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Accelerated parallel non-conjugate sampling for Bayesian non-parametric models

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Abstract

Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where the integration is tractable, we can sample new feature assignments according to a predictive likelihood. We present a novel method to accelerate the mixing of latent variable model inference by proposing feature locations based on the data, as opposed to the prior. First, we introduce an accelerated feature proposal mechanism that we show is a valid MCMC algorithm for posterior inference. Next, we propose an approximate inference strategy to perform accelerated inference in parallel. A two-stage algorithm that combines the two approaches provides a computationally attractive method that can quickly reach local convergence to the posterior distribution of our model, while allowing us to exploit parallelization.

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Notes

  1. For a more substantial introduction to Bayesian non-parametrics, we direct the reader to Ghosh and Ramamoorthi (2003); Hjort et al. (2010); Müller et al. (2015) and a recent survey on Bayesian non-parametrics (Xuan et al. 2019).

  2. Code is available at https://github.com/michaelzhang01/acceleratedDP

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Hong Kong, Pok Fu Lam, Hong Kong

    Michael Minyi Zhang

  2. Department of Statistics and Data Science, The University of Texas at Austin, Austin, United States

    Sinead A. Williamson

  3. Swiss Data Science Center, ETH Zürich, Zürich, Switzerland

    Fernando Pérez-Cruz

Authors
  1. Michael Minyi Zhang
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  2. Sinead A. Williamson
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  3. Fernando Pérez-Cruz
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Corresponding author

Correspondence to Michael Minyi Zhang.

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Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The contribution of Michael Zhang and Sinead Williamson was funded by NSF grant IIS 1447721. The contribution of Michael Zhang was also funded by the University of Hong Kong’s Seed Fund for Basic Research for New Staff.

Appendix

Appendix

See Figs. 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20.

Fig. 8
figure 8

Yale faces features (left), MNIST features (middle) and CIFAR features (right) obtained via uncollapsed sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 9
figure 9

MNIST features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 10
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Yale faces features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 11
figure 11

CIFAR features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 12
figure 12

MNIST features obtained via variational inference, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 13
figure 13

Yale faces features obtained via variational inference, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 14
figure 14

CIFAR features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 15
figure 15

MNIST features obtained via collapsed sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 16
figure 16

Yale faces features obtained via variational inference, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 17
figure 17

CIFAR faces features obtained via collapsed sampling, sorted in descending order of popularity for the multinomial-Dirichlet model

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Fig. 18
figure 18

MNIST features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-log normal model

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Fig. 19
figure 19

Yale faces features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-log normal model

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Fig. 20
figure 20

CIFAR features obtained via accelerated sampling, sorted in descending order of popularity for the multinomial-log normal model

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Zhang, M.M., Williamson, S.A. & Pérez-Cruz, F. Accelerated parallel non-conjugate sampling for Bayesian non-parametric models. Stat Comput 32, 50 (2022). https://doi.org/10.1007/s11222-022-10108-z

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