Reliable Categorical Variational Inference with Mixture of Discrete Normalizing Flows

• URL: http://arxiv.org/abs/2006.15568v2
• Date: Mon, 8 Feb 2021 17:56:38 GMT
• Title: Reliable Categorical Variational Inference with Mixture of Discrete Normalizing Flows
• Authors: Tomasz Ku\'smierczyk, Arto Klami
• Abstract summary: Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one.
• Score: 10.406659081400354
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Handling discrete latent variables is then challenging because the sampling process is not differentiable. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one, causing problems especially with models having strong meaningful priors. We provide an alternative differentiable reparameterization for categorical distribution by composing it as a mixture of discrete normalizing flows. It defines a proper discrete distribution, allows directly optimizing the evidence lower bound, and is less sensitive to the hyperparameter controlling relaxation.

Related papers

• SoftCVI: Contrastive variational inference with self-generated soft labels [2.5398014196797614]
  Variational inference and Markov chain Monte Carlo methods are the predominant tools for this task. We introduce Soft Contrastive Variational Inference (SoftCVI), which allows a family of variational objectives to be derived through a contrastive estimation framework. We find that SoftCVI can be used to form objectives which are stable to train and mass-covering, frequently outperforming inference with other variational approaches.
  arXiv  Detail & Related papers  (2024-07-22T14:54:12Z)
• Sobolev Space Regularised Pre Density Models [51.558848491038916]
  We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive validation model clear and consistent.
  arXiv  Detail & Related papers  (2023-07-25T18:47:53Z)
• Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations [0.0]
  Variational mixtures with full-covariance structures suffer from a quadratic growth due to variational parameters with the number of parameters. We propose a method for constructing an initial Gaussian model approximation that can be used to warm-start variational inference.
  arXiv  Detail & Related papers  (2023-07-12T19:30:04Z)
• Differentiating Metropolis-Hastings to Optimize Intractable Densities [51.16801956665228]
  We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers. We apply gradient-based optimization to objectives expressed as expectations over intractable target densities.
  arXiv  Detail & Related papers  (2023-06-13T17:56:02Z)
• Variational Classification [51.2541371924591]
  We derive a variational objective to train the model, analogous to the evidence lower bound (ELBO) used to train variational auto-encoders. Treating inputs to the softmax layer as samples of a latent variable, our abstracted perspective reveals a potential inconsistency. We induce a chosen latent distribution, instead of the implicit assumption found in a standard softmax layer.
  arXiv  Detail & Related papers  (2023-05-17T17:47:19Z)
• Faithful Heteroscedastic Regression with Neural Networks [2.2835610890984164]
  Parametric methods that employ neural networks for parameter maps can capture complex relationships in the data. We make two simple modifications to optimization to produce a heteroscedastic model with mean estimates that are provably as accurate as those from its homoscedastic counterpart. Our approach provably retains the accuracy of an equally flexible mean-only model while also offering best-in-class variance calibration.
  arXiv  Detail & Related papers  (2022-12-18T22:34:42Z)
• ReCAB-VAE: Gumbel-Softmax Variational Inference Based on Analytic Divergence [17.665255113864795]
  We present a novel divergence-like metric which corresponds to the upper bound of the Kullback-Leibler divergence (KLD) of a relaxed categorical distribution. We also propose a relaxed categorical analytic bound variational autoencoder (ReCAB-VAE) that successfully models both continuous and relaxed latent representations.
  arXiv  Detail & Related papers  (2022-05-09T08:11:46Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence [77.06203118175335]
  Variational Inference (VI) is a popular alternative to exact sampling in Bayesian inference. Importance sampling (IS) is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. We propose a novel combination of optimization and sampling techniques for approximate Bayesian inference.
  arXiv  Detail & Related papers  (2021-06-30T11:00:24Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Generalized Gumbel-Softmax Gradient Estimator for Various Discrete Random Variables [16.643346012854156]
  Esting the gradients of nodes is one of the crucial research questions in the deep generative modeling community. This paper proposes a general version of the Gumbel-Softmax estimator with continuous relaxation.
  arXiv  Detail & Related papers  (2020-03-04T01:13:15Z)

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.