Entropic Projections and Dominating Points

Entropic Projections and Dominating Points

Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived fo...

Dominating Points and Entropic Projections

Some Conditional Laws of Large Numbers (CLLN) are related to minimization problems: the limit of the CLLN is the minimizer of a large deviation rate function on the limiting conditioning set. When the CLLN is concerned with empirical means, the minimizer is called a dominating point; if it is concerned with empirical measures, it is called an entropic projection. CLLNs are obtained both for emp...

Dominating Subsets under Projections

Abstract. Let d be a fixed integer, and let W be any d-dimensional linear subspace of Rn. There then exists a subset I of the n coordinates {1, 2, . . . , n} of Rn of cardinality at least ( 1 2 − o(1))n such that for every vector w = (w1, . . . , wn) ∈ W we have ∑ i∈I |wi| ≤ ∑ i/ ∈I |wi|. Equivalently, let P be any multiset of n arbitrary vectors in Rd. Then there exists a subset S of P of size...

Lüders' and quantum Jeffrey's rules as entropic projections

We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Lüders’ rules, is a special case of the constrained maximisation of a quantum relative entropy functional. This result is a quantum analogue of the derivation of the Bayes–Laplace rule as a special case of the constrained maximisation of relative entropy. The proof is provided for th...

Numerical Irreducible Decomposition Using Projections from Points