On the Identifiability of Quantized Factors

Vitória Barin-Pacela, Kartik Ahuja, Simon Lacoste-Julien, Pascal Vincent
Proceedings of the Third Conference on Causal Learning and Reasoning, PMLR 236:384-422, 2024.

Abstract

Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be impossible in the unsupervised i.i.d. setting under a general nonlinear map from factors to observations. In this work, however, we demonstrate that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism. We only assume that the latent factors have independent discontinuities in their density, without requiring the factors to be statistically independent. We introduce this novel form of identifiability, termed quantized factor identifiability, and provide a comprehensive proof of the recovery of the quantized factors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v236-barin-pacela24a, title = {On the Identifiability of Quantized Factors}, author = {Barin-Pacela, Vit\'oria and Ahuja, Kartik and Lacoste-Julien, Simon and Vincent, Pascal}, booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning}, pages = {384--422}, year = {2024}, editor = {Locatello, Francesco and Didelez, Vanessa}, volume = {236}, series = {Proceedings of Machine Learning Research}, month = {01--03 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v236/barin-pacela24a/barin-pacela24a.pdf}, url = {https://proceedings.mlr.press/v236/barin-pacela24a.html}, abstract = {Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be impossible in the unsupervised i.i.d. setting under a general nonlinear map from factors to observations. In this work, however, we demonstrate that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism. We only assume that the latent factors have independent discontinuities in their density, without requiring the factors to be statistically independent. We introduce this novel form of identifiability, termed quantized factor identifiability, and provide a comprehensive proof of the recovery of the quantized factors.} }
Endnote
%0 Conference Paper %T On the Identifiability of Quantized Factors %A Vitória Barin-Pacela %A Kartik Ahuja %A Simon Lacoste-Julien %A Pascal Vincent %B Proceedings of the Third Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2024 %E Francesco Locatello %E Vanessa Didelez %F pmlr-v236-barin-pacela24a %I PMLR %P 384--422 %U https://proceedings.mlr.press/v236/barin-pacela24a.html %V 236 %X Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be impossible in the unsupervised i.i.d. setting under a general nonlinear map from factors to observations. In this work, however, we demonstrate that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism. We only assume that the latent factors have independent discontinuities in their density, without requiring the factors to be statistically independent. We introduce this novel form of identifiability, termed quantized factor identifiability, and provide a comprehensive proof of the recovery of the quantized factors.
APA
Barin-Pacela, V., Ahuja, K., Lacoste-Julien, S. & Vincent, P.. (2024). On the Identifiability of Quantized Factors. Proceedings of the Third Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 236:384-422 Available from https://proceedings.mlr.press/v236/barin-pacela24a.html.

Related Material