Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping

• URL: http://arxiv.org/abs/2409.04140v2
• Date: Sat, 14 Sep 2024 03:57:25 GMT
• Title: Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping
• Authors: Yuan-Hao Wei, Yan-Jie Sun, Chen Zhang,
• Abstract summary: Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. This study explores the potential of VAEs for solving inverse problems, such as Independent Component Analysis (ICA) Unlike other VAE-based ICA methods, this approach discards the encoder in the VAE architecture, directly setting the latent variables as trainable parameters.
• Score: 5.212606755867746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a variety of problems, including those related to causal inference. Variational inference, a subset of Bayesian inference, is primarily used to efficiently approximate complex posterior distributions. Variational Autoencoders (VAEs), which combine variational inference with deep learning, have become widely applied across various domains. This study explores the potential of VAEs for solving inverse problems, such as Independent Component Analysis (ICA), without relying on an explicit inverse mapping process. Unlike other VAE-based ICA methods, this approach discards the encoder in the VAE architecture, directly setting the latent variables as trainable parameters. In other words, the latent variables are no longer outputs of the encoder but are instead optimized directly through the objective function to converge to appropriate values. We find that, with a suitable prior setup, the latent variables, represented by trainable parameters, can exhibit mutually independent properties as the parameters converge, all without the need for an encoding process. This approach, referred to as the Half-VAE, bypasses the inverse mapping process by eliminating the encoder. This study demonstrates the feasibility of using the Half-VAE to solve ICA without the need for an explicit inverse mapping process.

Related papers

• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• Semi-supervised Invertible DeepONets for Bayesian Inverse Problems [8.594140167290098]
  DeepONets offer a powerful, data-driven tool for solving parametric PDEs by learning operators. In this work, we employ physics-informed DeepONets in the context of high-dimensional, Bayesian inverse problems.
  arXiv  Detail & Related papers  (2022-09-06T18:55:06Z)
• InteL-VAEs: Adding Inductive Biases to Variational Auto-Encoders via Intermediary Latents [60.785317191131284]
  We introduce a simple and effective method for learning VAEs with controllable biases by using an intermediary set of latent variables. In particular, it allows us to impose desired properties like sparsity or clustering on learned representations. We show that this, in turn, allows InteL-VAEs to learn both better generative models and representations.
  arXiv  Detail & Related papers  (2021-06-25T16:34:05Z)
• Consistency Regularization for Variational Auto-Encoders [14.423556966548544]
  Variational auto-encoders (VAEs) are a powerful approach to unsupervised learning. We propose a regularization method to enforce consistency in VAEs.
  arXiv  Detail & Related papers  (2021-05-31T10:26:32Z)
• Learning Invariant Representations using Inverse Contrastive Loss [34.93395633215398]
  We introduce a class of losses for learning representations that are invariant to some extraneous variable of interest. We show that if the extraneous variable is binary, then optimizing ICL is equivalent to optimizing a regularized MMD divergence.
  arXiv  Detail & Related papers  (2021-02-16T18:29:28Z)
• Autoencoding Variational Autoencoder [56.05008520271406]
  We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. We show that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks.
  arXiv  Detail & Related papers  (2020-12-07T14:16:14Z)
• Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding [52.48298164494608]
  Variational autoencoder (VAE) estimates the posterior parameters of latent variables corresponding to each input data. This paper provides a quantitative understanding of VAE property through the differential geometric and information-theoretic interpretations of VAE.
  arXiv  Detail & Related papers  (2020-07-30T02:37:46Z)
• Pairwise Supervised Hashing with Bernoulli Variational Auto-Encoder and Self-Control Gradient Estimator [62.26981903551382]
  Variational auto-encoders (VAEs) with binary latent variables provide state-of-the-art performance in terms of precision for document retrieval. We propose a pairwise loss function with discrete latent VAE to reward within-class similarity and between-class dissimilarity for supervised hashing. This new semantic hashing framework achieves superior performance compared to the state-of-the-arts.
  arXiv  Detail & Related papers  (2020-05-21T06:11:33Z)
• On the Encoder-Decoder Incompatibility in Variational Text Modeling and Beyond [82.18770740564642]
  Variational autoencoders (VAEs) combine latent variables with amortized variational inference. We observe the encoder-decoder incompatibility that leads to poor parameterizations of the data manifold. We propose Coupled-VAE, which couples a VAE model with a deterministic autoencoder with the same structure.
  arXiv  Detail & Related papers  (2020-04-20T10:34:10Z)
• NestedVAE: Isolating Common Factors via Weak Supervision [45.366986365879505]
  We identify the connection between the task of bias reduction and that of isolating factors common between domains. To isolate the common factors we combine the theory of deep latent variable models with information bottleneck theory. Two outer VAEs with shared weights attempt to reconstruct the input and infer a latent space, whilst a nested VAE attempts to reconstruct the latent representation of one image, from the latent representation of its paired image.
  arXiv  Detail & Related papers  (2020-02-26T15:49:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.