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Minimum Stein Discrepancy Estimators

Barp, A; Briol, F-X; Duncan, AB; Girolami, MA; Mackey, LW; (2019) Minimum Stein Discrepancy Estimators. In: Wallach, H and Larochelle, H and Beygelzimer, A and d'Alché-Buc, F and Fox, E and Garnett., R, (eds.) Proceedings of Advances in Neural Information Processing Systems 32 (NIPS 2019). NIPS: Massachusetts, USA. Green open access

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Abstract

When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kernel Stein discrepancy (DKSD) and diffusion score matching (DSM) estimators with complementary strengths. We establish the consistency, asymptotic normality, and robustness of DKSD and DSM estimators, then derive stochastic Riemannian gradient descent algorithms for their efficient optimisation. The main strength of our methodology is its flexibility, which allows us to design estimators with desirable properties for specific models at hand by carefully selecting a Stein discrepancy. We illustrate this advantage for several challenging problems for score matching, such as non-smooth, heavy-tailed or light-tailed densities.

Type: Proceedings paper
Title: Minimum Stein Discrepancy Estimators
Event: Advances in Neural Information Processing Systems 32 (NIPS 2019)
Open access status: An open access version is available from UCL Discovery
Publisher version: https://papers.nips.cc/paper/9457-minimum-stein-di...
Language: English
Additional information: This version is the author accepted manuscript. 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-pp.ucl.ac.uk/id/eprint/10087555
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