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Unlike much of the previous venerable work in this area, the new framework is built on standard methods for approximate inference (variational free-energy, EP and Power EP methods) rather than employing approximations to the probabilistic generative model itself.In this way all of the approximation is performed at `inference time' rather than at `modelling time', resolving awkward philosophical and empirical questions that trouble previous approaches. Abstract: Techniques known as Nonlinear Set Membership prediction, Kinky Inference or Lipschitz Interpolation are fast and numerically robust approaches to nonparametric machine learning that have been proposed to be utilised in the context of system identification and learning-based control.Furthermore, existing techniques to estimate the Lipschitz constants from the data are not robust to noise or seem to be ad-hoc and typically are decoupled from the ultimate learning and prediction task.

To avoid poor performance due to local minima, we propose to utilise Lipschitz properties of the optimisation objective to ensure global optimisation success.

The resulting approach is a new flexible method for nonparametric black-box learning.

[ Balog | Bauer | Bui | Dziugaite | Ge | Ghahramani | Gu | Hernández-Lobato | Kilbertus | Kok | Li | Matthews | Navarro | Peharz | Rasmussen | Rojas-Carulla | Rowland | Ścibior | Shah | Steinrücken | Rich Turner | Weller ] [ Borgwardt | Bratières | Calliess | Chen | Cunningham | Davies | Deisenroth | Duvenaud | Eaton | Frellsen | Frigola | Van Gael | Gal | Heaukulani | Heller | Hoffman | Houlsby | Huszár | Knowles | Lacoste-Julien | Lloyd | Lopez-Paz | Mc Allister | Mc Hutchon | Mohamed | Orbanz | Ortega | Palla | Quadrianto | Roy | Saatçi | Tobar | Ryan Turner | Snelson | van der Wilk | Williamson | Wilson ] , Toulon, France, April 2017.

Abstract: We develop a first line of attack for solving programming competition-style problems from input-output examples using deep learning.

We propose a re-parametrisation of the alpha-divergence objectives, deriving a simple inference technique which, together with dropout, can be easily implemented with existing models by simply changing the loss of the model.

We demonstrate improved uncertainty estimates and accuracy compared to VI in dropout networks.

We show how a subfamily of our new methods adapts to this setting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Abstract: Sparse approximations for Gaussian process models provide a suite of methods that enable these models to be deployed in large data regime and enable analytic intractabilities to be sidestepped.

Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results. However, the field lacks a principled method to handle streaming data in which the posterior distribution over function values and the hyperparameters are updated in an online fashion.

Crucially, we demonstrate that the new framework includes new pseudo-point approximation methods that outperform current approaches on regression and classification tasks. Lipschitz optimisation for Lipschitz interpolation. They utilise presupposed Lipschitz properties in order to compute inferences over unobserved function values.

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