Upper concave envelopes and auxiliary random variables
نویسنده
چکیده
We propose a new characterization of inner and outer bounds of some network information theoretic regions in terms of upper concave envelopes of certain functions of mutual information. While this characterization is related to the characterization using auxiliary random variables, it is shown that the new characterization can make computations of boundary points much simpler. Further this representation also leads to some new kinds of factorization inequalities concerning information theoretic quantities. It also provides some new pathways into proving optimality of certain achievable rate regions.
منابع مشابه
Some results on the strength of relaxations of multilinear functions
We study approaches for obtaining convex relaxations of global optimization problems containing multilinear functions. Specifically, we compare the concave and convex envelopes of these functions with the relaxations that are obtained with a standard relaxation approach, due to McCormick. The standard approach reformulates the problem to contain only bilinear terms and then relaxes each term in...
متن کاملCommon Randomness and Key Generation with Limited Interaction
A basic two-terminal secret key generation model is considered, where the interactive communication rate between the terminals may be limited, and in particular may not be enough to achieve the maximum key rate. We first prove a multi-letter characterization of the key-communication rate region (where the number of auxiliary random variables depend on the number of rounds of the communication),...
متن کاملMoment inequalities for sums of certain independent symmetric random variables
This paper gives upper and lower bounds for moments of sums of independent random variables (Xk) which satisfy the condition that P (|X|k ≥ t) = exp(−Nk(t)), where Nk are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which N(t) = |t| for some fixed 0 < r ≤ 1. This complements work of Glus...
متن کاملEstimation Efficiency Under Privacy Constraints
We investigate the problem of estimating a random variable Y ∈ Y under a privacy constraint dictated by another correlated random variable X ∈ X , where estimation efficiency and privacy are assessed in terms of two different loss functions. In the discrete case, we use the Hamming loss function and express the corresponding utility-privacy tradeoff in terms of the privacy-constrained guessing ...
متن کاملOn Convex Probabilistic Programming with Discrete Distributions
We consider convex stochastic programming problems with probabilistic constraints involving integer valued random variables The concept of a p e cient point of a probability distribution is used to derive various equivalent problem for mulations Next we introduce the concept of r concave discrete probability distri butions and analyse its relevance for problems under consideration These notions...
متن کامل