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We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function.
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Risk bounds for mode clustering
M. Azizyan, Y.-C. Chen, A. Singh, and L. Wasserman · 2015
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A population background for nonparametric density-based clustering
J. E. Chacón et al · 2015
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Asymptotic theory for density ridges
Y.-C. Chen, C. R. Genovese, and L. Wasserman · 2015
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Regularized m-estimators with nonconvexity: Statistical and algorithmic theory for local optima
P.-L. Loh and M. J. Wainwright · 2015
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On the estimation of the gradient lines of a density and the consistency of the mean-shift algorithm
E. Arias-Castro, D. Mason, and B. Pelletier · 2016
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A comprehensive approach to mode clustering
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E. Gine and A. Guillou · 2002
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Stochastic approximation and recursive algorithms and applications , volume 35
H. Kushner and G. G. Yin · 2003
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Convex optimization
S. Boyd and L. Vandenberghe · 2004
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Bump hunting with non-gaussian kernels
P. Hall, M. C. Minnotte, and C. Zhang · 2004
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Finite mixture models
G. McLachlan and D. Peel · 2004
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Uniform in bandwidth consistency for kernel-type function estimators
U. Einmahl and D. M. Mason · 2005
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Y.-C. Chen, C. R. Genovese, L. Wasserman, et al · 2016
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Non-parametric inference for density modes
C. R. Genovese, M. Perone-Pacifico, I. Verdinelli, and L. Wasserman · 2016
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Local maxima in the likelihood of gaussian mixture models: Structural results and algorithmic consequences
C. Jin, Y. Zhang, S. Balakrishnan, M. J. Wainwright, and M. I. Jordan · 2016
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Gradient descent only converges to minimizers
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht · 2016
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Consistency and fluctuations for stochastic gradient langevin dynamics
Y. W. Teh, A. H. Thiery, and S. J. Vollmer · 2016
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Statistical guarantees for the em algorithm: From population to sample-based analysis
S. Balakrishnan, M. J. Wainwright, and B. Yu · 2017
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Variational inference: A review for statisticians
D. M. Blei, A. Kucukelbir, and J. D. McAuliffe · 2017
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Robust topological inference: Distance to a measure and kernel distance
F. Chazal, B. Fasy, F. Lecci, B. Michel, A. Rinaldo, A. Rinaldo, and L. Wasserman · 2017
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Statistical inference using the morse-smale complex
Y.-C. Chen, C. R. Genovese, L. Wasserman, et al · 2017
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Statistical consistency and asymptotic normality for high-dimensional robust m m -estimators
P.-L. Loh · 2017
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Gradient descent only converges to minimizers: Non-isolated critical points and invariant regions
I. Panageas and G. Piliouras · 2017
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Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis
M. Raginsky, A. Rakhlin, and M. Telgarsky · 2017
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Modal regression using kernel density estimation: A review
Y.-C. Chen · 2018
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Sharp oracle inequalities for stationary points of nonconvex penalized m-estimators
A. Elsener and S. van de Geer · 2018
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The landscape of empirical risk for nonconvex losses
S. Mei, Y. Bai, and A. Montanari · 2018
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Generalization error bounds for noisy, iterative algorithms
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Statistical inference for the population landscape via moment-adjusted stochastic gradients
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