Lattice theory of causation I am working on a
larger project where I explore concepts related to cause
and effect using lattice theory. I recently published a
paper entitled Entropy
Inequalities on Lattices where the basic results
on the relation between lattices and extreme polymatroid
functions is described. I am now working on a paper
draft where influence diagrams are described in terms of
Foundation of quantum theory The paper Entropy on
Spin Factors was published last year. It is part
of a series of papers related to foundation of quantum
theory. At ISIT2017 I gave a talk entitled Information
Theory on Spectral Sets. The results strongly
indicate that information theory is only possible in
mathematical structures that can be represented on
Jordan algebras. There are 5 basic types of Jordan
algebras, and density matrices with complex entries is
the most important in the sense that quantum information
theory is normally represented on this type of algebra.
I guess that many results from quantum information
theory can be generalized to Jordan algebras. This work
follows up on a paper entitled Divergence
and Sufficiency for Convex Optimization that I
recently published in Entropy.
MDL I have presented the following paper to ISIT 2018. It extends previous reults on horizont independent MDL by relating it to exactness of saddle point approximations.
Tail bounds I published a long paper with various bounds on tail probabilities in terms of the signed log-likelihood function in Kybernetika. It has just been awarded the best paper in Kybernetika 2016. Although the inequalities are quite sharp I am sure even sharper inequalities of these types can be obtained. I think the results can be generalized to cover all exponential families with simple variance functions. Even more general inequalities may exist, but at the moment I don't know how to attack the general problem.
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