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  1. Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from the posterior distribution of the parameters of a statistical model given the input data and the prior distribution over the model parameters. However, these algorithms do not apply to the decentralized learning setting, when a network of agents are working collaboratively to learn the parameters of a statistical model without sharing their individual data due to privacy reasons or communication constraints. We study two algorithms: Decentralizedmore »SGLD (DE-SGLD) and Decentralized SGHMC (DE-SGHMC) which are adaptations of SGLD and SGHMC methods that allow scaleable Bayesian inference in the decentralized setting for large datasets. We show that when the posterior distribution is strongly log-concave and smooth, the iterates of these algorithms converge linearly to a neighborhood of the target distribution in the 2-Wasserstein distance if their parameters are selected appropriately. We illustrate the efficiency of our algorithms on decentralized Bayesian linear regression and Bayesian logistic regression problems« less
  2. Abstract The Environmental Effects Assessment Panel of the Montreal Protocol under the United Nations Environment Programme evaluates effects on the environment and human health that arise from changes in the stratospheric ozone layer and concomitant variations in ultraviolet (UV) radiation at the Earth’s surface. The current update is based on scientific advances that have accumulated since our last assessment (Photochem and Photobiol Sci 20(1):1–67, 2021). We also discuss how climate change affects stratospheric ozone depletion and ultraviolet radiation, and how stratospheric ozone depletion affects climate change. The resulting interlinking effects of stratospheric ozone depletion, UV radiation, and climate change aremore »assessed in terms of air quality, carbon sinks, ecosystems, human health, and natural and synthetic materials. We further highlight potential impacts on the biosphere from extreme climate events that are occurring with increasing frequency as a consequence of climate change. These and other interactive effects are examined with respect to the benefits that the Montreal Protocol and its Amendments are providing to life on Earth by controlling the production of various substances that contribute to both stratospheric ozone depletion and climate change.« less
    Free, publicly-accessible full text available March 1, 2023