Approximation Based Variance Reduction for Reparameterization Gradients

• URL: http://arxiv.org/abs/2007.14634v2
• Date: Fri, 23 Oct 2020 08:36:43 GMT
• Title: Approximation Based Variance Reduction for Reparameterization Gradients
• Authors: Tomas Geffner, Justin Domke
• Abstract summary: Flexible variational distributions improve variational inference but are harder to optimize. We present a control variate that is applicable for any reizable distribution with known mean and covariance matrix. It leads to large improvements in gradient variance and optimization convergence for inference with non-factorized variational distributions.
• Score: 38.73307745906571
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g. Gaussians with any covariance structure. The control variate is based on a quadratic approximation of the model, and its parameters are set using a double-descent scheme by minimizing the gradient estimator's variance. We empirically show that this control variate leads to large improvements in gradient variance and optimization convergence for inference with non-factorized variational distributions.

Related papers

• Variational Bayesian surrogate modelling with application to robust design optimisation [0.9626666671366836]
  Surrogate models provide a quick-to-evaluate approximation to complex computational models. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and dimensionality reduction. We demonstrate intrinsic and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.
  arXiv  Detail & Related papers  (2024-04-23T09:22:35Z)
• 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)
• Manifold Gaussian Variational Bayes on the Precision Matrix [70.44024861252554]
  We propose an optimization algorithm for Variational Inference (VI) in complex models. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models.
  arXiv  Detail & Related papers  (2022-10-26T10:12:31Z)
• Amortized backward variational inference in nonlinear state-space models [0.0]
  We consider the problem of state estimation in general state-space models using variational inference. We establish for the first time that, under mixing assumptions, the variational approximation of expectations of additive state functionals induces an error which grows at most linearly in the number of observations.
  arXiv  Detail & Related papers  (2022-06-01T08:35:54Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Robust, Accurate Stochastic Optimization for Variational Inference [68.83746081733464]
  We show that common optimization methods lead to poor variational approximations if the problem is moderately large. Motivated by these findings, we develop a more robust and accurate optimization framework by viewing the underlying algorithm as producing a Markov chain.
  arXiv  Detail & Related papers  (2020-09-01T19:12:11Z)
• Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization [62.47170258504037]
  This paper presents a framework that encompasses and generalizes existing approaches that use controls, kernels and neural networks. Novel theoretical results are presented to provide insight into the variance reduction that can be achieved, and an empirical assessment, including applications to Bayesian inference, is provided in support.
  arXiv  Detail & Related papers  (2020-06-12T22:03:25Z)
• Variational Variance: Simple, Reliable, Calibrated Heteroscedastic Noise Variance Parameterization [3.553493344868413]
  We propose critiques to test predictive mean and variance calibration and the predictive distribution's ability to generate sensible data. We find that our solution, to treat heteroscedastic variance variationally, sufficiently regularizes variance to pass these PPCs.
  arXiv  Detail & Related papers  (2020-06-08T19:58:35Z)
• The k-tied Normal Distribution: A Compact Parameterization of Gaussian Mean Field Posteriors in Bayesian Neural Networks [46.677567663908185]
  Variational Bayesian Inference is a popular methodology for approxing posteriorimating over Bayesian neural network weights. Recent work has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. We find that by decomposing these variational parameters into a low-rank factorization, we can make our variational approximation more compact without decreasing the models' performance.
  arXiv  Detail & Related papers  (2020-02-07T07:33:15Z)

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.