Statistical Decision Rules and Optimal Inference

By N. Čencov. 2000

846 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e1d92fc8a8d8736a17a790d832d71fec48625250

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Citations in the corpus

Innovative tools for radar signal processing Based on Cartan’s geometry of SPD matrices & Information Geometry (2008, background): “Chentsov [13] has introduced a distance between parametric families of probability distributions { } Θ ∈ = Θ θ θ : ) / (.”
Natural Gradient Works Eciently in Learning (background): “This is the only invariant metric to be given to the statistical model (Chentsov, 1972; Campbell, 1985; Amari, 1985).”
Natural Gradient Works Efficiently in Learning (1998, background): “This is the only invariant metric to be given to the statistical model (Chentsov, 1972; Campbell, 1985; Amari, 1985).”
Differential Geometry of Special Mappings (2019, background): “In turn, Chentsov defined (see [35]) a 1-parameter group of affine connections in the space of statistic distributions.”
Information Theory and Statistics: A Tutorial (2004, methodology): “The remarkable analogy of certain information theoretic concepts and results to geometric ones, instrumental in this Chapter and later on, has a profound background in a differential geometric structure of probability distributions, beyond the scope of this tutorial, see C̆encov [49], Amari [1].”
Symmetrizing the Kullback-Leibler Distance (2001, background): “Despite these difficulties, recent work has shown that the Kullback-Leibler distance is geometrically important [4, 8].”
Geometry of Quantum States: Index (2007, methodology): “3 The statistical geometry of α-connections is the work of Čencov [199] and Amari [30].”
On the toric algebra of graphical models (2006, background): “This type of analysis leads to the treatment of nonpositive distributions as special limiting cases such as the “boundaries at infinity” of Čencov [5].”
Information geometry of divergence functions (2010, methodology): “Then we study the class of invariant divergences [1, 11].”
Information geometry on hierarchy of probability distributions (2001, methodology): “It was Chentsov [19] who developed Rao's idea further and introduced new invariant affine connections in the manifolds of probability distributions.”
Orthogonal series density estimation (2010, background): “Let us find an appropriate sample mean estimate of Fourier coefficients (2).”
Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy (2017, methodology): “12 Our characterization of invariance is related to the definition in Hébert and La’O (2020), who build on the work of Chentsov (1982) and Amari and Nagaoka (2000).”
Maximum Likelihood Estimation in Log-Linear Models: Theory and Algorithms (2011, background): “e general theory of exponential families and, in particular, of extended exponential families, originally put forward by Bardorff-Nielsen (1978) and then Brown (1986). See also the important work by ˇCencov (1982). According to this theory, there is a natural notion of closure of the space of model ”
Covariant policy search (2003, methodology): “[Chentsov, 1980] This metric is well-known in statistical inference as the Fisher-Rao metric and it can be written as the Fisher information matrix [DeGroot, 19701:”
Cramer-Rao Lower Bound and Information Geometry (2013, background): “We shall discuss later more on the concepts of invariance in statistical manifolds [18, 38].”