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Keywords
(1)
Mixture of Distributions
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A Concentration Theorem for Projections
A Concentration Theorem for Projections,Sanjoy Dasgupta,Daniel Hsu,Nakul Verma
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A Concentration Theorem for Projections
(
Citations: 5
)
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Sanjoy Dasgupta
,
Daniel Hsu
,
Nakul Verma
Suppose the random vector X ∈ RD has mean zero and finite second moments. We show that there is a pre cise sense in which almost all linear projections of X into Rd (for d < D) look like a scalemixture of spherical Gaussians—specifically, a
mixture of distributions
N(0,�2Id) where thevalues follow the same distribution as k Xk / √ D. The extent of this effect depends upon the ratio of d to D, and upon a particular coefficient of eccentricity of X's distribution.
Conference:
Uncertainty in Artificial Intelligence  UAI
, 2006
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uai.sis.pitt.edu
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(
www.informatik.unitrier.de
)
Citation Context
(3)
...assuming the distribution of X is unimodal, as proved in [
13
], the smaller k is, the more the distribution of RX will be like a spherical Gaussian, with a covariance matrix (� U ) which is diagonal...
...have no essential difference from U. By [
13
], when some zeromean data X is randomly projected into a lower dimensional space, the distribution of projected data U is like a spherical Gaussian whose covariance matrix is a diagonal matrix...
Yingpeng Sang
,
et al.
Effective Reconstruction of Data Perturbed by Random Projections
...Proof: In [
18
], Dasgupta et al. have shown that almost all p linear projections behave like a scale...
...Specifically, in this case, the main theorem of [
18
] reads app roximately like the following: For any ball B ∈ R p and for almost all W ,...
...Interestingly, such an order O(p 2 /d) appears also in [
18
] (e.g...
Hyun Sung Chang
,
et al.
Informative Sensing
...Although PCA analysis is widely used in a variety of applications, random projections have recently emerged as a powerful method for dimensionality reduction that offers many benefits over PCA for data sets that do not follow a multivariate Gaussian distribution [
5
]...
...This value of K was chosen using the model selection techniques described in section IID.3 (Fig. 7). We performed experiments with 2 [1;
5
] and 2 [1; 50] and obtained error rates that are comparable to those reported above and in Table I...
S. RuizCorrea
,
et al.
A Bayesian hierarchical model for classifying craniofacial malformatio...
References
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(
Citations: 64
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Arora Sanjeev
,
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Conference:
ACM Symposium on Theory of Computing  STOC
, pp. 247257, 2001
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Citations: 385
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(
Citations: 16
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Assaf Naor
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Journal:
Annales De L Institut Henri Poincareprobabilites Et Statistiques  ANN INST HENRI POINCAREPROB
, vol. 39, no. 2, pp. 241261, 2003
MODELING PHARMACOKINETIC DATA USING HEAVYTAILED MULTIVARIATE DISTRIBUTIONS
(
Citations: 3
)
J. K. Lindsey
,
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Journal:
Journal of Biopharmaceutical Statistics  J BIOPHARM STAT
, vol. 10, no. 3, pp. 369381, 2000
A TwoRound Variant of EM for Gaussian Mixtures
(
Citations: 44
)
Sanjoy Dasgupta
,
Leonard J. Schulman
Conference:
Uncertainty in Artificial Intelligence  UAI
, pp. 152159, 2000
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Citations
(5)
Effective Reconstruction of Data Perturbed by Random Projections
Yingpeng Sang
,
Hong Shen
,
Hui Tian
Journal:
IEEE Transactions on Computers  TC
, vol. 61, no. 1, pp. 101117, 2012
Informative Sensing
(
Citations: 3
)
Hyun Sung Chang
,
Yair Weiss
,
William T. Freeman
Journal:
Computing Research Repository  CORR
, vol. abs/0901.4, 2009
Reconstructing Data Perturbed by Random Projections When the Mixing Matrix Is Known
(
Citations: 2
)
Yingpeng Sang
,
Hong Shen
,
Hui Tian
Conference:
Principles of Data Mining and Knowledge Discovery  PKDD
, pp. 334349, 2009
Robust Probabilistic Multivariate Calibration Model
(
Citations: 1
)
Yi Fang
,
Myong K. Jeong
Journal:
Technometrics
, vol. 50, no. 3, pp. 305316, 2008
A Bayesian hierarchical model for classifying craniofacial malformations from CT imaging
(
Citations: 1
)
S. RuizCorrea
,
D. GaticaPerez
,
H. J. Lin
,
L. G. Shapiro
,
R. W. Sze
Conference:
Annual International Conference of the IEEE Engineering in Medicine and Biology Society  EMBC
, pp. 40634069, 2008