Archive for ENS Paris-Saclay
far south
Posted in Books, Statistics, Travel, University life with tags Biometrika, Computo, ENS Paris-Saclay, habilitation, HDR, MCMC convergence, overdamped Langevin algorithm, PDMP, Saclay, stochastic gradient descent, stochastic optimisation, unadjusted Langevin algorithm, Université Paris-Saclay on February 23, 2022 by xi'an
Julyan’s talk on priors in Bayesian neural networks [cancelled!]
Posted in pictures, Statistics, Travel, University life with tags All about that Bayes, École Normale de Cachan, Bayesian deep learning, Bayesian neural networks, Cachan, conference cancellation, coronavirus epidemics, ENS Paris-Saclay, Gaussian priors, machine learning, neural network, ReLU, seminar, Université Paris-Saclay on March 5, 2020 by xi'an
Next Friday, 13 March at 1:30p.m., Julyan Arbel, researcher at Inria Grenoble will give a All about that Bayes talk at CMLA, ENS Paris-Saclay (building D’Alembert, room Condorcet, Cachan, RER stop Bagneux) on
Understanding Priors in Bayesian Neural Networks at the Unit Level
We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L², “weight decay”, regularization. Our results characterize a more intricate regularization effect at the level of the unit activations. Our main result establishes that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. We show that first layer units are Gaussian, second layer units are sub-exponential, and units in deeper layers are characterized by sub-Weibull distributions. Our results provide new theoretical insight on deep Bayesian neural networks, which we corroborate with simulation experiments.
Xi'an's Og 