mlsanityData to 7 Oct 2026

Manifold Gaussian Variational Bayes on the Precision Matrix

arXiv 2210.14598 ↗First posted 26 Oct 2022stat.ML cs.LGcited by 1

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Abstract (arXiv)

We propose an optimization algorithm for Variational Inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Our Manifold Gaussian Variational Bayes on the Precision matrix (MGVBP) solution provides simple update rules, is straightforward to implement, and the use of the precision matrix parametrization has a significant computational advantage. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models. Over five datasets, we empirically validate our feasible approach on different statistical and econometric models, discussing its performance with respect to baseline methods.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 23 of its 57 references that are in the map. First posted on arXiv 26 Oct 2022.

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23 of 57 references.

References · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Variational Inference: A Review for Statisticianscited by 1,466
  3. 2013Black Box Variational Inferencecited by 317
  4. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 281
  5. 2019Practical Deep Learning with Bayesian Principlescited by 158
  6. 2018Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adamcited by 131
  7. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 112
  8. 2017Noisy Natural Gradient as Variational Inferencecited by 94
  9. 2017Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Modelscited by 65
  10. 2017Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methodscited by 49
  11. 2017Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysiscited by 46
  12. 2018Variance reduction properties of the reparameterization trickcited by 41
11 more
  1. 2018Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Modelscited by 37
  2. 2021On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometrycited by 32
  3. 2020Handling the Positive-Definite Constraint in the Bayesian Learning Rulecited by 31
  4. 2015Automatic Variational Inference in Stancited by 24
  5. 2021An Introduction to Variational Inferencecited by 11
  6. 2021A practical tutorial on Variational Bayescited by 10
  7. 2019Variational Bayes on Manifoldscited by 9
  8. 2021Structured second-order methods via natural gradient descentcited by 7
  9. 2022Bayesian Bilinear Neural Network for Predicting the Mid-price Dynamics in Limit-Order Book Marketscited by 5
  10. 2020Multivariate Gaussian Variational Inference by Natural Gradient Descentcited by 3
  11. 2022Quasi Black-Box Variational Inference with Natural Gradients for Bayesian Learningcited by 3

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