Quantum Speedup of Natural Gradient for Variational Bayes
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Abstract (arXiv)
Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively computationally expensive in high dimensions. We propose a computationally efficient regression-based method for natural gradient estimation, with convergence guarantees under standard assumptions. The method enables the use of quantum matrix inversion to further speed up VB. We demonstrate that the problem setup fulfills the conditions required for quantum matrix inversion to deliver computational efficiency. The method works with a broad range of statistical models and does not require special-purpose or simplified variational distributions.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 27 of its 89 references that are in the map. First posted on arXiv 10 Jun 2021.
Builds on
27 of 89 references.
References · 27
- 2013Auto-Encoding Variational Bayescited by 3,980
- 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
- 2015Optimizing Neural Networks with Kronecker-factored Approximate Curvaturecited by 776
- 2019Benign Overfitting in Linear Regressioncited by 544
- 2014New insights and perspectives on the natural gradient methodcited by 435
- 2020The power of quantum neural networkscited by 377
- 2017Advances in Variational Inferencecited by 236
- 2019Quantum Natural Gradientcited by 104
- 2017Fisher-Rao Metric, Geometry, and Complexity of Neural Networkscited by 99
- 2020Recurrent Quantum Neural Networkscited by 79
- 2016Quantum Recommendation Systemscited by 69
- 2018Optimal ridge penalty for real-world high-dimensional data can be zero or negative due to the implicit ridge regularizationcited by 52
15 more
- 2015Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selectioncited by 39
- 2018SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradientcited by 34
- 2014Quantum Deep Learningcited by 31
- 2019Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithmscited by 31
- 2014Quantum Inference on Bayesian Networkscited by 19
- 2018Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimensioncited by 18
- 2020Adiabatic Quantum Linear Regressioncited by 17
- 2020Quantum computing for energy systems optimization: Challenges and opportunitiescited by 15
- 2019Geometry of learning neural quantum statescited by 14
- 2015Variational Bayes with Intractable Likelihoodcited by 12
- 2018Bayesian Deep Learning on a Quantum Computercited by 12
- 2021A practical tutorial on Variational Bayescited by 10
- 2019Variational Bayes on Manifoldscited by 9
- 2017A Quantum Extension of Variational Bayes Inferencecited by 5
- 2014Quantum Algorithm for Linear Regressioncited by 3
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