FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders

• URL: http://arxiv.org/abs/2209.12806v1
• Date: Mon, 26 Sep 2022 15:59:54 GMT
• Title: FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders
• Authors: Lisa Bonheme and Marek Grzes
• Abstract summary: In this paper, we explore the intrinsic dimension estimation (IDE) of the data and latent representations learned by VAEs. We show that the discrepancies between theIDE of the mean and sampled representations of a VAE after only a few steps of training reveal the presence of passive variables in the latent space. We propose FONDUE: an algorithm which quickly finds the number of latent dimensions after which the mean and sampled representations start to diverge.
• Score: 2.969705152497174
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: When training a variational autoencoder (VAE) on a given dataset, determining the optimal number of latent variables is mostly done by grid search: a costly process in terms of computational time and carbon footprint. In this paper, we explore the intrinsic dimension estimation (IDE) of the data and latent representations learned by VAEs. We show that the discrepancies between the IDE of the mean and sampled representations of a VAE after only a few steps of training reveal the presence of passive variables in the latent space, which, in well-behaved VAEs, indicates a superfluous number of dimensions. Using this property, we propose FONDUE: an algorithm which quickly finds the number of latent dimensions after which the mean and sampled representations start to diverge (i.e., when passive variables are introduced), providing a principled method for selecting the number of latent dimensions for VAEs and autoencoders.

Related papers

• Deep Variational Multivariate Information Bottleneck -- A Framework for Variational Losses [0.0]
  We introduce a framework to unify existing variational methods and design new ones. We show that algorithms that are better matched to the structure of the data produce better latent spaces.
  arXiv  Detail & Related papers  (2023-10-05T04:59:58Z)
• GFlowNet-EM for learning compositional latent variable models [115.96660869630227]
  A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational algorithms.
  arXiv  Detail & Related papers  (2023-02-13T18:24:21Z)
• Vector Quantized Wasserstein Auto-Encoder [57.29764749855623]
  We study learning deep discrete representations from the generative viewpoint. We endow discrete distributions over sequences of codewords and learn a deterministic decoder that transports the distribution over the sequences of codewords to the data distribution. We develop further theories to connect it with the clustering viewpoint of WS distance, allowing us to have a better and more controllable clustering solution.
  arXiv  Detail & Related papers  (2023-02-12T13:51:36Z)
• f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformation [56.04628143914542]
  Diffusion models (DMs) have recently emerged as SoTA tools for generative modeling in various domains. We propose f-DM, a generalized family of DMs which allows progressive signal transformation. We apply f-DM in image generation tasks with a range of functions, including down-sampling, blurring, and learned transformations.
  arXiv  Detail & Related papers  (2022-10-10T18:49:25Z)
• RENs: Relevance Encoding Networks [0.0]
  This paper proposes relevance encoding networks (RENs): a novel probabilistic VAE-based framework that uses the automatic relevance determination (ARD) prior in the latent space to learn the data-specific bottleneck dimensionality. We show that the proposed model learns the relevant latent bottleneck dimensionality without compromising the representation and generation quality of the samples.
  arXiv  Detail & Related papers  (2022-05-25T21:53:48Z)
• Sparse Infinite Random Feature Latent Variable Modeling [6.063419970703021]
  A posteriori, the number of instantiated dimensions in the latent space is guaranteed to be finite. We show that we can obtain superior test set performance compared to previous latent variable models.
  arXiv  Detail & Related papers  (2022-05-20T00:29:28Z)
• Representation Learning for Sequence Data with Deep Autoencoding Predictive Components [96.42805872177067]
  We propose a self-supervised representation learning method for sequence data, based on the intuition that useful representations of sequence data should exhibit a simple structure in the latent space. We encourage this latent structure by maximizing an estimate of predictive information of latent feature sequences, which is the mutual information between past and future windows at each time step. We demonstrate that our method recovers the latent space of noisy dynamical systems, extracts predictive features for forecasting tasks, and improves automatic speech recognition when used to pretrain the encoder on large amounts of unlabeled data.
  arXiv  Detail & Related papers  (2020-10-07T03:34:01Z)
• 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)
• Longitudinal Variational Autoencoder [1.4680035572775534]
  A common approach to analyse high-dimensional data that contains missing values is to learn a low-dimensional representation using variational autoencoders (VAEs) Standard VAEs assume that the learnt representations are i.i.d., and fail to capture the correlations between the data samples. We propose the Longitudinal VAE (L-VAE), that uses a multi-output additive Gaussian process (GP) prior to extend the VAE's capability to learn structured low-dimensional representations. Our approach can simultaneously accommodate both time-varying shared and random effects, produce structured low-dimensional representations
  arXiv  Detail & Related papers  (2020-06-17T10:30:14Z)
• Improve Variational Autoencoder for Text Generationwith Discrete Latent Bottleneck [52.08901549360262]
  Variational autoencoders (VAEs) are essential tools in end-to-end representation learning. VAEs tend to ignore latent variables with a strong auto-regressive decoder. We propose a principled approach to enforce an implicit latent feature matching in a more compact latent space.
  arXiv  Detail & Related papers  (2020-04-22T14:41:37Z)
• Deterministic Decoding for Discrete Data in Variational Autoencoders [5.254093731341154]
  We study a VAE model with a deterministic decoder (DD-VAE) for sequential data that selects the highest-scoring tokens instead of sampling. We demonstrate the performance of DD-VAE on multiple datasets, including molecular generation and optimization problems.
  arXiv  Detail & Related papers  (2020-03-04T16:36:52Z)

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.