Variational Autoencoders and Nonlinear ICA: A Unifying Framework

Ilyes Khemakhem, Diederik Kingma, Ricardo Monti, Aapo Hyvarinen
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2207-2217, 2020.

Abstract

The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model’s marginal distribution over observed variables fits the data. Often, we’re interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to very simple transformations, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-khemakhem20a, title = {Variational Autoencoders and Nonlinear ICA: A Unifying Framework}, author = {Khemakhem, Ilyes and Kingma, Diederik and Monti, Ricardo and Hyvarinen, Aapo}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2207--2217}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/khemakhem20a/khemakhem20a.pdf}, url = { http://proceedings.mlr.press/v108/khemakhem20a.html }, abstract = {The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model’s marginal distribution over observed variables fits the data. Often, we’re interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to very simple transformations, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case. } }
Endnote
%0 Conference Paper %T Variational Autoencoders and Nonlinear ICA: A Unifying Framework %A Ilyes Khemakhem %A Diederik Kingma %A Ricardo Monti %A Aapo Hyvarinen %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-khemakhem20a %I PMLR %P 2207--2217 %U http://proceedings.mlr.press/v108/khemakhem20a.html %V 108 %X The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model’s marginal distribution over observed variables fits the data. Often, we’re interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to very simple transformations, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case.
APA
Khemakhem, I., Kingma, D., Monti, R. & Hyvarinen, A.. (2020). Variational Autoencoders and Nonlinear ICA: A Unifying Framework. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2207-2217 Available from http://proceedings.mlr.press/v108/khemakhem20a.html .

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