Black-box density function estimation using recursive partitioning

Erik Bodin, Zhenwen Dai, Neill Campbell, Carl Henrik Ek
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:1015-1025, 2021.

Abstract

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as building blocks to treat a larger class of estimation problems. The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and real-world problems including parameter inference for gravitational-wave physics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-bodin21a, title = {Black-box density function estimation using recursive partitioning}, author = {Bodin, Erik and Dai, Zhenwen and Campbell, Neill and Ek, Carl Henrik}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {1015--1025}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/bodin21a/bodin21a.pdf}, url = {https://proceedings.mlr.press/v139/bodin21a.html}, abstract = {We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as building blocks to treat a larger class of estimation problems. The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and real-world problems including parameter inference for gravitational-wave physics.} }
Endnote
%0 Conference Paper %T Black-box density function estimation using recursive partitioning %A Erik Bodin %A Zhenwen Dai %A Neill Campbell %A Carl Henrik Ek %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-bodin21a %I PMLR %P 1015--1025 %U https://proceedings.mlr.press/v139/bodin21a.html %V 139 %X We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as building blocks to treat a larger class of estimation problems. The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and real-world problems including parameter inference for gravitational-wave physics.
APA
Bodin, E., Dai, Z., Campbell, N. & Ek, C.H.. (2021). Black-box density function estimation using recursive partitioning. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:1015-1025 Available from https://proceedings.mlr.press/v139/bodin21a.html.

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