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Copula-like variational inference

Hirt, M; Dellaportas, P; Durmus, A; (2019) Copula-like variational inference. In: Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS 2019). 33rd Conference on Neural Information Processing Systems (NeurIPS 2019): Vancouver, Canada. Green open access

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Abstract

This paper considers a new family of variational distributions motivated by Sklar's theorem. This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i.e. with a complexity linear in the dimension d of the state space. Then, the proposed variational densities that we suggest can be seen as arising from these copula-like densities used as base distributions on the hypercube with Gaussian quantile functions and sparse rotation matrices as normalizing flows. The latter correspond to a rotation of the marginals with complexity O(d log d). We provide some empirical evidence that such a variational family can also approximate non-Gaussian posteriors and can be beneficial compared to Gaussian approximations. Our method performs largely comparably to state-of-the-art variational approximations on standard regression and classification benchmarks for Bayesian Neural Networks.

Type: Proceedings paper
Title: Copula-like variational inference
Event: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019)
Location: Vancouver, Canada
Dates: 8th-14th September 2019
Open access status: An open access version is available from UCL Discovery
Publisher version: https://papers.nips.cc/paper/8561-copula-like-vari...
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10081210
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