Sum-Product-Transform Networks: Exploiting Symmetries using Invertible Transformations

Tomáš Pevný, Václav Smídl, Martin Trapp, Ondřej Poláček, Tomáš Oberhuber
Proceedings of the 10th International Conference on Probabilistic Graphical Models, PMLR 138:341-352, 2020.

Abstract

In this work, we propose Sum-Product-Transform Networks (SPTN), an extension of sum-product networks that uses invertible transformations as additional internal nodes. The type and placement of transformations determine properties of the resulting SPTN with many interesting special cases. Importantly, SPTN with Gaussian leaves and affine transformations pose the same inference task tractable that can be computed efficiently in SPNs. We propose to store and optimize affine transformations in their SVD decompositions using an efficient parametrization of unitary matrices by a set of Givens rotations. Last but not least, we demonstrate that G-SPTNs pushes the state-of-the-art on the density estimation task on used datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v138-pevny20a, title = {Sum-Product-Transform Networks: Exploiting Symmetries using Invertible Transformations}, author = {Pevn\'{y}, Tom\'{a}\v{s} and Sm\'{i}dl, V\'{a}clav and Trapp, Martin and Pol\'{a}\v{c}ek, Ond\v{r}ej and Oberhuber, Tom\'{a}\v{s}}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models}, pages = {341--352}, year = {2020}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, volume = {138}, series = {Proceedings of Machine Learning Research}, month = {23--25 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v138/pevny20a/pevny20a.pdf}, url = {https://proceedings.mlr.press/v138/pevny20a.html}, abstract = {In this work, we propose Sum-Product-Transform Networks (SPTN), an extension of sum-product networks that uses invertible transformations as additional internal nodes. The type and placement of transformations determine properties of the resulting SPTN with many interesting special cases. Importantly, SPTN with Gaussian leaves and affine transformations pose the same inference task tractable that can be computed efficiently in SPNs. We propose to store and optimize affine transformations in their SVD decompositions using an efficient parametrization of unitary matrices by a set of Givens rotations. Last but not least, we demonstrate that G-SPTNs pushes the state-of-the-art on the density estimation task on used datasets. } }
Endnote
%0 Conference Paper %T Sum-Product-Transform Networks: Exploiting Symmetries using Invertible Transformations %A Tomáš Pevný %A Václav Smídl %A Martin Trapp %A Ondřej Poláček %A Tomáš Oberhuber %B Proceedings of the 10th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2020 %E Manfred Jaeger %E Thomas Dyhre Nielsen %F pmlr-v138-pevny20a %I PMLR %P 341--352 %U https://proceedings.mlr.press/v138/pevny20a.html %V 138 %X In this work, we propose Sum-Product-Transform Networks (SPTN), an extension of sum-product networks that uses invertible transformations as additional internal nodes. The type and placement of transformations determine properties of the resulting SPTN with many interesting special cases. Importantly, SPTN with Gaussian leaves and affine transformations pose the same inference task tractable that can be computed efficiently in SPNs. We propose to store and optimize affine transformations in their SVD decompositions using an efficient parametrization of unitary matrices by a set of Givens rotations. Last but not least, we demonstrate that G-SPTNs pushes the state-of-the-art on the density estimation task on used datasets.
APA
Pevný, T., Smídl, V., Trapp, M., Poláček, O. & Oberhuber, T.. (2020). Sum-Product-Transform Networks: Exploiting Symmetries using Invertible Transformations. Proceedings of the 10th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 138:341-352 Available from https://proceedings.mlr.press/v138/pevny20a.html.

Related Material