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There is a growing interest in probabilistic models defined in hyper-spherical spaces, be it to accommodate observed data or latent structure.
Computer Generation of Distributions on the m m -Sphere
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Gradient-based learning applied to document recognition
LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P · 1998
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An introduction to variational methods for graphical models
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Bessel function of the first kind
Weisstein, E. W · 2002
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Clustering on the unit hypersphere using von mises-fisher distributions
Banerjee, A., Dhillon, I. S., Ghosh, J., and Sra, S · 2005
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Mixture of watson distributions: a generative model for hyperspherical embeddings
Bijral, A. S., Breitenbach, M., and Grudic, G · 2007
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Directional statistics , volume 494
Mardia, K. V. and Jupp, P. E · 2009
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Spherical topic models
Reisinger, J., Waters, A., Silverthorn, B., and Mooney, R. J · 2010
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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Auto-encoding variational bayes
Kingma, D. P. and Welling, M · 2014
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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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Variational inference with normalizing flows
Rezende, D. and Mohamed, S · 2015
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Sphereface: Deep hypersphere embedding for face recognition
Liu, W., Wen, Y., Yu, Z., Li, M., Raj, B., and Song, L · 2017
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Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms
Naesseth, C., Ruiz, F., Linderman, S., and Blei, D · 2017
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Neural ordinary differential equations
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K · 2018
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Hyperspherical variational auto-encoders
Davidson, T. R., Falorsi, L., De Cao, N., Kipf, T., and Tomczak, J. M · 2018
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Explorations in homeomorphic variational auto-encoding
Falorsi, L., de Haan, P., Davidson, T. R., De Cao, N., Weiler, M., Forré, P., and Cohen, T. S · 2018
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Block neural autoregressive flow
De Cao, N., Titov, I., and Aziz, W · 2019
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A rad approach to deep mixture models
Dinh, L., Sohl-Dickstein, J., Pascanu, R., and Larochelle, H · 2019
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Reparameterizing distributions on lie groups
Falorsi, L., de Haan, P., Davidson, T. R., and Forré, P · 2019
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Von mises-fisher loss for training sequence to sequence models with continuous outputs
Kumar, S. and Tsvetkov, Y · 2019
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Continuous hierarchical representations with poincaré variational auto-encoders
Mathieu, E., Le Lan, C., Maddison, C. J., Tomioka, R., and Teh, Y. W · 2019
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A wrapped normal distribution on hyperbolic space for gradient-based learning
Nagano, Y., Yamaguchi, S., Fujita, Y., and Koyama, M · 2019
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Implicit reparameterization gradients
Figurnov, M., Mohamed, S., and Mnih, A · 2018
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Neural autoregressive flows
Huang, C.-W., Krueger, D., Lacoste, A., and Courville, A · 2018
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Directional statistics in machine learning: a brief review
Sra, S · 2018
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Relaxing bijectivity constraints with continuously indexed normalising flows
Cornish, R., Caterini, A. L., Deligiannidis, G., and Doucet, A · 2019
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Increasing expressivity of a hyperspherical vae
Davidson, T. R., Tomczak, J. M., and Gavves, E · 2019
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Flows for simultaneous manifold learning and density estimation
Brehmer, J. and Cranmer, K · 2020
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Neural ordinary differential equations on manifolds
Falorsi, L. and Forré, P · 2020
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Normalizing flows on tori and spheres
Rezende, D. J., Papamakarios, G., Racanière, S., Albergo, M. S., Kanwar, G., Shanahan, P. E., and Cranmer, K · 2020
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Wu, H., Köhler, J., and Noé, F · 2020
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