Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912949376909312 |
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| author | Xu, Jian Du, Shian Yang, Junmei Ma, Qianli Zeng, Delu Paisley, John |
| author_facet | Xu, Jian Du, Shian Yang, Junmei Ma, Qianli Zeng, Delu Paisley, John |
| contents | Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted version of the Bayesian GPLVMs has been proposed to obtain a tighter variational bound. However, this version of the approach is primarily limited to analyzing simple data structures, as the generation of an effective proposal distribution can become quite challenging in high-dimensional spaces or with complex data sets. In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. By transforming the posterior into a sequence of intermediate distributions using annealing, we combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. We further propose an efficient algorithm by reparameterizing all variables in the evidence lower bound (ELBO). Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_06710 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling Xu, Jian Du, Shian Yang, Junmei Ma, Qianli Zeng, Delu Paisley, John Machine Learning Artificial Intelligence Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted version of the Bayesian GPLVMs has been proposed to obtain a tighter variational bound. However, this version of the approach is primarily limited to analyzing simple data structures, as the generation of an effective proposal distribution can become quite challenging in high-dimensional spaces or with complex data sets. In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. By transforming the posterior into a sequence of intermediate distributions using annealing, we combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. We further propose an efficient algorithm by reparameterizing all variables in the evidence lower bound (ELBO). Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence. |
| title | Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2408.06710 |