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–Neural Information Processing Systems
Even these ideas are not so novel. For example, the local reparametrization trick is something that we use all the time when we do Variational Bayes (VB) (say in a logistic regression model) and transform high-dimensional integrals into one-dimensional integrals under a Gaussian approximate posterior. For example, if you have a likelihood of the form \prod_{i 1} n \sigma(w T x_i) and apply VB with q(w mu,Sigma), then you end up with a sum of expectations of the form \sum_{i 1} n q(w mu,Sigma) \log \sigma(w T x_i) d w and then the local reparametrization trick is applied to transform each separate (initially high-dimensional integral over the vector w) into a 1-D integral over the univariate standard normal. The authors essentially use this separately for each activation unit and apply stochastic approximation instead of integration. Having said that, I must admit that as far as the stochastic variational inference algorithms are concerned and the related research community (born a couple of years ago!) the use of this local reparametrization trick, as far as I know, is novel and people should know about it because it is useful.
Neural Information Processing Systems
Feb-7-2025, 23:38:24 GMT
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