Variational Mixture of HyperGenerators for Learning Distributions over Functions

Batuhan Koyuncu, Pablo Sanchez Martin, Ignacio Peis, Pablo M. Olmos, Isabel Valera
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:17660-17683, 2023.

Abstract

Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VaMoH. VaMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VaMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VaMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VaMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-koyuncu23a, title = {Variational Mixture of {H}yper{G}enerators for Learning Distributions over Functions}, author = {Koyuncu, Batuhan and Sanchez Martin, Pablo and Peis, Ignacio and Olmos, Pablo M. and Valera, Isabel}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {17660--17683}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/koyuncu23a/koyuncu23a.pdf}, url = {https://proceedings.mlr.press/v202/koyuncu23a.html}, abstract = {Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VaMoH. VaMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VaMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VaMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VaMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.} }
Endnote
%0 Conference Paper %T Variational Mixture of HyperGenerators for Learning Distributions over Functions %A Batuhan Koyuncu %A Pablo Sanchez Martin %A Ignacio Peis %A Pablo M. Olmos %A Isabel Valera %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-koyuncu23a %I PMLR %P 17660--17683 %U https://proceedings.mlr.press/v202/koyuncu23a.html %V 202 %X Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VaMoH. VaMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VaMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VaMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VaMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.
APA
Koyuncu, B., Sanchez Martin, P., Peis, I., Olmos, P.M. & Valera, I.. (2023). Variational Mixture of HyperGenerators for Learning Distributions over Functions. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:17660-17683 Available from https://proceedings.mlr.press/v202/koyuncu23a.html.

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