ARD-VAE: A Statistical Formulation to Find the Relevant Latent Dimensions of Variational Autoencoders

The variational autoencoder (VAE) [19], [41] is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a...

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Published in:Proceedings / IEEE Workshop on Applications of Computer Vision pp. 889 - 898
Main Authors: Saha, Surojit, Joshi, Sarang, Whitaker, Ross
Format: Conference Proceeding
Language:English
Published: IEEE 26.02.2025
Subjects:
Autoencoders
automatic relevancy detection
Benchmark testing
Computer architecture
Computer vision
Data models
hierarchical prior
Linear programming
Measurement
Neural networks
Robustness
Stability analysis
variational autoencoders
ISSN:2642-9381
Online Access:Get full text
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Abstract The variational autoencoder (VAE) [19], [41] is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a crucial design choice, and it has strong ramifications for the model's performance, such as finding the hidden explanatory factors of a dataset using the representations learned by the VAE. However, the size of the latent dimension of the VAE is often treated as a hyperparameter estimated empirically through trial and error. To this end, we propose a statistical formulation to discover the relevant latent factors required for modeling a dataset. In this work, we use a hierarchical prior in the latent space that estimates the variance of the latent axes using the encoded data, which identifies the relevant latent dimensions. For this, we replace the fixed prior in the VAE objective function with a hierarchical prior, keeping the remainder of the formulation unchanged. We call the proposed method the automatic relevancy detection in the variational autoencoder (ARD-VAE) 1 1 https://github.com/Surojit-Utah/ARD-VAE. We demonstrate the efficacy of the ARD-VAE on multiple benchmark datasets in finding the relevant latent dimensions and their effect on different evaluation metrics, such as FID score and disentanglement analysis.
AbstractList The variational autoencoder (VAE) [19], [41] is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a crucial design choice, and it has strong ramifications for the model's performance, such as finding the hidden explanatory factors of a dataset using the representations learned by the VAE. However, the size of the latent dimension of the VAE is often treated as a hyperparameter estimated empirically through trial and error. To this end, we propose a statistical formulation to discover the relevant latent factors required for modeling a dataset. In this work, we use a hierarchical prior in the latent space that estimates the variance of the latent axes using the encoded data, which identifies the relevant latent dimensions. For this, we replace the fixed prior in the VAE objective function with a hierarchical prior, keeping the remainder of the formulation unchanged. We call the proposed method the automatic relevancy detection in the variational autoencoder (ARD-VAE) 1 1 https://github.com/Surojit-Utah/ARD-VAE. We demonstrate the efficacy of the ARD-VAE on multiple benchmark datasets in finding the relevant latent dimensions and their effect on different evaluation metrics, such as FID score and disentanglement analysis.
Author Saha, Surojit
Whitaker, Ross
Joshi, Sarang
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  organization: The University of Utah,USA
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Snippet The variational autoencoder (VAE) [19], [41] is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data...
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SubjectTerms Autoencoders
automatic relevancy detection
Benchmark testing
Computer architecture
Computer vision
Data models
hierarchical prior
Linear programming
Measurement
Neural networks
Robustness
Stability analysis
variational autoencoders
Title ARD-VAE: A Statistical Formulation to Find the Relevant Latent Dimensions of Variational Autoencoders
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