Elliptically Symmetric Distributions: A Review and Bibliography

Chmielewski, Margaret A.

doi:10.2307/1403038

Cited by 168 publications

(49 citation statements)

References 49 publications

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“…The preceding result confirms that A1 is very broadly applicable, since the class of elliptically contoured distributions covers a wide range of distributions including multivariate normal, logistic, symmetric stable, generalized-hyperbolic and t-distributions as well as their truncated versions [12].…”

Section: Controller Information Structuresupporting

confidence: 72%

An efficient method to estimate the suboptimality of affine controllers

Hadjiyiannis¹,

Goulart²,

Kuhn³

2010

UKACC International Conference on CONTROL 2010

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Abstract. We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally intractable, but suboptimal policies can be computed by restricting the class of admissible policies to be affine on the observation. By using a suitable re-parameterization and robust optimization techniques, these approximations can be solved efficiently as convex optimization problems. We investigate the loss of optimality due to the use of such affine policies. Using duality arguments and by imposing an affine structure on the dual variables, we provide an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data. This lower bound can then be used to quantify the loss of optimality incurred by the affine policy.

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Section: Controller Information Structuresupporting

confidence: 72%

An efficient method to estimate the suboptimality of affine controllers

Hadjiyiannis¹,

Goulart²,

Kuhn³

2010

UKACC International Conference on CONTROL 2010

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“…Applications to correlational studies are reviewed in [21] and to minimax estimation, stochastic processes, pattern recognition, fiducial inference, and probability inequalities in [19]. For a recent brief overview, see ELLIPTICALLY CONTOURED DISTRIBUTIONS.…”

Section: Elliptical Symmetrymentioning

confidence: 99%

Multivariate Symmetry and Asymmetry

Serfling¹

2014

Wiley StatsRef: Statistics Reference Online

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“…In the implementation of the above definition of saliency, the distributions of v given H and v given B are assumed to be elliptically symmetric (Chmielewski 1981), with probability density functions p(v|H) and p(v|B) respectively. These two pdfs are estimated using two images for which the pairs of corresponding regions are known.…”

Section: Of P(v(2)|v(1) B) From P(v(2)|v(1) H) (Cover and Thomas 19mentioning

confidence: 99%

“…A spherically symmetric distribution is one which is invariant under all orthogonal transformations of the Euclidean space on which it is defined (Chmielewski 1981). If an ESD has a probability density function then this pdf is constant on each member of a one parameter family of ellipsoids.…”

Section: The Elliptically Symmetric Distributionmentioning

confidence: 99%

A probabilistic definition of salient regions for image matching

Maybank

2013

Neurocomputing

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Abstract. A probabilistic definition of saliency is given in a form suitable for applications to image matching. In order to make this definition, the values of the pixels in pairs of matching regions are modeled using an elliptically symmetric distribution (ESD). The values of the pixels in background pairs of regions are also modeled using an ESD. If a region is given in one image, then the conditional probability density function for the pixel values in a matching region can be calculated. The saliency of the given region is defined to be the Kullback-Leibler divergence between this conditional pdf and a background conditional pdf. Experiments carried out using images in the Middlebury stereo database show that if the salience of a given image region is high, then there are relatively few background regions that have a better match to the given region than the true matching region.

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Elliptically Symmetric Distributions: A Review and Bibliography

Cited by 168 publications

References 49 publications

An efficient method to estimate the suboptimality of affine controllers

An efficient method to estimate the suboptimality of affine controllers

Multivariate Symmetry and Asymmetry

A probabilistic definition of salient regions for image matching

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