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A Variational Perspective on Accelerated Methods in Optimization [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2016 Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is the natural ...
Jordan, Michael I. +2 more
core +2 more sources
Improved variational methods in statistical data assimilation [PDF]
Nonlinear Processes in Geophysics, 2015 Data assimilation transfers information from an observed system to a physically based model system with state variables x(t). The observations are typically noisy, the model has errors, and the initial state x(t0) is uncertain: the data assimilation ...
J. Ye +4 more
doaj +2 more sources
Variational methods for simulation-based inference [PDF]
International Conference on Learning Representations, 2022 We present Sequential Neural Variational Inference (SNVI), an approach to perform Bayesian inference in models with intractable likelihoods. SNVI combines likelihood-estimation (or likelihood-ratio-estimation) with variational inference to achieve a ...
Manuel Glöckler +2 more
semanticscholar +1 more source
Performance comparison of optimization methods on variational quantum algorithms [PDF]
Physical Review A, 2021 Variational quantum algorithms (VQAs) offer a promising path toward using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing a parametrized
Xavier Bonet-Monroig +7 more
semanticscholar +1 more source
Network element methods for linear elasticity
Comptes Rendus. Mécanique, 2023 We explain how to derive a network element for the linear elasticity problem. After presenting sufficient conditions on the network for the validity of a discrete Korn inequality, we also propose several variations of the presented method and in ...
Coatléven, Julien
doaj +1 more source
On three-step iterative schemes associated with general quasi-variational inclusions
Alexandria Engineering Journal, 2022 In this paper, we investigate new classes of general quasi-variational inclusions. In this regard, we prove that general quasi-variational inclusions and fixed point problems are equivalent.
Muhammad Aslam Noor +3 more
doaj +1 more source
Geometry of variational methods: dynamics of closed quantum systems [PDF]
, 2020 We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we ...
L. Hackl +5 more
semanticscholar +1 more source
The variational method of moments
Journal of the Royal Statistical Society Series B: Statistical Methodology, 2023 Abstract The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation
Bennett, Andrew, Kallus, Nathan
openaire +2 more sources
Variational Inference: A Review for Statisticians [PDF]
arXiv.org, 2016 One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the ...
D. Blei, A. Kucukelbir, Jon D. McAuliffe
semanticscholar +1 more source
Variational Methods in Optical Quantum Machine Learning
IEEE Access, 2023 The computing world is rapidly evolving and advancing, with new ground-breaking technologies emerging. Quantum Computing and Quantum Machine Learning have opened up new possibilities, providing unprecedented computational power and problem-solving ...
Marco Simonetti +2 more
doaj +1 more source