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Minimum Stein Discrepancy Estimators
Alessandro Barp · Francois-Xavier Briol · Andrew Duncan · Mark Girolami · Lester Mackey

Thu Dec 05:00 PM -- 07:00 PM PST @ East Exhibition Hall B + C #9

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.

Author Information

Alessandro Barp (Imperial College London)
Francois-Xavier Briol (University of Cambridge)
Andrew Duncan (Imperial College London)
Mark Girolami (University of Cambridge)
Lester Mackey (Microsoft Research)

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