BLISS Seminar: Causality and directed information
Seminar | February 27 | 3-4 p.m. | 380 Soda Hall
Haim Permuter, Ben Gurion University
In this talk we will present a fundamental role that directed information and causal conditioning has in communication with feedback, gambling with causal side information, causal MMSE estimation, statistical physics, and causal inference between two processes.
We will begin by defining and establishing some key properties of the notions of causal conditioning and directed information. These properties will be seen to be natural counterparts, for the case where feedback is present, of the well-known properties of regular conditioning and mutual information.
Applications of these multi-letter capacity expressions will be discussed. In particular we will show a framework for the computation of capacity of unifilar channels. We will also detail how the framework can lead to closed form analytical solutions, such as in the case of binary erasure channel with no repeated ones, the trapdoor/chemical channel, the Ising channel and the Dicode channel.
As time permits, we will discuss application of directed information and causal conditioning in fields other than communication such as horse-race gambling, stock investment with causal side information, a relation between causal MMSE estimation and directed information, extraction of energy using casual information from systems like Szilard engine and, finally, we will present how to measure causal dependency between sequences using the directed information.