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There is a lot of often overlooked evidence that standard p(w) = N(0, a*I) priors combined with a NN f(x,w) induce a distribution over functions p(f(x)) with useful properties!... 1/15

In practice, standard "deep ensembles" of independently trained models provides a relatively compelling Bayesian model average. This point is often overlooked because we are used to viewing Bayesian methods as sampling from some (approximate) posterior... 1/10

...to form a model average, via simple Monte Carlo. But if we instead directly consider what we ultimately want to compute, the integral corresponding to the marginal predictive distribution (the predictive distribution not conditioning on weights)... 2/10

...then deep ensembles are in practice a _better_ approximation to the Bayesian model average than methods that are conventionally accepted as Bayesian (such as Laplace, variational methods with a Gaussian posterior, etc.). 3/10

We can greatly simplify Hamiltonian and Lagrangian neural nets by working in Cartesian coordinates with explicit constraints, leading to dramatic performance improvements! Our #NeurIPS2020 paper: arxiv.org/abs/2010.13581

with @m_finzi, @KAlexanderWang. 1/5

with @m_finzi, @KAlexanderWang. 1/5

Effective dimension compares favourably to popular path-norm and PAC-Bayes flatness measures, including double descent and width-depth trade-offs! We have just posted this new result in section 7 of our paper on posterior contraction in BDL: arxiv.org/abs/2003.02139. 1/16

The plots are most interpretable for comparing models of similar train loss (e.g. above the green partition). N_eff(Hess) = effective dimension of the Hessian at convergence. 2/16

Both path-norm and PAC-Bayes flatness variants perform well in the recent fantastic generalization measures paper of Jiang et. al (2019): arxiv.org/abs/1912.02178.

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Our new paper "Bayesian Deep Learning and a Probabilistic Perspective of Generalization": arxiv.org/abs/2002.08791. Includes (1) benefits of BMA; (2) BMA <-> Deep Ensembles; (3) new methods; (4) BNN priors; (5) generalization in DL; (6) tempering in BDL. With @Pavel_Izmailov. 1/19

Since neural nets can fit images with noisy labels, it has been suggested we should rethink generalization. But this behaviour is understandable from a probabilistic perspective: we want to support any possible solution, but also have good inductive biases. 2/19

Bayesian methods are *especially* compelling for deep neural networks. The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. This difference will be greatest for underspecified models like DNNs. 1/18

In particular, the predictive distribution we often want to find is p(y|x,D) = \int p(y|x,w) p(w|D) dw. 'y' is an output, 'x' an input, 'w' the weights, and D the data. This is not a controversial equation, it is simply the sum and product rules of probability. 2/18

Rather than betting everything on a single hypothesis, we want to use every setting of parameters, weighted by posterior probabilities. This procedure is known as a Bayesian model average (BMA). 3/18