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Flow Annealed Importance Sampling Bootstrap
Laurence Midgley · Vincent Stimper · Gregor Simm · Bernhard Schölkopf · José Miguel Hernández-Lobato
Event URL: https://openreview.net/forum?id=OFZ-78-CnO »
Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated by expensive MCMC simulations, or use stochastic losses that have high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass-covering $\alpha$-divergence with $\alpha=2$, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We apply FAB to complex multimodal targets and show that we can approximate them accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density, without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting samples, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth.
Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated by expensive MCMC simulations, or use stochastic losses that have high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass-covering $\alpha$-divergence with $\alpha=2$, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We apply FAB to complex multimodal targets and show that we can approximate them accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density, without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting samples, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth.
Author Information
Laurence Midgley (InstaDeep/University of Cambridge)
Vincent Stimper (University of Cambridge)
Gregor Simm (Microsoft Research)
Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)
Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.
José Miguel Hernández-Lobato (University of Cambridge)
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2009 Poster: Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions »
Bharath Sriperumbudur · Kenji Fukumizu · Arthur Gretton · Gert Lanckriet · Bernhard Schölkopf -
2009 Oral: Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions »
Bharath Sriperumbudur · Kenji Fukumizu · Arthur Gretton · Gert Lanckriet · Bernhard Schölkopf -
2008 Workshop: Causality: objectives and assessment »
Isabelle Guyon · Dominik Janzing · Bernhard Schölkopf -
2008 Mini Symposium: Computational Photography »
Bill Freeman · Bernhard Schölkopf -
2008 Poster: Characteristic Kernels on Groups and Semigroups »
Kenji Fukumizu · Bharath Sriperumbudur · Arthur Gretton · Bernhard Schölkopf -
2008 Oral: Characteristic Kernels on Groups and Semigroups »
Kenji Fukumizu · Bharath Sriperumbudur · Arthur Gretton · Bernhard Schölkopf -
2008 Poster: Nonlinear causal discovery with additive noise models »
Patrik O Hoyer · Dominik Janzing · Joris M Mooij · Jonas Peters · Bernhard Schölkopf -
2008 Poster: Effects of Stimulus Type and of Error-Correcting Code Design on BCI Speller Performance »
Jeremy Hill · Jason Farquhar · Suzanne Martens · Felix Bießmann · Bernhard Schölkopf -
2008 Poster: Bayesian Experimental Design of Magnetic Resonance Imaging Sequences »
Matthias Seeger · Hannes Nickisch · Rolf Pohmann · Bernhard Schölkopf -
2008 Spotlight: Nonlinear causal discovery with additive noise models »
Patrik O Hoyer · Dominik Janzing · Joris M Mooij · Jonas Peters · Bernhard Schölkopf -
2008 Spotlight: Bayesian Experimental Design of Magnetic Resonance Imaging Sequences »
Matthias Seeger · Hannes Nickisch · Rolf Pohmann · Bernhard Schölkopf -
2008 Spotlight: Effects of Stimulus Type and of Error-Correcting Code Design on BCI Speller Performance »
Jeremy Hill · Jason Farquhar · Suzanne Martens · Felix Bießmann · Bernhard Schölkopf -
2008 Poster: An empirical Analysis of Domain Adaptation Algorithms for Genomic Sequence Analysis »
Gabriele B Schweikert · Christian Widmer · Bernhard Schölkopf · Gunnar Rätsch -
2008 Poster: Diffeomorphic Dimensionality Reduction »
Christian Walder · Bernhard Schölkopf -
2007 Spotlight: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Poster: An Analysis of Inference with the Universum »
Fabian H Sinz · Olivier Chapelle · Alekh Agarwal · Bernhard Schölkopf -
2007 Poster: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Spotlight: An Analysis of Inference with the Universum »
Fabian H Sinz · Olivier Chapelle · Alekh Agarwal · Bernhard Schölkopf -
2007 Spotlight: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2007 Poster: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2007 Poster: Regulator Discovery from Gene Expression Time Series of Malaria Parasites: a Hierachical Approach »
José Miguel Hernández-Lobato · Tjeerd M Dijkstra · Tom Heskes -
2006 Poster: Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions »
Christian Walder · Bernhard Schölkopf · Olivier Chapelle -
2006 Poster: Learning Dense 3D Correspondence »
Florian Steinke · Bernhard Schölkopf · Volker Blanz -
2006 Poster: A Local Learning Approach for Clustering »
Mingrui Wu · Bernhard Schölkopf -
2006 Poster: A Kernel Method for the Two-Sample-Problem »
Arthur Gretton · Karsten Borgwardt · Malte J Rasch · Bernhard Schölkopf · Alexander Smola -
2006 Poster: Correcting Sample Selection Bias by Unlabeled Data »
Jiayuan Huang · Alexander Smola · Arthur Gretton · Karsten Borgwardt · Bernhard Schölkopf -
2006 Spotlight: Correcting Sample Selection Bias by Unlabeled Data »
Jiayuan Huang · Alexander Smola · Arthur Gretton · Karsten Borgwardt · Bernhard Schölkopf -
2006 Talk: A Kernel Method for the Two-Sample-Problem »
Arthur Gretton · Karsten Borgwardt · Malte J Rasch · Bernhard Schölkopf · Alexander Smola -
2006 Poster: A Nonparametric Approach to Bottom-Up Visual Saliency »
Wolf Kienzle · Felix A Wichmann · Bernhard Schölkopf · Matthias Franz -
2006 Poster: Learning with Hypergraphs: Clustering, Classification, and Embedding »
Denny Zhou · Jiayuan Huang · Bernhard Schölkopf