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Many methods that build powerful variational distributions based on unadjusted Langevin transitions exist.
Continuous markov processes and stochastic equations
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Beta-binomial anova for proportions
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Time reversal of diffusions
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Analysis of hidden units in a layered network trained to classify sonar targets
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Annealed importance sampling
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An auxiliary variational method
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Sequential monte carlo samplers
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Design of quasisymplectic propagators for langevin dynamics
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Long-run accuracy of variational integrators in the stochastic context
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Mcmc using hamiltonian dynamics
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Auto-encoding variational bayes
Kingma, D. P. and Welling, M · 2013
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Rational construction of stochastic numerical methods for molecular sampling
Leimkuhler, B. and Matthews, C · 2013
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Stochastic backpropagation and approximate inference in deep generative models
Rezende, D. J., Mohamed, S., and Wierstra, D · 2014
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Score-based generative modeling with critically-damped langevin diffusion
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