Abstract
We propose a framework called HyperVAE for encoding distributions of distributions. When a target distribution is modeled by a VAE, its neural network parameters are sampled from a distribution in the model space modeled by a hyper-level VAE. We propose a variational inference framework to implicitly encode the parameter distributions into a low dimensional Gaussian distribution. Given a target distribution, we predict the posterior distribution of the latent code, then use a matrix-network decoder to generate a posterior distribution for the parameters. HyperVAE can encode the target parameters in full in contrast to common hyper-networks practices, which generate only the scale and bias vectors to modify the target-network parameters. Thus HyperVAE preserves information about the model for each task in the latent space. We derive the training objective for HyperVAE using the minimum description length (MDL) principle to reduce the complexity of HyperVAE. We evaluate HyperVAE in density estimation tasks, outlier detection and discovery of novel design classes, demonstrating its efficacy.
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Notes
- 1.
This is not the same as zero-shot learning where label description is available.
- 2.
We use \(\theta =(\theta _{p},\theta _{q})\) to denote the set of parameters for p and q.
- 3.
We assume a Dirac delta distribution for \(\gamma \), i.e. a point estimate, in this study.
- 4.
We abused the notation and use p to denote both a density and a probability mass function. Bits-back coding is applicable to continuous distributions [10].
- 5.
We assumed a matrix multiplication takes O(1) time in GPU.
- 6.
Batched matrix multiplication can be paralleled in GPU.
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Acknowledgements
This research was partially funded by the Australian Government through the Australian Research Council (ARC). Prof Venkatesh is the recipient of an ARC Australian Laureate Fellowship (FL170100006).
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Nguyen, P., Tran, T., Gupta, S., Rana, S., Dam, HC., Venkatesh, S. (2021). Variational Hyper-encoding Networks. In: Oliver, N., Pérez-Cruz, F., Kramer, S., Read, J., Lozano, J.A. (eds) Machine Learning and Knowledge Discovery in Databases. Research Track. ECML PKDD 2021. Lecture Notes in Computer Science(), vol 12976. Springer, Cham. https://doi.org/10.1007/978-3-030-86520-7_7
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