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Probabilistic Integration
Michael A Osborne · Philipp Hennig

Fri Dec 11 05:30 AM -- 03:30 PM (PST) @ 512 a
Event URL: http://probabilistic-numerics.org/meetings/NIPS2015 »

Integration is the central numerical operation required for Bayesian machine learning (in the form of marginalization and conditioning). Sampling algorithms still abound in this area, although it has long been known that Monte Carlo methods are fundamentally sub-optimal. The challenges for the development of better performing integration methods are mostly algorithmic. Moreover, recent algorithms have begun to outperform MCMC and its siblings, in wall-clock time, on realistic problems from machine learning.

The workshop will review the existing, by now quite strong, theoretical case against the use of random numbers for integration, discuss recent algorithmic developments, relationships
between conceptual approaches, and highlight central research challenges going forward.

Among the questions to be addressed by the workshop are
* How fast can a practical integral estimate on a deterministic function converge (polynomially, super-polynomially, not just “better than sqrt(N)”)?
* How are these rates related, precisely, to prior assumptions about the integrand, and to the design rules of the integrator?
* To which degree can the source code of an integration problem be parsed to choose informative priors?
* Are random numbers necessary and helpful for efficient multivariate integration, or are they a conceptual crutch that cause inefficiencies?
* What are the practical challenges in the design of efficient multivariate integration methods that use such prior information?

The workshop builds upon the growing field of probabilistic numerics, for which Probabilistic Integration is a core component. A community website for probabilistic numerics can be found at http://probabilistic-numerics.org.

Fri 6:10 a.m. - 6:40 a.m.
*Christian Robert* Can We Estimate a Constant? (Talk) Christian X Robert
Fri 6:40 a.m. - 7:00 a.m.
*François-Xavier Briol* Theoretical Guarantees for Probabilistic Integration (Talk) François-Xavier Briol
Fri 7:30 a.m. - 8:00 a.m.
*Arthur Gretton* Learning with Probabilities as Inputs, Using Kernels (Talk) Arthur Gretton
Fri 8:00 a.m. - 8:30 a.m.
*Roman Garnett* Bayesian Quadrature: Lessons Learned and Looking Forwards (Talk) Roman Garnett
Fri 8:30 a.m. - 8:45 a.m.
*George Papamakarios* Distilling Intractable Generative Models (Talk) George Papamakarios
Fri 8:45 a.m. - 9:00 a.m.
*Jan Calliess* Bayesian Lipschitz Constant Estimation and Quadrature (Talk) Jan-Peter Calliess
Fri 11:30 a.m. - 12:00 p.m.
Convergence Rates of Kernel Quadrature Rules (Talk) Francis Bach
Fri 12:00 p.m. - 12:30 p.m.
*David Duvenaud* Automatic Differentiation: The most criminally underused tool in probabilistic numerics (Talk) David Duvenaud
Fri 12:30 p.m. - 1:00 p.m.
*Max Welling* Optimization Monte Carlo (Talk) Max Welling

Author Information

Michael A Osborne (U Oxford)
Philipp Hennig (MPI Tübingen)

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