Fisher information and matrix-valued valuations
نویسندگان
چکیده
منابع مشابه
Ellipsoids and Matrix valued Valuations
A classification is obtained of Borel measurable, GL(n) covariant, symmetric matrix valued valuations on the space of n-dimensional convex polytopes. The only ones turn out to be the moment matrix corresponding to the classical Legendre ellipsoid and the matrix corresponding to the ellipsoid recently discovered by Lutwak, Yang, and Zhang. A classical concept from mechanics is the Legendre ellip...
متن کاملRelations between Renyi Distance and Fisher Information
In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...
متن کاملOn weighted Fisher information matrix properties
In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously established in [6] is given. Further, along with generalized De-Bruijn's identity, we provide new interpretation of the concavity for the entropy power.
متن کاملOperator-valued Free Fisher Information of Random Matrices
We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ...
متن کاملExtended Fisher Criterion Based on Auto-correlation Matrix Information
Fisher’s linear discriminant analysis (FLDA) has been attracting many researchers and practitioners for several decades thanks to its ease of use and low computational cost. However, FLDA implicitly assumes that all the classes share the same covariance: which implies that FLDA might fail when thhis assumption is not necessarily satisfied. To overcome this problem, we propose a simple extension...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2011
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.08.021