have been broadly believed to be only marginally helpful for strong classifiers such as deep neural networks, our analyses and experiments show that they are naturally a perfect fit to boost BNNs. We find that our BENN, which is faster and much more robust than state-of-the-art binary networks, can even surpass the accuracy of the full-precision floating number network with the same architecture.