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Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean.
Riemannian Geometry
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Stochastic analysis on manifolds , volume 38
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Probabilistic non-linear principal component analysis with gaussian process latent variable models
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Pattern Recognition and Machine Learning (Information Science and Statistics)
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Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements
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Probabilistic solutions to differential equations and their application to riemannian statistics
Hennig, P. and Hauberg, S · 2014
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Auto-Encoding Variational Bayes
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Stochastic backpropagation and variational inference in deep latent gaussian models
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Metrics for Probabilistic Geometries
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
He, K., Zhang, X., Ren, S., and Sun, J · 2015
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Adam: A method for stochastic optimization
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A locally adaptive normal distribution
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Chen, X., Kingma, D. P., Salimans, T., Duan, Y., Dhariwal, P., Schulman, J., Sutskever, I., and Abbeel, P · 2016
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Elbo surgery: yet another way to carve up the variational evidence lower bound
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Improved variational inference with inverse autoregressive flow
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Stick-breaking variational autoencoders
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Directional statistics with the spherical normal distribution
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Distribution matching in variational inference
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Spherical latent spaces for stable variational autoencoders
Xu, J. and Durrett, G · 2018
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Fast and robust shortest paths on manifolds learned from data
Arvanitidis, G., Hauberg, S., Hennig, P., and Schober, M · 2019
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Reliable training and estimation of variance networks
Detlefsen, N. S., Jørgensen, M., and Hauberg, S · 2019
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Variational diffusion autoencoders with random walk sampling
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Continuous hierarchical representations with poincaré variational auto-encoders
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