Given n (discrete or continuous) random variables Xi, the (2 n − 1)-dimensional vector obtained by evaluating the joint entropy of all non-empty subsets of {X1,. .. , Xn} is called an entropic vector. Determining the region of entropic vectors is an important open problem with many applications in information theory. Recently, it has been shown that the entropy regions for discrete and continuo...

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, called Gaussian free fields, which arise in semi-supervised learning and computer ...

When addressing various financial problems, such as estimating stock portfolio risk, it is necessary to derive the distribution of sum dependent random variables. Although deriving this requires identifying joint these variables, exact estimation variables difficult. Therefore, in recent years, studies have been conducted on bound with dependence uncertainty. In stu...

which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...

The stochastic processes of almost exclusive interest in modeling channel noise are the Gaussian processes. Gaussian processes are stochastic processes for which the random variables N(t1), N(t2), . . . , N(tk) are jointly Gaussian for all t1, . . . , tk and all k > 0. Today we start by giving a more complete discussion of jointly Gaussian random variables. We restrict our attention to zero mea...

A new synthesis scheme is proposed to generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is shown by vanishing total variation distance between the synthesized and desired statistics. The proposed layered and successive synthesis scheme relies on the learned structure of tree to use sufficient number of common random ...