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Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications.
Accelerating langevin sampling with birth-death
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Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
Kiefer, J. and Wolfowitz, J. (1956) · 1956
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Mixtures of exponential distributions
Jewell, N. P. (1982) · 1982
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The geometry of mixture likelihoods: a general theory
Lindsay, B. G. (1983) · 1983
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Uniqueness of estimation and identifiability in mixture models
Lindsay, B. G. and Roeder, K. (1993) · 1993
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The variational formulation of the fokker–planck equation
Jordan, R., Kinderlehrer, D., and Otto, F. (1998) · 1998
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The geometry of dissipative evolution equations: the porous medium equation
Otto, F. (2001) · 2001
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Gradient flows: in metric spaces and in the space of probability measures
Ambrosio, L., Gigli, N., and Savaré, G. (2008) · 2008
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The support reduction algorithm for computing non-parametric function estimates in mixture models
Groeneboom, P., Jongbloed, G., and Wellner, J. A. (2008) · 2008
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Self-regularizing property of nonparametric maximum likelihood estimator in mixture models
Polyanskiy, Y. and Wu, Y. (2020) · 2008
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General maximum likelihood empirical bayes estimation of normal means
Jiang, W. and Zhang, C.-H. (2009) · 2009
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Optimal transport: old and new
Villani, C. (2009) · 2009
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Generalized maximum likelihood estimation of normal mixture densities
Zhang, C.-H. (2009) · 2009
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Convex optimization, shape constraints, compound decisions, and empirical bayes rules
Koenker, R. and Mizera, I. (2014) · 2014
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Convex optimization: algorithms and complexity
Bubeck, S. (2015) · 2015
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Uniqueness of the fisher–rao metric on the space of smooth densities
Bauer, M., Bruveris, M., and Michor, P. W. (2016) · 2016
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High-dimensional classification via nonparametric empirical bayes and maximum likelihood inference
Dicker, L. H. and Zhao, S. D. (2016) · 2016
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Local maxima in the likelihood of gaussian mixture models: Structural results and algorithmic consequences
A mean field view of the landscape of two-layer neural networks
Mei, S., Montanari, A., and Nguyen, P.-M. (2018) · 2018
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A convergence theory for deep learning via over-parameterization
Allen-Zhu, Z., Li, Y., and Song, Z. (2019) · 2019
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High-dimensional statistics: A non-asymptotic viewpoint
Wainwright, M. J. (2019) · 2019
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Gradient descent algorithms for bures-wasserstein barycenters
Chewi, S., Maunu, T., Rigollet, P., and Stromme, A. J. (2020) · 2020
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On the nonparametric maximum likelihood estimator for gaussian location mixture densities with application to gaussian denoising
Saha, S. and Guntuboyina, A. (2020) · 2020
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The wasserstein proximal gradient algorithm
Salim, A., Korba, A., and Luise, G. (2020) · 2020
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Jin, C., Zhang, Y., Balakrishnan, S., Wainwright, M. J., and Jordan, M. I. (2016) · 2016
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A new optimal transport distance on the space of finite radon measures
Kondratyev, S., Monsaingeon, L., and Vorotnikov, D. (2016) · 2016
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A jko splitting scheme for kantorovich–fisher–rao gradient flows
Gallouët, T. O. and Monsaingeon, L. (2017) · 2017
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{ \{ Euclidean, metric, and Wasserstein } \} gradient flows: an overview
Santambrogio, F. (2017) · 2017
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On the global convergence of gradient descent for over-parameterized models using optimal transport
Chizat, L. and Bach, F. (2018) · 2018
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An interpolating distance between optimal transport and fisher–rao metrics
Chizat, L., Peyré, G., Schmitzer, B., and Vialard, F.-X. (2018) · 2018
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Optimal entropy-transport problems and a new hellinger–kantorovich distance between positive measures
Liero, M., Mielke, A., and Savaré, G. (2018) · 2018
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Averaging on the bures-wasserstein manifold: dimension-free convergence of gradient descent
Altschuler, J., Chewi, S., Gerber, P. R., and Stromme, A. (2021) · 2021
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Log-concave sampling
Chewi, S. (2022) · 2022
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Variational inference via wasserstein gradient flows
Lambert, M., Chewi, S., Bach, F., Bonnabel, S., and Rigollet, P. (2022) · 2022
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Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
Lu, Y., Slepčev, D., and Wang, L. (2022) · 2022
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Sinkformers: Transformers with doubly stochastic attention
Sander, M. E., Ablin, P., Blondel, M., and Peyré, G. (2022) · 2022
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Zhang, Y., Cui, Y., Sen, B., and Toh, K.-C. (2022) · 2022
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