Statistical Query Lower Bounds for Robust Estimation of High-Dimensional Gaussians and Gaussian Mixtures

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) ◽

10.1109/focs.2017.16 ◽

2017 ◽

Author(s):

Ilias Diakonikolas ◽

Daniel M. Kane ◽

Alistair Stewart

Keyword(s):

Lower Bounds ◽

Robust Estimation ◽

High Dimensional ◽

Gaussian Mixtures

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Robust Estimation of a High-Dimensional Integrated Covariance Matrix

SSRN Electronic Journal ◽

10.2139/ssrn.1996261 ◽

2012 ◽

Author(s):

Takayuki Morimoto ◽

Shuichi Nagata

Keyword(s):

Covariance Matrix ◽

Robust Estimation ◽

High Dimensional ◽

Integrated Covariance

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Robust estimation of gaussian mixtures from noisy input data

2008 IEEE Conference on Computer Vision and Pattern Recognition ◽

10.1109/cvpr.2008.4587467 ◽

2008 ◽

Author(s):

Shaobo Hou ◽

Aphrodite Galata

Keyword(s):

Robust Estimation ◽

Gaussian Mixtures ◽

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Asymptotic Lower Bounds for Risk in Robust Estimation

The Annals of Statistics ◽

10.1214/aos/1176345198 ◽

1980 ◽

Vol 8 (6) ◽

pp. 1252-1264 ◽

Author(s):

Rudolf Beran

Keyword(s):

Lower Bounds ◽

Robust Estimation

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Efficiently learning high-dimensional observation models for Monte-Carlo localization using Gaussian mixtures

2008 IEEE/RSJ International Conference on Intelligent Robots and Systems ◽

10.1109/iros.2008.4650711 ◽

2008 ◽

Author(s):

P. Pfaff ◽

C. Stachniss ◽

C. Plagemann ◽

W. Burgard

Keyword(s):

Monte Carlo ◽

High Dimensional ◽

Gaussian Mixtures ◽

Monte Carlo Localization

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Robust estimation of a high-dimensional integrated covariance matrix

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918.2014.991038 ◽

2016 ◽

Vol 46 (2) ◽

pp. 1102-1112 ◽

Author(s):

Takayuki Morimoto ◽

Shuichi Nagata

Keyword(s):

Covariance Matrix ◽

Robust Estimation ◽

High Dimensional ◽

Integrated Covariance

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Wide flat minima and optimal generalization in classifying high-dimensional Gaussian mixtures

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/abcd31 ◽

2020 ◽

Vol 2020 (12) ◽

pp. 124012

Author(s):

Carlo Baldassi ◽

Enrico M Malatesta ◽

Matteo Negri ◽

Riccardo Zecchina

Keyword(s):

High Dimensional ◽

Gaussian Mixtures

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CHIME: Clustering of high-dimensional Gaussian mixtures with EM algorithm and its optimality

The Annals of Statistics ◽

10.1214/18-aos1711 ◽

2019 ◽

Vol 47 (3) ◽

pp. 1234-1267 ◽

Author(s):

T. Tony Cai ◽

Jing Ma ◽

Linjun Zhang

Keyword(s):

Em Algorithm ◽

High Dimensional ◽

Gaussian Mixtures

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Prediction with high dimensional regression via hierarchically structured Gaussian mixtures and latent variables

Journal of the Royal Statistical Society Series C (Applied Statistics) ◽

10.1111/rssc.12370 ◽

2019 ◽

Vol 68 (5) ◽

pp. 1485-1507

Author(s):

Chun‐Chen Tu ◽

Florence Forbes ◽

Benjamin Lemasson ◽

Naisyin Wang

Keyword(s):

Latent Variables ◽

High Dimensional ◽

Gaussian Mixtures ◽

High Dimensional Regression

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Evaluating and selecting features via information theoretic lower bounds of feature inner correlations for high-dimensional data

European Journal of Operational Research ◽

10.1016/j.ejor.2020.09.028 ◽

2021 ◽

Vol 290 (1) ◽

pp. 235-247 ◽

Author(s):

Yishi Zhang ◽

Ruilin Zhu ◽

Zhijun Chen ◽

Jie Gao ◽

De Xia

Keyword(s):

Lower Bounds ◽

High Dimensional Data ◽

High Dimensional ◽

Information Theoretic

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Smooth Mappings with Higher Dimensional Critical Sets

Canadian Mathematical Bulletin ◽

10.4153/cmb-2010-057-8 ◽

2010 ◽

Vol 53 (3) ◽

pp. 542-549 ◽

Author(s):

Cornel Pintea

Keyword(s):

Lower Bounds ◽

High Dimensional ◽

Higher Dimensional ◽

AbstractIn this paper we provide lower bounds for the dimension of various critical sets, and we point out some differential maps with high dimensional critical sets.

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