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Mixed Variational Inference

Abstract (Expand)

The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the … volume of posterior density lies. Variational approaches avoid this issue by explicitly minimising the Kullback-Leibler divergence DKL between a postulated posterior and the true (unnormalised) logarithmic posterior. However, they rely on a closed form DKL in order to update the variational parameters. To address this, stochastic versions of variational inference have been devised that approximate the intractable DKL with a Monte Carlo average. This approximation allows calculating gradients with respect to the variational parameters. However, variational methods often postulate a factorised Gaussian approximating posterior. In doing so, they sacrifice a-posteriori correlations. In this work, we propose a method that combines the Laplace approximation with the variational approach. The advantages are that we maintain: applicability on non-conjugate models, posterior correlations and a reduced number of free variational parameters. Numerical experiments demonstrate improvement over the Laplace approximation and variational inference with factorised Gaussian posteriors.

Author: Nikolaos Gianniotis

Date Published: 1st Jul 2019

Publication Type: InCollection

Surface groups acting on CAT (-1) spaces

Abstract (Expand)

Harmonic map theory is used to show that a convex cocompact surface group action on a \mathrmCAT(-1) metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only … if the Hausdorff dimension of the limit set of the action is equal to 1. This provides another proof of a result of Bonk and Kleiner. More generally, we show that the limit set of every convex cocompact surface group action on a \mathrmCAT(-1) space has Hausdorff dimension ≥1, where the inequality is strict unless the action is Fuchsian.

Authors: GEORGIOS DASKALOPOULOS, CHIKAKO MESE, ANDREW SANDERS, ALINA VDOVINA

Date Published: 1st Jul 2019

Publication Type: Journal

Hydrodynamical moving-mesh simulations of the tidal disruption of stars by supermassive black holes

Abstract

Not specified

Authors: Felipe G Goicovic, Volker Springel, Sebastian T Ohlmann, Rüdiger Pakmor

Date Published: 1st Jul 2019

Publication Type: Journal

Specifications of Standards in Systems and Synthetic Biology: Status and Developments in 2019

Abstract

Not specified

Authors: Falk Schreiber, Björn Sommer, Gary D. Bader, Padraig Gleeson, Martin Golebiewski, Michael Hucka, Sarah M. Keating, Matthias König, Chris Myers, David Nickerson, Dagmar Waltemath

Date Published: 26th Jun 2019

Publication Type: Journal

Improved leakage-equilibration-absorption scheme (ILEAS) for neutrino physics in compact object mergers

Abstract

Not specified

Authors: R Ardevol-Pulpillo, H-T Janka, O Just, A Bauswein

Date Published: 1st Jun 2019

Publication Type: Journal

A census of massive stars in NGC 346. Stellar parameters and rotational velocities

Abstract

Not specified

Authors: P. L. Dufton, C. J. Evans, I. Hunter, D. J. Lennon, F. R. N. Schneider

Date Published: 1st Jun 2019

Publication Type: Journal

From Supernova to Supernova Remnant: The Three-dimensional Imprint of a Thermonuclear Explosion

Abstract

Not specified

Authors: Gilles Ferrand, Donald C. Warren, Masaomi Ono, Shigehiro Nagataki, Friedrich K. Röpke, Ivo R. Seitenzahl

Date Published: 1st Jun 2019

Publication Type: Journal

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